U.S. patent application number 15/343827 was filed with the patent office on 2018-05-10 for integrated fourier transform optical spectrometer.
This patent application is currently assigned to COM DEV International Ltd.. The applicant listed for this patent is COM DEV International Ltd.. Invention is credited to Hugh Podmore, Alan Scott.
Application Number | 20180128592 15/343827 |
Document ID | / |
Family ID | 59686819 |
Filed Date | 2018-05-10 |
United States Patent
Application |
20180128592 |
Kind Code |
A1 |
Scott; Alan ; et
al. |
May 10, 2018 |
INTEGRATED FOURIER TRANSFORM OPTICAL SPECTROMETER
Abstract
A spectrometer and method for determining an emitted light
spectrum. An input light signal is received and directed to an
array of interferometers using waveguides. A plurality of
self-interfering signals are detected from a first plurality of
interferometers in the array of interferometers. The first
plurality of interferometers has fewer interferometers than
required to satisfy the Nyquist criterion for reconstructing the
emitted light spectrum. The emitted light spectrum is reconstructed
from the plurality of self-interfering signals using compressive
sensing. The plurality of self-interfering signals can provide an
interference pattern used to reconstruct the emitted light
spectrum. A second plurality of interferometers may output a second
plurality of self-interfering signals to reconstruct a low
resolution spectrum of the input light signal satisfying the
Nyquist criterion. Low resolution signal components can be detected
from the low resolution spectrum and used to pre-process the
interference pattern.
Inventors: |
Scott; Alan; (Arnprior,
CA) ; Podmore; Hugh; (Toronto, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
COM DEV International Ltd. |
Cambridge |
|
CA |
|
|
Assignee: |
COM DEV International Ltd.
Cambridge
CA
|
Family ID: |
59686819 |
Appl. No.: |
15/343827 |
Filed: |
November 4, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01J 3/0218 20130101;
G01B 9/02044 20130101; G01B 9/02051 20130101; G01J 3/0272 20130101;
G01B 9/02027 20130101; G01J 3/45 20130101; G01J 3/4531 20130101;
G01B 9/02097 20130101 |
International
Class: |
G01B 9/02 20060101
G01B009/02 |
Claims
1. A spectrometer comprising: a) an input aperture configured to
receive an input light signal; b) an array of interferometers, each
interferometer having a signal input and a signal output and
configured to output a self-interfering signal with a known phase
shift, the array including a first plurality of interferometers
where the phase shift for each interferometer in the first
plurality of interferometers is different from the phase shift of
every other interferometer in the first plurality of
interferometers; c) a plurality of input waveguides optically
coupled to the input aperture and to the array of interferometers
to receive the input light signal from the input aperture and
direct the received light signal to the array of interferometers;
d) a detector array optically coupled to the array of
interferometers to detect a first plurality of self-interfering
signals from the first plurality of interferometers, the first
plurality of self-interfering signals including the
self-interfering signal output by each of the interferometers in
the first plurality of interferometers; and e) a computer-readable
storage medium coupled to the detector array, the computer-readable
storage medium configured to store at least one first
interferometric output signal based on the first plurality of
self-interfering signal detected by the detector array; wherein,
the number of interferometers in the first plurality of
interferometers is fewer than the number of interferogram samples
required to satisfy the Nyquist criterion for reconstructing an
emitted light spectrum with a spectral bandwidth B and a spectral
resolution .DELTA..lamda.; and the interferogram samples required
to satisfy the Nyquist criterion for the spectral bandwidth B and
spectral resolution .DELTA..lamda. correspond to a first plurality
of Nyquist phase shifts, and for each interferometer in the first
plurality of interferometers the phase shift is selected from the
first plurality of Nyquist phase shifts to permit reconstruction of
the emitted light spectrum with the spectral bandwidth B and the
spectral resolution .DELTA..lamda. from the stored at least one
first interferometric output signal using compressive sensing.
2. The spectrometer of claim 1, further comprising a processor
coupled to the computer-readable storage medium, the processor
configured to: a) determine a discrete interference pattern from
the first plurality of self-interfering signals detected by the
detector array; and b) reconstruct the emitted light spectrum from
the discrete interference pattern by: i) determining a plurality of
potential emitted spectra; ii) determining a distance value for
each of the potential emitted spectra based on the discrete
interference pattern and defined signal acquisition parameters of
the spectrometer; iii) identifying a lowest distance potential
emitted spectrum as the potential emitted spectrum from the
plurality of potential emitted spectra that corresponds to the
lowest distance value; and iv) reconstructing the emitted light
spectrum as the lowest distance potential emitted spectrum.
3. The spectrometer of claim 2, wherein the processor is configured
to reconstruct the emitted light spectrum by: a) identifying
low-resolution spectral signal components in the discrete
interference pattern; b) generating a pre-processed discrete
interference pattern by removing the low-resolution spectral signal
components from the discrete interference pattern; and c)
reconstructing the emitted light spectrum from the discrete
interference pattern using the pre-processed discrete interference
pattern.
4. The spectrometer of claim 1, wherein: a) the array of
interferometers further comprises a second plurality of
interferometers, the second plurality of interferometers including
fewer interferometers than the first plurality of interferometers;
b) the detector array is optically coupled to the array of
interferometers to detect a second plurality of self-interfering
signals from the second plurality of interferometers, the second
plurality of self-interfering signals including the
self-interfering signal output by each of the interferometers in
the second plurality of interferometers; and c) the
computer-readable storage medium is further configured to store at
least one low resolution interferometric output signal based on the
second plurality of self-interfering signals; wherein the number of
interferometers in the second plurality of interferometers is not
less than the number of interferogram samples required to satisfy
the Nyquist criterion for reconstructing a low resolution spectrum
of the input light signal, the low resolution spectrum having the
spectral bandwidth B and a spectral resolution of
.DELTA..lamda..sub.low where
.DELTA..lamda..sub.low>2.DELTA..lamda.; the interferogram
samples required to satisfy the Nyquist criterion for the spectral
bandwidth B and the spectral resolution of .DELTA..lamda..sub.low
correspond to a second plurality of Nyquist phase shifts, and the
phase shifts of the interferometers in the second plurality of
interferometers are selected to correspond to the second plurality
of Nyquist phase shifts.
5. The spectrometer of claim 4, further comprising a processor
coupled to the computer-readable storage medium, the processor
configured to: a) determine a discrete interference pattern from
the first plurality of self-interfering signals detected by the
detector array; b) determine a low resolution spectrum of the input
light signal from the second plurality of self-interfering signals
detected by the detector array; c) identify low-resolution spectral
signal components from the low resolution spectrum; d) generate a
pre-processed discrete interference pattern by removing the
low-resolution spectral signal components from the discrete
interference pattern; and e) reconstruct the emitted light spectrum
from the pre-processed discrete interference pattern.
6. The spectrometer of claim 5, wherein the processor is configured
to reconstruct the emitted light spectrum from the pre-processed
discrete interference pattern by: a) determining a plurality of
potential emitted spectra; b) determining a distance value for each
of the potential emitted spectra based on the pre-processed
discrete interference pattern and defined signal acquisition
parameters of the spectrometer; c) identifying a lowest distance
potential emitted spectrum as the potential emitted spectrum from
the plurality of potential emitted spectra that corresponds to the
lowest distance value; and d) reconstruct the emitted light
spectrum as the lowest distance potential emitted spectrum.
7. The spectrometer of claim 1, wherein the phase shifts for the
first plurality of interferometers are selected randomly from the
first plurality of Nyquist phase shifts.
8. The spectrometer of claim 1, wherein: a) the optical coupling
between the input aperture and the plurality of input waveguides
comprises a mirror array having a plurality of mirrors; and b) each
of the input waveguides has a corresponding mirror in the mirror
array where the corresponding mirror is angled to direct a portion
of the input light signal from the input aperture along that input
waveguide.
9. The spectrometer of claim 8, further comprising a planar
spectrometer surface, wherein: a) each of the input waveguides is a
substantially planar waveguide on the spectrometer surface; and b)
each mirror in the mirror array is mounted on the spectrometer
surface and angled to direct the portion of the input light signal
that is incident on the mirror at the spectrometer surface along
the corresponding input waveguide.
10. The spectrometer of claim 9, wherein: a) the input aperture
comprises a plurality of lenses including a lens corresponding to
each of the mirrors in the mirror array, each lens being focused to
direct the portion of the input light signal to the corresponding
mirror.
11. The spectrometer of claim 1, wherein the array of
interferometers and the plurality of input waveguides are provided
on a single chip.
12. A method for determining a emitted light spectrum having a
spectral bandwidth B and a spectral resolution .DELTA..lamda., the
method comprising: a) receiving an input light signal; b) directing
the input light signal to an array of interferometers; c)
concurrently detecting a first plurality of self-interfering
signals from a first plurality of interferometers in the array of
interferometers, the number of self-interfering signals in the
first plurality of self-interfering signals being fewer than the
number of samples required to satisfy the Nyquist criterion to
reconstruct the emitted light spectrum; and d) reconstructing the
emitted light spectrum from the plurality of self-interfering
signals using compressive sensing.
13. The method of claim 12, wherein reconstructing the emitted
light spectrum comprises: a) determining a discrete interference
pattern from the first plurality of self-interfering signals; b)
determining a plurality of potential emitted spectra; c)
determining a distance value for each of the potential emitted
spectra based on the discrete interference pattern and defined
signal acquisition parameters of the spectrometer; d) identifying a
lowest distance potential emitted spectrum as the potential emitted
spectrum from the plurality of potential emitted spectra that
corresponds to the lowest distance value; and e) reconstructing the
emitted light spectrum as the lowest distance potential emitted
spectrum.
14. The method of claim 13, further comprising: a) generating a
pre-processed discrete interference pattern by removing
low-resolution spectral signal components from the discrete
interference pattern; and b) reconstructing the emitted light
spectrum using the pre-processed discrete interference pattern.
15. The method of claim 14, further comprising: a) concurrently
detecting a second plurality of self-interfering signals from a
second plurality of interferometers in the array of
interferometers; b) determining a low resolution spectrum of the
input light signal with the spectral bandwidth B and a spectral
resolution of .DELTA..lamda..sub.low where
.DELTA..lamda..sub.low>2.DELTA..lamda. from the second plurality
of self-interfering signals using a Fourier transform, wherein the
number of self-interfering signals in the second plurality of
self-interfering signals is not less than the number of
interferogram samples required to satisfy the Nyquist criterion for
reconstructing the low resolution spectrum; and c) identifying the
low-resolution spectral signal components from the low resolution
spectrum.
Description
FIELD
[0001] The present subject-matter relates generally to
spectrometry, and more particularly to Fourier transform optical
spectrometry.
INTRODUCTION
[0002] Spectrometry involves the analysis of matter based on its
interaction with electromagnetic radiation. Optical spectrometry
analyzes the distribution of light across the optical spectrum
emitted from a sample or location of interest. For example, a
sample of interest may be excited using a pulse of electromagnetic
radiation such as a laser light pulse. Light emitted by the sample
in response to the excitation pulse can be analyzed to determine
the elements present in the sample being analyzed.
[0003] Many applications may have use for optical spectrometry. For
example, optical spectrometry may be used to analyze soil samples
for geological applications or to analyze the composition of
pharmaceutical products. Optical spectrometry may also find
applications in interstellar and planetary exploration, for
instance in detecting organic compound or target minerals.
[0004] Depending on the application, there may be limits imposed on
the size or weight of a spectrometry device. For example, in some
applications it may be desirable to have a handheld device to allow
optical spectrometry data to be easily acquired. In some cases,
spectrometry devices may be required to detect an emitted spectrum
while operating at low power or in low light conditions.
SUMMARY
[0005] It would thus be highly desirable to be provided with a
device or system that would at least partially address the
disadvantages of the existing technologies.
[0006] The embodiments described herein provide in an aspect a
spectrometer. In some embodiments, the spectrometer may be provided
as a spectrometer system. In some embodiments, the spectrometer may
be provided as a spectrometer device. In some examples, the
spectrometer may be handheld. The spectrometer may include an input
aperture. The input aperture can be configured to receive an input
light signal. The spectrometer can also include an array of
interferometers. Each interferometer can have a signal input and a
signal output and can be configured to output a self-interfering
signal with a known phase shift. The array of interferometers can
include a first plurality of interferometers where the phase shift
for each interferometer in the first plurality of interferometers
can be different from the phase shift of every other interferometer
in the first plurality of interferometers. The spectrometer can
also include a plurality of input waveguides optically coupled to
the input aperture and to the array of interferometers. The
plurality of input waveguides can receive the input light signal
from the input aperture. The plurality of input waveguides can also
direct the received light signal to the array of interferometers.
The spectrometer can include a detector array optically coupled to
the array of interferometers to detect a first plurality of
self-interfering signals from the first plurality of
interferometers. The first plurality of self-interfering signals
can include the self-interfering signal output by each of the
interferometers in the first plurality of interferometers. The
spectrometer can include a computer-readable storage medium coupled
to the detector array. The computer-readable storage medium can be
configured to store at least one first interferometric output
signal based on the first plurality of self-interfering signal
detected by the detector array. The number of interferometers in
the first plurality of interferometers can be fewer than the number
of interferogram samples required to satisfy the Nyquist criterion
for reconstructing an emitted light spectrum with a spectral
bandwidth B and a spectral resolution .DELTA..lamda.. The
interferogram samples required to satisfy the Nyquist criterion for
the spectral bandwidth B and spectral resolution .DELTA..lamda. may
correspond to a first plurality of Nyquist phase shifts, and for
each interferometer in the first plurality of interferometers the
phase shift can be selected from the first plurality of Nyquist
phase shifts to permit reconstruction of the emitted light spectrum
with the spectral bandwidth B and the spectral resolution
.DELTA..lamda. from the stored at least one first interferometric
output signal using compressive sensing.
[0007] In some examples, the spectrometer may also include a
processor coupled to the computer-readable storage medium. The
processor may be configured to determine a discrete interference
pattern from the first plurality of self-interfering signals
detected by the detector array. The processor can also be
configured to reconstruct the emitted light spectrum from the
discrete interference pattern. The processor may reconstruct the
emitted light spectrum from the discrete interference pattern by
determining a plurality of potential emitted spectra; determining a
distance value for each of the potential emitted spectra based on
the discrete interference pattern and defined signal acquisition
parameters of the spectrometer; identifying a lowest distance
potential emitted spectrum as the potential emitted spectrum from
the plurality of potential emitted spectra that corresponds to the
lowest distance value; and reconstructing the emitted light
spectrum as the lowest distance potential emitted spectrum.
[0008] In some examples, the processor may be configured to
reconstruct the emitted light spectrum using a pre-processed
discrete interference pattern. The processor may be configured to
reconstruct the emitted light spectrum by identifying
low-resolution spectral signal components in the discrete
interference pattern; generating a pre-processed discrete
interference pattern by removing the low-resolution spectral signal
components from the discrete interference pattern; and
reconstructing the emitted light spectrum from the discrete
interference pattern using the pre-processed discrete interference
pattern.
[0009] In some examples, the array of interferometers may include a
second plurality of interferometers. The second plurality of
interferometers can include fewer interferometers than the first
plurality of interferometers. The detector array can be optically
coupled to the array of interferometers to detect a second
plurality of self-interfering signals from the second plurality of
interferometers. The second plurality of self-interfering signals
may include the self-interfering signal output by each of the
interferometers in the second plurality of interferometers. The
computer-readable storage medium may be further configured to store
at least one low resolution interferometric output signal based on
the second plurality of self-interfering signals. The number of
interferometers in the second plurality of interferometers may be
not less than the number of interferogram samples required to
satisfy the Nyquist criterion for reconstructing a low resolution
spectrum of the input light signal. The low resolution spectrum can
have the spectral bandwidth B and a spectral resolution of
.DELTA..lamda..sub.low where
.DELTA..lamda..sub.low>2.DELTA..lamda.. The interferogram
samples required to satisfy the Nyquist criterion for the spectral
bandwidth B and the spectral resolution of .DELTA..lamda..sub.low,
may correspond to a second plurality of Nyquist phase shifts and
the phase shifts of the interferometers in the second plurality of
interferometers can be selected to correspond to the second
plurality of Nyquist phase shifts.
[0010] In some examples, a processor may be coupled to the
computer-readable storage medium. The processor may be configured
to determine a discrete interference pattern from the first
plurality of self-interfering signals detected by the detector
array. The processor may be configured to determine a low
resolution spectrum of the input light signal from the second
plurality of self-interfering signals detected by the detector
array. The processor may be configured to identify low-resolution
spectral signal components from the low resolution spectrum. The
processor may be configured to generate a pre-processed discrete
interference pattern by removing the low-resolution spectral signal
components from the discrete interference pattern. The processor
may be configured to reconstruct the emitted light spectrum from
the pre-processed discrete interference pattern.
[0011] In some examples, the processor may be configured to
reconstruct the emitted light spectrum from the pre-processed
discrete interference pattern by determining a plurality of
potential emitted spectra; determining a distance value for each of
the potential emitted spectra based on the pre-processed discrete
interference pattern and defined signal acquisition parameters of
the spectrometer; identifying a lowest distance potential emitted
spectrum as the potential emitted spectrum from the plurality of
potential emitted spectra that corresponds to the lowest distance
value; and reconstruct the emitted light spectrum as the lowest
distance potential emitted spectrum.
[0012] In some examples, the phase shifts for the first plurality
of interferometers can be selected randomly from the first
plurality of Nyquist phase shifts. The phase shifts for the first
plurality of interferometers may be selected as a set of phase
shifts from the first plurality of Nyquist phase shifts that
satisfy the restricted isometry principle.
[0013] In some examples, the optical coupling between the input
aperture and the plurality of input waveguides may include a mirror
array having a plurality of mirrors. Each of the input waveguides
may have a corresponding mirror in the mirror array. For each input
waveguide, the corresponding mirror can be angled to direct a
portion of the input light signal from the input aperture along
that input waveguide.
[0014] In some examples, the spectrometer may include a planar
spectrometer surface. Each of the input waveguides may be a
substantially planar waveguide on the spectrometer surface. Each
mirror in the mirror array can be mounted on the spectrometer
surface and angled to direct the portion of the input light signal
that is incident on the mirror at the spectrometer surface along
the corresponding input waveguide.
[0015] In some examples, the input aperture may include a plurality
of lenses. The plurality of lenses may include a lens corresponding
to each of the mirrors in the mirror array. Each lens may be
focused to direct a portion of the input light signal to the
corresponding mirror.
[0016] In some examples, the array of interferometers and the
plurality of input waveguides may be provided on a single chip. The
array of interferometers and the plurality of input waveguides may
be etched onto the chip.
[0017] In some examples, the number of interferometers in the array
of interferometers may be less than or equal to half the number of
interferogram samples required to satisfy the Nyquist criterion. In
some examples, the number of interferometers in the first plurality
of interferometers may be less than or equal to 1/4 the number of
interferogram samples required to satisfy the Nyquist
criterion.
[0018] In some examples, the spectrometer may include a light
source. The light source may be configured to transmit a source
light signal with a known wavelength towards a location of
interest. The input light signal may be a scattered light signal
received from the location of interest. In some examples, the
spectrometer may also include a processor coupled to the
computer-readable storage medium. The processor may be configured
to identify a source spectral component from the received input
light signal; determine at least one correction factor based on the
identified source spectral component and the known wavelength of
the light source; and adjust the reconstructed spectrum of the
input light signal based on the at least one correction factor.
[0019] The embodiments described herein provide in another aspect a
method for determining an emitted light spectrum. The emitted light
spectrum may have a spectral bandwidth B and a spectral resolution
.DELTA..lamda.. The method may include receiving an input light
signal. The method may also include directing the input light
signal to an array of interferometers. The method may also include
concurrently detecting a first plurality of self-interfering
signals from a first plurality of interferometers in the array of
interferometers. The number of self-interfering signals in the
first plurality of self-interfering signals can be fewer than the
number of samples required to satisfy the Nyquist criterion to
reconstruct the emitted light spectrum. The method may also include
reconstructing the emitted light spectrum from the plurality of
self-interfering signals using compressive sensing.
[0020] In some examples, reconstructing the emitted light spectrum
may include determining a discrete interference pattern from the
first plurality of self-interfering signals; determining a
plurality of potential emitted spectra; determining a distance
value for each of the potential emitted spectra based on the
discrete interference pattern and defined signal acquisition
parameters of the spectrometer; identifying a lowest distance
potential emitted spectrum as the potential emitted spectrum from
the plurality of potential emitted spectra that corresponds to the
lowest distance value; and reconstructing the emitted light
spectrum as the lowest distance potential emitted spectrum.
[0021] In some examples, the emitted light spectrum may be
reconstructed using a pre-processed discrete interference pattern.
In some examples, the method may include generating a pre-processed
discrete interference pattern by removing low-resolution spectral
signal components from the discrete interference pattern; and
reconstructing the emitted light spectrum using the pre-processed
discrete interference pattern.
[0022] In some examples, the method may include concurrently
detecting a second plurality of self-interfering signals from a
second plurality of interferometers in the array of
interferometers. The method may also include determining a low
resolution spectrum of the input light signal with the spectral
bandwidth B and a spectral resolution of .DELTA..lamda..sub.low
where .DELTA..lamda..sub.low>2.DELTA..lamda. from the second
plurality of self-interfering signals using a Fourier transform.
The number of self-interfering signals in the second plurality of
self-interfering signals may be not less than the number of
interferogram samples required to satisfy the Nyquist criterion for
reconstructing the low resolution spectrum. The method may also
include identifying the low-resolution spectral signal components
from the low resolution spectrum.
[0023] In some examples, the method may include identifying a
source spectral component from the input light signal. The source
spectral component may correspond to a light source having a known
wavelength. The method may also include determining at least one
correction factor based on the identified source spectral component
and the known wavelength. The method may further include adjusting
the reconstructed spectrum of the input light signal using the at
least one correction factor.
[0024] In some examples, the number of self-interfering signals in
the first plurality of self-interfering signals is less than or
equal to half the number of samples required to satisfy the Nyquist
criterion for the spectrum of the input light signal. In some
examples, the number of self-interfering signals in the first
plurality of self-interfering signals is less than or equal to 1/4
the number of samples required to satisfy the Nyquist criterion for
the spectrum of the input light signal.
[0025] It will be appreciated by a person skilled in the art that a
spectrometer may include any one or more of the features contained
herein and that the features may be used in any particular
combination or sub-combination suitable for a spectrometry device,
system and/or method.
DRAWINGS
[0026] For a better understanding of the embodiments described
herein and to show more clearly how they may be carried into
effect, reference will now be made, by way of example only, to the
accompanying drawings which show at least one exemplary embodiment,
and in which:
[0027] FIG. 1 illustrates an example of a spectrometer in
accordance with an example embodiment;
[0028] FIG. 2 illustrates an example of a process for determining
an emitted light spectrum in accordance with an example
embodiment;
[0029] FIG. 3 illustrates an example of a process for removing
low-resolution signal components in accordance with an example
embodiment;
[0030] FIG. 4 illustrates a graph plotting an example of an input
signal spectrum;
[0031] FIG. 5 illustrates a graph plotting an example of Raman
spectral signal components of the input signal spectrum of FIG.
4;
[0032] FIG. 6 illustrates a graph plotting example reconstructions
of the emitted light spectrum of FIG. 4;
[0033] FIG. 7 illustrates another graph plotting further example
reconstructions of the emitted light spectrum of FIG. 4;
[0034] FIG. 8 illustrates a graph plotting example reconstructions
of a second emitted light spectrum;
[0035] FIG. 9 illustrates another graph plotting example
reconstructions of the second emitted light spectrum;
[0036] FIG. 10 illustrates a further graph plotting example
reconstructions of the second emitted light spectrum.
DESCRIPTION OF VARIOUS EMBODIMENTS
[0037] It will be appreciated that, for simplicity and clarity of
illustration, where considered appropriate, reference numerals may
be repeated among the figures to indicate corresponding or
analogous elements or steps. In addition, numerous specific details
are set forth in order to provide a thorough understanding of the
exemplary embodiments described herein. However, it will be
understood by those of ordinary skill in the art that the
embodiments described herein may be practiced without these
specific details. In other instances, well-known methods,
procedures and components have not been described in detail so as
not to obscure the embodiments described herein. Furthermore, this
description is not to be considered as limiting the scope of the
embodiments described herein in any way but rather as merely
describing the implementation of the various embodiments described
herein.
[0038] It should also be noted that the terms "coupled" or
"coupling" as used herein can have several different meanings
depending in the context in which these terms are used. For
example, the terms coupled or coupling may be used to indicate that
an element or device can electrically, optically, or wirelessly
send data to another element or device as well as receive data from
another element or device.
[0039] It should be noted that terms of degree such as
"substantially", "about" and "approximately" as used herein mean a
reasonable amount of deviation of the modified term such that the
end result is not significantly changed. These terms of degree may
also be construed as including a deviation of the modified term if
this deviation would not negate the meaning of the term it
modifies.
[0040] Furthermore, any recitation of numerical ranges by endpoints
herein includes all numbers and fractions subsumed within that
range (e.g. 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.90, 4, and 5). It
is also to be understood that all numbers and fractions thereof are
presumed to be modified by the term "about" which means a variation
of up to a certain amount of the number to which reference is being
made if the end result is not significantly changed.
[0041] The example embodiments of the systems and methods described
herein may be implemented as a combination of hardware or software.
In some cases, the example embodiments described herein may be
implemented, at least in part, by using one or more computer
programs, executing on one or more programmable devices comprising
at least one processing element, and a data storage element
(including volatile memory, non-volatile memory, storage elements,
or any combination thereof). These devices may also have at least
one input device (e.g. a pushbutton keyboard, mouse, a touchscreen,
and the like), and at least one output device (e.g. a display
screen, a printer, a wireless radio, and the like) depending on the
nature of the device.
[0042] It should also be noted that there may be some elements that
are used to implement at least part of one of the embodiments
described herein that may be implemented via software that is
written in a high-level computer programming language such as
object oriented programming. Accordingly, the program code may be
written in C, C++ or any other suitable programming language and
may comprise modules or classes, as is known to those skilled in
object oriented programming. Alternatively, or in addition thereto,
some of these elements implemented via software may be written in
assembly language, machine language or firmware as needed. In
either case, the language may be a compiled or interpreted
language.
[0043] At least some of these software programs may be stored on a
storage media (e.g. a computer readable medium such as, but not
limited to, ROM, magnetic disk, optical disc) or a device that is
readable by a general or special purpose programmable device. The
software program code, when read by the programmable device,
configures the programmable device to operate in a new, specific
and predefined manner in order to perform at least one of the
methods described herein.
[0044] Furthermore, at least some of the programs associated with
the systems, devices and methods of the embodiments described
herein may be capable of being distributed in a computer program
product comprising a computer readable medium that bears computer
usable instructions for one or more processors. The medium may be
provided in various forms, including non-transitory forms such as,
but not limited to, flash drives, one or more diskettes, compact
disks, tapes, and magnetic and electronic storage.
[0045] The embodiments described herein relate generally to
spectrometry. In particular, some embodiments described herein may
provide a spectrometry system that can be used to determine an
emitted light spectrum from an input light signal. Embodiments may
also provide a spectrometry device that can be used to determine an
emitted light spectrum from an input light signal. Some embodiments
described herein may also provide spectrometry methods for
determining an emitted light spectrum from an input light signal.
In general, the various systems, devices, and methods described in
embodiments herein may be combined as part of a combined
spectrometry system or spectrometry device.
[0046] In many spectrometry applications size and mass play an
important role. Smaller and lighter spectrometers may be desirable
for applications in distributed sensor networks, such as
constellations of earth-observation (EO) satellites, or as part of
a pipeline-health monitoring network. Handheld spectrometry
devices, such as devices that may be used for geological or
pharmaceutical purposes, can introduce size and/or weight
limitations. Spectrometry devices for space and planetary
exploration (e.g. planetary rovers) may involve highly constrained
mass and size/volume budgets. Accordingly, spectrometry devices
that may have reduced size and/or weight may be desirable.
[0047] Spectrometry devices may be required to determine the
spectrum of an emitted light signal while operating at low power
levels or with low light intensity signals. In some cases, a sample
being interrogated may be small and may not allow for multiple
repeated excitations. Increasing the level of light measured in
each sample of an input light signal can improve the signal to
noise ratio of the measured samples.
[0048] An increase in signal to noise ratio may provide more
accurate spectrometry devices. Accuracy may be particularly
important in applications such as security (e.g. bomb compound
detection) to ensure that potentially volatile samples are
correctly identified.
[0049] High-speed detection can also be important in spectrometry
application. In general, high speed detection may allow samples of
more input light signals to be acquired and analyzed in a period of
time. In some applications it may be particularly important that
the spectrum be identified quickly, e.g. in security applications
so that security procedures can be implemented if necessary (e.g.
if a bomb is detected).
[0050] Embodiments described herein may provide examples of Fourier
transform spectrometers, Fourier transform spectrometer systems,
and Fourier transform spectrometer methods. Fourier transform
spectrometry involves the collection of spectra by measuring
coherence of a radiation source. A plurality of samples of the
electromagnetic radiation can be acquired from a radiation source.
The intensity of each sample can be detected and the plurality of
samples combined to provide an interferogram.
[0051] Embodiments described herein may use an array of
interferometers. The interferometers in the array may have
wavelength-dependent transmission characteristics. This may permit
an output spatial light distribution pattern or interference
pattern to be generated. A spectrum of light emitted from the
radiation source of interest may be reconstructed based on this
distribution pattern or interference pattern.
[0052] An interferogram may be collected point-by-point over time
using a single interferometer, or a few interferometers with
temporally varying phase shifts. An interferogram or interference
pattern may also be measured substantially instantaneously using
spatially distributed or physically separated interferometers with
different phase shifts.
[0053] A plurality of interferometers may be spatially distributed
or arrayed. This may allow the plurality of interferometric samples
to be captured substantially simultaneously/concurrently. This
configuration may also provide mechanical robustness as the
plurality of samples may be acquired without moving parts. For
example, the interferometers may be arrayed on the surface of a
planar photonic chip or optical waveguide chip. In some examples,
the array of interferometers may include an array of spliced fiber
optic cables.
[0054] Each interferometer can be configured to output a
self-interfering signal with a known phase shift. The array of
interferometers may include a first plurality of interferometers
where the phase shift for each interferometer is different from the
phase shift of every other interferometer in the first plurality of
interferometers. The phase shifts of the interferometers in the
first plurality of interferometers may increase with each
subsequent interferometer. In some embodiments, the phase shifts
may increase linearly, while in other embodiments this may not be
the case.
[0055] An input light signal can be coupled to the array of
interferometers using an input aperture. The input aperture can
direct the input light signal towards a plurality of waveguides
e.g. using optical couplings. The plurality of waveguides can be
optically coupled to the input aperture and to the array of
interferometers. The waveguides can receive the input light signal
from the input aperture. The waveguides may then direct the
received light signal to the array of interferometers.
[0056] The plurality of waveguides may define a waveguide section
of the spectrometer. The waveguide section may include an input
waveguide region coupled to the aperture. The input waveguide
region may include a plurality of input waveguides defining input
waveguide paths. The plurality of input waveguides may provide
optical coupling between the input aperture and the array of
interferometers. In some cases, the array of interferometers may be
defined as an interferometer region of the waveguide section. That
is, the interferometers may be provided using waveguides in the
waveguide section.
[0057] The plurality of self-interfering signals output by the
interferometers can be detected using a detector array. The
detector array may be positioned to span the spatial distribution
of the interferometer signal outputs. This may allow for rapid
collection of samples required to reconstruct an emitted signal
spectrum. In some cases, all the samples required to reconstruct
the emitted signal spectrum may be acquired substantially
instantaneously.
[0058] The plurality of self-interfering signals detected by the
detector array can be used to generate a discrete interference
pattern. The discrete interference pattern may then be used to
reconstruct the emitted signal spectrum. In some cases, the
spectrometer device may include an on-board controller or processor
that can be configured to reconstruct the emitted signal
spectrum.
[0059] In some cases, the reconstruction of the emitted signal
spectrum may be performed remotely. For example, the spectrometer
device may include on-board memory that can be used to store at
least one interferometric output signal such as the plurality of
self-interfering signals and/or the discrete interference pattern.
The interferometric output signal(s) may be transmitted to a remote
processor to allow the emitted signal spectrum to be reconstructed.
In some cases, interferometric output signals for a plurality of
radiation sources/targets/samples may be acquired and stored in the
on-board memory for subsequent processing.
[0060] In some embodiments described herein, the array of
interferometers may include Mach-Zehnder interferometers (MZIs). In
some embodiments described herein the interferometers may include
Fabry-Perot interferometers.
[0061] In embodiments using MZIs, each interferometer generally
includes a reference arm or first signal path and a delay arm or
second signal path. The phase shift for each interferometer may be
defined by an optical path delay (OPD) between the first arm (i.e.
first signal path) of an interferometer and the second arm (i.e.
second signal path) of that interferometer. Each interferometer in
the first plurality of interferometers may be configured to have a
different optical path delay. In some cases, the length of the
first signal path may be fixed across all interferometers, while
the length of the second signal path can be varied between
interferometers.
[0062] As mentioned, the array of interferometers may be
implemented using waveguides, e.g. as an interferometer region of a
waveguide section. For instance, where MZIs are used, each of the
waveguides may split in the interferometer region of the waveguide
section to define a first signal path and second signal path for
the corresponding interferometer.
[0063] The array of interferometers can be used to generate a
plurality of self-interfering signal outputs. For example, the
signals from the delay and reference arms (i.e. from the first
signal path and the second signal path) of an interferometer can be
recombined to provide a self-interfering signal at the signal
output of that interferometer. The plurality of self-interfering
signals from the signal outputs of the array of interferometers can
be detected using a detector array optically coupled to the array
of interferometers. The detector array may detect the
self-interfering signals from the signal output of each of the
interferometers substantially simultaneously.
[0064] The plurality of self-interfering signals may be considered
analogous to discrete samples of the input light signal. For a
waveguide implemented MZI the self-interfering signal output from
the i.sup.th interferometer, F(i), may correspond to a single
coefficient of a cosine transformation given by
F(i)=.intg..sub..sigma..sub.min.sup..sigma..sup.maxp.sup.in(.sigma.)cos(-
2.pi..sigma.n.sub.effL.sub.i)d.sigma. (1)
or by the discrete cosine transformation (DCT)
F(i)=.delta..sigma..SIGMA..sub.k=1.sup..DELTA..sigma./.delta..sigma.p.su-
p.in(k.delta..sigma.)cos(2.pi.(k.delta..sigma.)n.sub.effL.sub.i)
(2)
where .sigma. is a shifted wavenumber
(.sigma.=.sigma.-.pi..sub.min) which may be used to replace an
un-shifted wavenumber (.sigma.) provided that low-frequency
components (i.e. wavenumbers .sigma.<.pi..sub.min) have been
eliminated, e.g. using an aliasing filter; .sigma..sub.min
corresponds to a cutoff frequency at low wavenumbers, and
.sigma..sub.max corresponds to a high-frequency cutoff; the OPD of
the i.sup.th interferometer is represented by OPD=n.sub.effL.sub.i
where n.sub.eff represents the effective index of a waveguide used
to implement the MZI and L.sub.i represents the difference in path
length between the MZI arms; p.sup.in(.sigma.) represents the
intensity of the input spectra in terms of shifted wavenumber; and
the incrementing number k and wavenumber resolution .delta..sigma.
are used to iterate over the input spectrum in the DCT.
[0065] Typically, to reconstruct an emitted light spectrum, the
Nyquist criterion (i.e. Nyquist-Shannon sampling theorem) is used
to determine the number of samples of the input light signal that
are required, i.e. the number of interferometers required. The
Nyquist criterion can also be used to determine the phase shift for
each of the interferometers. For example, the Nyquist criterion can
be used to define the number of MZIs and the optical path length
differences required to sample a particular spectrum. Given a
maximum desired wavenumber .sigma..sub.max, a minimum desired
wavenumber .sigma..sub.min, and a desired wavenumber resolution
.delta..sigma. the minimum number of sampling points (N.sub.min)
required to reconstruct an emitted spectrum from an input light
signal according to the Nyquist criterion can be determined by
N min = 2 .sigma. max - .sigma. min .delta. .sigma. ( 3 )
##EQU00001##
[0066] Equation (3) establishes the minimum number of sampling
points (N.sub.min) required to reconstruct the emitted spectrum
according to the Nyquist criterion. Equation (3) can also be
represented as:
N min = 2 B .DELTA. .lamda. ( 3 ' ) ##EQU00002##
where B represents the spectral bandwidth of the emitted spectrum
(i.e. the wavelength range of the spectrum to be reconstructed) and
.DELTA..lamda. represents the spectral resolution (i.e. the space
between adjacent data points in the reconstructed spectrum).
[0067] The path length increment .delta.L=L.sub.(i+1)-L.sub.i
according to the Nyquist criterion (i.e. the phase shift for an
MZI) can be determined by
.delta. L = 1 N min .delta. .sigma. n eff = 1 2 ( .sigma. max -
.sigma. min ) n eff ( 4 ) ##EQU00003##
and the maximum physical path length delay (L.sub.max) according to
the Nyquist criterion can be determined by
L max = N min .delta. L = 1 .delta. .sigma. n eff ( 5 )
##EQU00004##
[0068] A process for determining the spectrum of a sampled input
signal may be represented in matrix notation. The received input
signal can be represented as a continuous input spectrum
p(.sigma.). The continuous input spectra may be discretized or
sampled at a certain resolution to form an input column vector X of
input spectra values or input spectra coefficients
x(k)=p(.delta.(.sigma.-.sigma..sub.k)). The output of the
spectrometer can be defined as an output column vector Y with
output spectra values or output spectra coefficients y. The output
spectra coefficients y of the output column vector can be
determined by applying a discrete cosine transformation (DCT)
matrix .THETA. to the input spectra coefficients x:
y=.THETA.x (6)
[0069] If the input signal has been sampled according to the
Nyquist criterion, and the DCT matrix .THETA. is known (or can be
determined e.g. experimentally) then the input spectra coefficients
x may be reconstructed from the output spectra coefficients y
according to:
x=(.THETA..THETA..sup.T).sup.-1.THETA.y (7)
[0070] Equation (7) may be considered generally equivalent to the
inverse DCT so long as the input spectra coefficients x are fully
sampled by the DCT matrix .THETA. according to the Nyquist
criterion. As a result, the Nyquist criterion has typically been
used to define the minimum number of samples to be acquired when
reconstructing a spectrum from an input signal. This may, in
effect, place a lower limit on the number of interferometers that
have been used in spectrometer devices using arrays of
interferometers. This can in turn place size and weight limitations
on the device for a particular bandwidth and resolution, because of
the number of interferometers required. Accordingly, to reduce the
size of such a spectrometer device, bandwidth or resolution would
typically have to be sacrificed.
[0071] Embodiments described herein may provide a spectrometer
device and/or a spectrometry system in which the number of
interferometers in the first plurality of interferometers can be
fewer than the number of interferogram samples required to satisfy
the Nyquist criterion for reconstructing an emitted spectrum with a
spectral bandwidth B and a spectral resolution .DELTA..lamda. from
the input light signal. The total number of interferometers in the
array of interferometers can also be fewer than the number of
interferogram samples required to satisfy the Nyquist
criterion.
[0072] In some cases, the number of interferometers in the first
plurality of interferometers may be fewer than half the number of
interferogram samples required to satisfy the Nyquist criterion. In
some cases, the number of interferometers in the first plurality of
interferometers may be less than 1/4 the number of interferogram
samples required to satisfy the Nyquist criterion.
[0073] The embodiments described herein may still permit an emitted
spectrum of the input light signal to be reconstructed with the
spectral bandwidth B and spectral resolution .DELTA..lamda.. This
may allow smaller and lighter spectrometers to be manufactured
while maintaining the same or similar bandwidth and resolution. In
embodiments described herein, the emitted spectrum can be
reconstructed using compressive sensing techniques.
[0074] Compressive sampling or compressive sensing techniques may
permit accurate reconstruction of emitted signal spectra with fewer
samples than required by the Nyquist criterion (see, for example,
E. Candes and M. Wakin, "An Introduction To Compressive Sampling,"
IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21-30, 2008;
D. A. Lorenz, M. E. Pfetsch, and A. M. Tillmann, "Solving Basis
Pursuit: Heuristic Optimality Check and Solver Comparison," ACM
Trans. Math. Softw., vol. 41, no. 2, pp. 1-28, 2015; and S. Qaisar,
R. M. Bilal, W. Iqbal, M. Naureen, and S. Lee, "Compressive
Sensing: From Theory to Applications, A Survey," Communications and
Networks, Journal of, vol. 15, no. 5, pp. 443-456, 2013, the
entirety of each of which is incorporated herein by reference).
[0075] In order to reconstruct a signal with fewer samples than
required by the Nyquist criterion, compressive sensing generally
relies on two characteristics of the signal being analyzed. The
first characteristic is that the signal to be analyzed is a sparse
signal. A signal may be considered sparse when there exists some
domain in which the signal may be represented as a combination of
coefficients, very few of which are non-zero. For instance, a
sinusoidal signal collected in the time domain would appear to be
information-rich, however in the frequency domain the entire signal
can defined using a single data point. Such a signal would be
considered to be sparse in the frequency space domain.
[0076] In embodiments described herein, the spectrometer devices,
systems and methods may be configured to measure input light
signals having sparsely filled spectral channels. Various types of
emitted signals, such as Raman emissions, laser-induced breakdown
spectroscopy (LIBS) emissions, atomic emissions and molecular
emissions may provide sparsely filled spectral channels. For
example, the inventors have recognized that Raman signals tend to
be sparse in the frequency domain and may thus be suitable for
reconstruction using compressive sensing techniques.
[0077] The second characteristic is that the input signal is
sampled in a basis that is incoherent with the representation
basis. Incoherence between the sampling basis and the
representation basis can increase the achievable undersampling rate
of a compressive sensing process.
[0078] Embodiments described herein may sample the
self-interference of an input light signal at various phase shifts
(i.e. an interferogram). For example, an array of interferometers
can be used to directly sample the phase coherence of an input
signal in a cosine transformation basis. The phase shifts of the
interferometers may correspond to points in time in what would be
recognized as a time-series representation of the spectrum as
provided by a classical temporally phase scanned Fourier Transform
Spectrometer. This may provide a sampling technique that is
incoherent with signals that are sparse in the frequency domain,
such as Raman emissions.
[0079] By analyzing a sparse signal and applying compressive
sensing, the inventors have found that the number of
interferometers used in a spectrometer device can be reduced below
that required by the Nyquist criterion. This may facilitate the
design and manufacture of spectrometer devices with fewer
interferometers. This may in turn lead to reductions in size and
weight. Furthermore, such spectrometer devices may provide improved
signal-to-noise ratio because each interferometer may receive a
greater portion of the input light signal when fewer
interferometers sample the input light signal.
[0080] In general, for a spectrum of length K, with S non-zero
components the Nyquist criterion would require M=2K interferometric
samples to reconstruct the input signal. As shown in Equation (3')
above, K can be determined based on the bandwidth and resolution of
the spectrum that is being reconstructed
( i . e . K = B .DELTA. .lamda. ) . ##EQU00005##
In embodiments described herein where an emitted spectrum is
reconstructed using compressive sensing, the number of samples M
required can be reduced according to:
M=cS log(K) (8)
where c represents a sensing constant reflecting achievable
undersampling of the particular compressive sensing technique
applied.
[0081] Equation (8) may also be represented in term of the spectral
bandwidth B, spectral resolution .DELTA..lamda. and an
undersampling coefficient c' of the compressive sensing
technique:
M = 2 B .DELTA. .lamda. c ' ( 8 ' ) ##EQU00006##
where 0<c'<1.
[0082] The undersampling coefficient can depend on the compressive
sensing technique used, as well as incoherence between the sampling
technique and the representation basis of the input signal.
[0083] Given a phase-varying sinusoidal signal x represented in the
cosine transformation basis .PSI., sampling of the cosine
transformation basis may be considered equivalent to multiplication
of .PSI. by a sensing matrix .PHI.. For example, the signal may be
a time-domain sinusoidal signal from a temporally phase scanning
FTS, or the signal may be comprised of a set of signals from a
spatially distributed array of fixed interferometers with different
phase shifts. If the coefficients of the phase-varying signal are
fully sampled in the cosine transformation basis, i.e. the system
is fully Nyquist sampled, then the sensing matrix .PHI. may be
determined as the identity matrix I:
y=.PHI..PSI.x (9)
y=I.PSI.x (10)
y .THETA.x (11)
[0084] In general, in a compressive sensing approach to
reconstructing an emitted spectrum (i.e. for sensing S non-sparse
spectral components), the sensing matrix .PHI. can be defined by
randomly selecting M cosine coefficients to measure or sample. This
may be considered equivalent to randomly selecting M rows of an
K.times.K identity matrix. The sensing matrix and the cosine
transformation basis matrix can then be applied in a minimization
process to solve Equation (9). The minimization process may involve
minimizing the l.sub.1-norm which can provide a stable solution to
Equation (9). For example, the l.sub.1-norm may be minimized using
a primal-dual interior point search. Such a minimization process
may be implemented using various minimization software applications
such as l.sub.1-Magic. Other examples of compressive sensing
methods used in embodiments herein may include basis-pursuit
routines, belief-propagation (BP) or seeded-belief-propagation
(s-BP) methods, greedy solvers, orthogonal matching-pursuit (OMP)
and least absolute shrinkage and selection operator (LASSO).
[0085] As mentioned, the compressive sensing techniques described
herein can be typically applied to sparse signals. However, real
emitted optical spectra (e.g. Raman, LIBS, atomic/molecular
spectra) may be contaminated by broadband/slowly-varying background
signals such as thermal Planck signals in the infrared spectrum,
and fluorescence in the visible spectrum. This may result in the
input light signal received by a spectrometer device being
non-sparse. Such background contamination may impact the
reliability of using compressive sensing to reconstruct the emitted
spectrum with below-Nyquist sampling of the input signal.
[0086] Embodiments described herein may remove signal components
that may correspond to the background contamination in an input
signal. This may allow the emitted spectrum to be reconstructed
from the input signal using below-Nyquist sampling even in the
presence of contamination. Embodiments described herein may
identify broadband signal components (also referred to as
slowly-varying signal components or low-resolution signal
components) in the input signal. These signal components can be
removed to provide a pre-processed signal that may be sparse and
can be used with compressive sensing techniques.
[0087] Such background or contamination signal components may be
generally consistent across the spectrum of interest (i.e. the
spectral range or bandwidth of the spectrometer
device/system/method). Accordingly, low-resolution samples of the
input signal may be used to reconstruct a low-resolution spectrum.
The low-resolution spectrum/low-resolution spectral signal
components can then be removed from the emitted spectrum samples of
the input signal in pre-processing. The low-resolution spectrum may
be considered an approximation of the background or contamination
signal components. The low-resolution spectrum may also be referred
to as a slowly-varying spectrum or background spectrum in some
cases.
[0088] In some cases, to identify the low-resolution spectrum the
input signal may be fully Nyquist sampled over the same spectral
bandwidth, but with a much lower resolution (i.e. a much larger
step size between adjacent samples) than the emitted spectrum
sampling. As mentioned, background contamination signals or signal
components such as fluorescence and Planck emissions may be
expected to vary slowly. Accordingly, such signal components may be
represented in a Nyquist sampled-spectrum with many fewer
samples.
[0089] A Fourier transform can be applied to the low-resolution
Nyquist samples, and smoothly varying/low-resolution spectral
components can be determined. These smoothly varying or
low-resolution spectral components may then be removed from the
samples of the input signal used to reconstruct the emitted
spectrum. This may result in a pre-processed discrete interference
pattern that includes only (or mostly) sharp line emission spectral
signals (i.e. sparse emitted signal components, such as Raman
signal components) that are suited for reconstruction using
compressive sensing.
[0090] The low-resolution spectral components may be determined
using the discrete cosine transform at the phase shift of each
interferometer in the array. For example, equation (2) may be used
to determine low-resolution spectral components corresponding to
the self-interfering signals output from each interferometer in the
first plurality of interferometers by substituting the determined
low-resolution spectrum for p.sup.in(.sigma.), and substituting the
phase shift of each interferometer for 2.pi..sub.effL.sub.i. These
low-resolution spectral components can then be subtracted from the
corresponding self-interfering signals to provide pre-processed
self-interfering signals. The pre-processed self-interfering
signals may be suitable for reconstruction using compressive
sensing methods. A pre-processed discrete interference pattern can
then be determined from the pre-processed self-interfering
signals.
[0091] In some cases, the phase shift of each interferometer may
vary as a result of the temperature of the system. In some case,
this phase shift variation may be measured directly. In other
cases, the phase shift variation may be determined based on
detection of reflected laser light wavelength. Deviations from the
design temperature may add an identifiable signal pattern
characteristic of the temperature of the interferometer array to
the plurality of self-interfering signals output from the array of
interferometers. Correction factors may be determined based on the
system temperature, and used to account for variations in the phase
shifts of the interferometers.
[0092] In some embodiments, the array of interferometers may
include a second plurality of interferometers. The second plurality
of interferometers may be used to detect low-resolution signal
components in the input light signal. The second plurality of
interferometers can generally include fewer interferometers than
the first plurality of interferometers. Even when the second
plurality of interferometers are included, the array of
interferometers can include fewer interferometers than would be
required by the Nyquist criterion between the first plurality of
interferometers and the second plurality of interferometers.
[0093] In some cases, the array of interferometers may include
fewer than 1/2 the number of interferometers that would be required
by the Nyquist criterion. The array of interferometers may include
fewer than 1/3 the number of interferometers that would be required
by the Nyquist criterion. In some cases, the array of
interferometers may include fewer than 1/6 the number of
interferometers that would be required by the Nyquist
criterion.
[0094] Each interferometer in the second plurality of
interferometers can be configured to output a low-resolution
self-interfering signal with a known phase shift. The plurality of
low-resolution self-interfering signals output by the second
plurality of interferometers may be referred to as a second
plurality of self-interfering signals or a plurality of
low-resolution (or slowly varying or broadband or background)
self-interfering signals.
[0095] The second plurality of interferometers can be configured to
provide a fully-Nyquist sampled reconstruction of the spectrum with
the spectral bandwidth B, but with a low-resolution spectral
resolution .DELTA..lamda..sub.low that is lower resolution than the
spectral resolution .DELTA..lamda. being used for the
reconstruction of the emitted spectrum. For example, in some cases
.DELTA..lamda..sub.low>2.DELTA..lamda.. In some cases,
.DELTA..lamda..sub.low>4.DELTA..lamda.. In some cases,
.DELTA..lamda..sub.low>10.DELTA..lamda..
[0096] The interferogram samples required to satisfy the Nyquist
criterion for the spectral bandwidth B and the low-resolution
spectral resolution of .DELTA..lamda..sub.low may correspond to a
second plurality of Nyquist phase shifts. The phase shifts of the
interferometers in the second plurality of interferometers can be
selected to correspond to the second plurality of Nyquist phase
shifts. A low-resolution spectrum of the input signal may then be
determined from the second plurality of self-interfering signal
outputs.
[0097] Low-resolution spectral signal components from the low
resolution spectrum can be identified. The low-resolution spectrum
may be identified as defining the low-resolution spectral signal
components. A pre-processed discrete interference pattern may then
be generated by removing the contribution of the low-resolution
spectral signal components from the discrete interference pattern
(generated from the self-interfering signal outputs from the first
plurality of interferometers). The pre-processed discrete
interference pattern may then provide a sparse signal suitable for
reconstruction of the emitted signal spectrum using compressive
sensing.
[0098] Embodiments described herein may provide a spectrometer
device, spectrometer system and spectrometer method that permits
the emitted spectrum from a sample or target or location of
interest to be reconstructed from an input light signal using fewer
samples than are required by the Nyquist criterion. Embodiments
herein may use compressive sensing to reconstruct the emitted
spectrum. This may provide a spectrometer with increased signal to
noise ratio. This may also provide a spectrometer with reduced size
and/or weight.
[0099] In some cases, the spectrometer may be implemented in an
optical waveguide chip. The spectrometer may be implemented using
planar waveguides on a single chip. Various materials may be used
for the chips, such as silicon, silicon dioxide or fused silica,
silicon nitride, germanium, indium phosphide and other wafer
materials. For example, the spectrometer may be Raman spectrometer
device implemented in an optical waveguide chip.
[0100] By reducing the number of interferometers required,
embodiments described herein may allow for greater bandwidth and
resolution to be achieved in devices implemented on a single
optical chip. In some cases, the waveguides and corresponding
interferometers may be implemented on a single 22.times.22 mm chip,
such as a single photolithography reticle.
[0101] As mentioned, the waveguides and corresponding
interferometers in the array of interferometers may be spatially
distributed. As a result, there may be gaps between adjacent
waveguides. It may be desirable to focus an input light signal into
the waveguides to improve the amount of light transmitted to each
waveguide, and in turn to each interferometer. Focusing the input
light signal into the waveguides may avoid losing some light that
would otherwise be directed towards gaps between the
waveguides.
[0102] Some embodiments described herein may provide optical
coupling or optical couplers to direct the input light signal to
the plurality of waveguides. The optical coupling can include a
mirror array with a plurality of mirrors. The plurality of mirrors
may correspond to the plurality of waveguides. Each waveguide can
have a corresponding mirror in the mirror array. Each mirror in the
mirror array may be angled to direct the input light signal to the
corresponding input waveguide.
[0103] In some cases, a plurality of lenses may also be provided to
couple the input light signal to the plurality of waveguides. The
plurality of lenses may be provided with the input aperture (or may
define an aperture output of the input aperture). The plurality of
lenses may be arranged as a grid of lenses. For example, a
micro-lens array may be used to provide the plurality of
lenses.
[0104] The plurality of lenses may correspond to the mirror array.
Each mirror in the mirror array can have a corresponding lens in
the plurality of lenses. The lenses in the plurality of lenses can
be directed to focus the input light signal on the mirrors in the
mirror array. Each lens can be directed to focus a portion of the
input light signal on the corresponding mirror in the mirror array.
The plurality of lenses may be fixed in this focused position to
provide repeatable and reliable optical coupling of an input light
signal to the mirror array and to the waveguides.
[0105] Referring now to FIG. 1, shown therein is an example of a
spectrometry system 100 in accordance with an embodiment. The
spectrometry system 100 generally includes an input aperture 102,
optical coupling 104, a plurality of input waveguides 106, an
interferometer array 108, a detector array 112, memory 114, and a
controller 116. The spectrometry system 100 can also include a
light source 118.
[0106] In some embodiments, components of the spectrometry system
100 such as the input aperture 102, optical coupling 104, input
waveguides 106, interferometer array 108, detector array 112,
memory 114, and controller 116 may be implemented as a spectrometer
device. The spectrometer device can also include the light source
118. In some cases, the spectrometer device may be a handheld
spectrometer device. In some cases, a multi-unit spectrometer may
be provided that includes multiple spectrometer devices that may
each correspond to spectrometer system 100.
[0107] The input aperture 102 can receive an input light signal
120. The input light signal 120 may be an emitted or scattered
signal from a sample of interest 126. The input light signal 120
may be scattered in response to excitation of the sample 126 using
an excitation source such as light source 118. The received input
light signal 120 can include emitted signal components from the
sample/target of interest 126. Emitted signal components may refer
to signal emissions from the sample/target of interest 126 that can
be used to spectroscopically analyze the sample/target of interest
126, such as Raman emissions, Laser-induced breakdown spectroscopy
(LIBS) emissions, atomic emissions, molecular emissions and the
like. The received input light signal 120 may also include
background and/or contaminant signals components, such as
fluorescence and/or Planck signals.
[0108] The input aperture 102 can be configured to direct the input
light signal 120 to the plurality of waveguides 106 using the
optical coupling 104. The input aperture 102 may be secured to
(although displaced from) the surface of the spectrometer system
100 on which the plurality of waveguides 106 are provided. The
input aperture 102 can include an aperture output facing towards
the surface of the spectrometer system 100.
[0109] The optical coupling 104 can be configured to direct the
input light signal 120 to each of the waveguides 106. The input
aperture 102 and optical coupling 104 may include one or more
optical components that function to direct the input light signal
120 from free space into the plurality of waveguides 106. The
optical coupling 104 may be used by itself in any suitable
spectrometer or in any suitable combination or sub-combination with
any other feature or features disclosed herein.
[0110] The plurality of waveguides 106 can be optically coupled to
the input aperture 102. As explained above, optical coupling 104
may couple the input aperture 102 to the plurality of waveguides
106. The plurality of waveguides 106 can also be optically coupled
to the array of interferometers 108. The plurality of waveguides
106 may receive input light signal 120 from the input aperture 102
(e.g. via optical coupling 104). The plurality of waveguides 106
may then direct the received light signal to the array of
interferometers 108.
[0111] The characteristics of the waveguides 106 may depend on the
spectrum of interest or spectral range of the spectrometry system
100. For example, the waveguides 106 may be designed to be single
mode for the wavelengths of interest in spectrometer system
100.
[0112] For instance, a spectrometry system 100 may operate with a
spectral range or waveband from 532 nm to 641 nm. The waveguides
106 may then be manufactured using materials that are single mode
in this waveband. For example, SiN may be transparent and signal
mode in the waveband from 532 nm to 641 nm. The waveguides 106 may
then be manufactured using SiN (e.g. using TriPleX.TM. waveguides
available from LioniX).
[0113] In some embodiments, the waveguides 106 may be designed
using a single strip configuration. In other embodiments,
double-strip configurations may be used. In some case, double strip
geometry may be preferred as it may provide a higher confinement
waveguide. This may in turn provide a more compact spectrometry
system 100. For instance, using the TriPleX.TM. waveguides
mentioned above, double-strip geometry may be used which is
approximately 350 nm wide and approximately 200 nm thick, and is
single mode in the waveband from 532 nm to 641 nm.
[0114] For different wavelength ranges/wavebands, the
characteristics and/or configuration of waveguides 106 may be
modified. In some cases, the cross-section of the waveguides 106
may be adjusted to maintain single-mode operation for different
wavelength ranges. For instance, a spectrometry system 100
operating in a range close to 1064 nm may require a larger
waveguide core. A spectrometry system 100 operating at in a range
<350 nm may require a waveguide core material with better
transmission properties in the U.V. shorter wavelengths.
[0115] In some cases the plurality of waveguides 106 may define a
waveguide section of the spectrometry system 100. The waveguide
section can include a plurality of waveguide regions within the
waveguide section defined by waveguides 106.
[0116] For example, the plurality of waveguides 106 may define an
input waveguide region coupled to the aperture 102. The waveguides
106 may also include a fan-out region (not shown) between the input
waveguide region and the interferometer array 108. For instance,
the plurality of waveguides 106 may define fewer separate waveguide
paths in the input waveguide region than there are interferometers
110 in the interferometer array 108. The fan-out region may then
fan out or split the waveguides 106 from the input waveguide region
into sufficient waveguide paths to direct light (i.e. a portion of
the input light signal 120) to each of the interferometers 110 in
the interferometer array 108.
[0117] For example, the waveguides 106 may define 40 separate input
waveguide paths in the input waveguide region while the
interferometer array 108 includes 200 interferometers 110. The
input aperture 102 may be coupled to the 40 input waveguide paths
in the input waveguide region. The fan-out region may then fan out
each of the 40 input waveguide paths 5:1 to direct a portion of the
input light signal 120 to each of the interferometers 110.
[0118] In some cases, the waveguide section may include an
interferometer region. The interferometer array 108 may be provided
in the interferometer region of the waveguide section. That is, the
plurality of waveguides 106 may be used to define the
interferometers 110 in the interferometer array 108 (e.g. by
splitting to provide a separate reference signal path and delay
signal path for each interferometer 110).
[0119] In some cases, the waveguides 106 may also be configured to
discard unwanted signal polarizations. For example, a 90 degree
bend may be added to the waveguides 106 in the input waveguide
region to discard TM polarization.
[0120] The array of interferometers 108 in system 100 includes
interferometers 110A-110N. Each interferometer 110 can have a
signal input and a signal output. Each interferometer 110 can be
configured to receive a portion of the input light signal 120 from
a waveguide 106. The interferometer 110 can be configured to output
a self-interfering signal 122 with a known phase shift in response
to receiving the portion of the input light signal 120. Each
interferometer 110 may output a fixed self-interfering signal 122
that represents self interference of the received portion of the
input light signal 120 at the phase shift of that interferometer
110. The array of interferometers 108 may be used by itself in any
suitable spectrometer or in any suitable combination or
sub-combination with any other feature or features disclosed
herein.
[0121] The array of interferometers 108 can include a first
plurality of interferometers. As shown in spectrometer system 100,
the first plurality of interferometers includes interferometers
110B, 110B, 110D, 110E, 110N. The phase shift for each
interferometer 110 in the first plurality of interferometers can be
different from the phase shift of every other interferometer 110 in
the first plurality of interferometers.
[0122] In some embodiments, each interferometer 110 may have a
defined optical path length difference between two substantially
equally divided portions of the signal. The equally divided
portions of the signal can later be re-combined to provide the
self-interfering signal at the signal output of the interferometer
110. This can be the case where the array of interferometers 108 is
implemented using Mach-Zehnder interferometers. In such cases, the
phase shift for each interferometer 110 can be defined by the
optical path length difference for that interferometer 110.
[0123] In general, the phase shift corresponding to each
interferometer 110 can be implemented by any method for creating
self-interference between a portion of the signal received from the
waveguide 106 and another portion of the signal received from the
waveguide 106 with a known relative phase shift. For example,
Fabry-Perot interferometers may be used to provide the
interferometers 110.
[0124] In the spectrometer system 100, the number of
interferometers 110 in the first plurality of interferometers can
be fewer than the number of interferogram samples required to
satisfy the Nyquist criterion for reconstructing an emitted
spectrum from the input light signal 120 with a spectral bandwidth
B and a spectral resolution .DELTA..lamda.. The first plurality of
interferometers in the spectrometer system 100 may be configured to
provide a first plurality (or emission spectrum plurality) of
self-interfering signals that can be used to reconstruct the
emitted spectrum using compressive sensing techniques.
[0125] The number of interferometers in the first plurality of
interferometers may be determined based on the spectral bandwidth
B, the spectral resolution .DELTA..lamda. and the achievable
undersampling of a particular compressive sensing process (e.g.
undersampling coefficient c'). For example, the undersampling
coefficient c' can be in the range of
c ' = 1 5 . ##EQU00007##
In some cases, the undersampling coefficient may be in the range
of
c ' = 1 8 . ##EQU00008##
[0126] The undersampling coefficient c' for a signal of interest
can vary based on the compressive sensing reconstruction method
employed. The density of information in the input signal, p (e.g.
the number of Raman signal components vs. the total number of
signal components) can also affect the undersampling coefficient c.
To achieve a perfect reconstruction (e.g. a root mean square error
of 0) for input signals with information density p=0.15 (comparable
to an FT Raman signal when measured against the number of Nyquist
samples required) a compressive sensing reconstruction method such
as an l1-minimization or basis-pursuit routine may achieve an
undersampling coefficient of 0.5>c'>0.4. Some compressive
sensing reconstruction methods, such as belief-propagation (BP)
methods or seeded-belief-propagation (s-BP) methods may achieve an
undersampling coefficient of 0.4>c'>0.3 or 0.1>c'>0.2
respectively. Various other compressive sensing reconstruction
methods may be used in embodiments herein such as greedy solvers,
orthogonal matching pursuit (OMP) and least absolute shrinkage and
selection operator (LASSO), each of which may have their own
signal-dependent undersampling coefficients (See, for example, F.
Krzakala, M. Mezard, F. Sausset, Y. F. Sun, and L. Zdeborova,
Statistical-Physics-Based Reconstruction in Compressed Sensing,
Phys. Rev. X 2, 021005, 2012; and B. L. Sturm, M. G. Christensen
and R. Gribonval, Cyclic pure greedy algorithms for recovering
compressively sampled sparse signals, 2011 Conference Record of the
Forty Fifth Asilomar Conference on Signals, Systems and Computers
(ASILOMAR) pp. 1143-1147., 2011, the entirety of both of which are
incorporated herein by reference).
[0127] The undersampling coefficient may permit a corresponding
reduction in the number of interferometers in the first plurality
of interferometers as compared to the number of samples or
interferometers that would be required by the Nyquist criterion.
For example, the number of interferometers x required for the first
plurality of interferometers may be determined by
x = 2 B .DELTA. .lamda. c ' ##EQU00009##
as shown by equation (8') above.
[0128] The interferogram samples required to satisfy the Nyquist
criterion for the spectral bandwidth B and spectral resolution
.DELTA..lamda. may generally correspond to a plurality of Nyquist
phase shifts. The phase shift for each interferometer 110 in the
first plurality of interferometers may be selected from the
plurality of Nyquist phase shifts to permit reconstruction of the
emitted spectrum with the spectral bandwidth B and the spectral
resolution .DELTA..lamda. from the first plurality of
self-interfering signals using compressive sensing.
[0129] The phase shifts of the interferometers 110 in the first
plurality of interferometers may be selected from amongst the phase
shifts that would be used to reconstruct the spectrum of the input
light signal 120 if the input light signal 120 was fully Nyquist
sampled. In other words, the phase shifts of the interferometers
110 in the first plurality of interferometers can be a proper
subset of the phase shifts for a fully Nyquist sampled set.
[0130] In some cases, e.g. using MZI interferometers implemented by
waveguides 106, the phase shifts for the fully Nyquist sampled set
(the plurality of Nyquist phase shifts) corresponding to the
spectral bandwidth B and the spectral resolution .DELTA..lamda. can
be determined based on the spectral bandwidth B, the spectral
resolution and the refractive index of the waveguide n. The maximum
phase shift may be determined according to equation (5) set out
above as
L max = 1 .DELTA. .sigma. n eff . ##EQU00010##
Using the Nyquist-Shannon theorem, the minimum phase shift may be
determined based on the maximum phase shift as
L min = L max 2 B / .DELTA. .lamda. . ##EQU00011##
The phase shifts in the plurality of Nyquist phase shifts can then
be determined as integer multiples of L.sub.min until L.sub.max is
reached. The phase shifts for the interferometers in the first
plurality of interferometers may then be selected from among the
plurality of Nyquist phase shifts.
[0131] The phase shifts may be selected as random elements from the
phase shifts for the fully Nyquist sampled set satisfying the
restricted isometry principle (i.e. a proper subset of phase shifts
in the plurality of Nyquist phase shifts satisfying the restricted
isometry principle). In some cases, deterministic methods for
selecting the phase shifts for the interferometers in the first
plurality of interferometers while satisfying the restricted
isometry principle may be used. In some cases, the phase shifts for
the first plurality of interferometers can be selected randomly
from the plurality of Nyquist phase shifts.
[0132] In some embodiments, one or more thermo-optic or waveguide
heaters may be included in spectrometry system 100. The waveguide
heaters may include interferometer-specific heaters associated with
each of the waveguide interferometers 110 (or each of the
interferometers 110 in the first plurality of interferometers). The
phase delays of the interferometers 110 may be adjusted by heating
an interferometer 100 using the corresponding heater. In some
embodiments, other phase shifting elements may be used in
spectrometer 100. For example, active electro-optic phase shifting
elements may be used to adjust the phase shifts of interferometers
110.
[0133] In some cases, the number of interferometers in the first
plurality of interferometers may be less than or equal to half the
number of interferogram samples required to satisfy the Nyquist
criterion. In some cases, the number of interferometers in the
first plurality of interferometers may be less than or equal to 1/4
the number of interferogram samples required to satisfy the Nyquist
criterion.
[0134] The number of interferometers in the interferometers array
108 may depend on the wavelength of interest and the application
for spectrometer system 100. In general, the array of
interferometers 108 can include not fewer than 10 interferometers.
Depending on the application, the array of interferometers 108 may
include many more interferometers 110.
[0135] In some cases, the array of interferometers 108 can be
provided on a single chip. The plurality of waveguides 106 may also
be provided on the chip. Thus, the number of interferometers 110
may be limited by the dimensions of the chip. For example, in some
embodiments the array of interferometers 108 may include not
greater than 1000 interferometers. In some embodiments, the array
of interferometers 108 may include not greater than 500
interferometers. In some embodiments, the array of interferometers
108 may include not greater than 250 interferometers.
[0136] Various different types of chips/wafers may be used, such as
fused silica chips, silicon chips, silicon nitride chips, germanium
chips, indium phosphide chips etc. The interferometers 110 may be
etched onto the surface of the chip. Similarly, the plurality of
waveguides 106 can be etched onto the surface of the chip.
[0137] In some cases, the array of interferometers 108 can also
include a second plurality of interferometers 110. In spectrometer
system 100, the second plurality of interferometers may include
interferometers 110C and 110N-1. The second plurality of
interferometers 110 may be used to generate a second plurality (or
low-resolution plurality) of self-interfering signals. The second
plurality of self-interfering signals may also be detected by the
detector array 112.
[0138] In some embodiments, the interferometers 110 in the second
plurality of interferometers may be interspersed among the
interferometers 110 in the first plurality of interferometers. In
some embodiments, the interferometers 110 in the second plurality
of interferometers may occupy a separate portion of the
interferometer array 108 from the interferometers 110 in the first
plurality of interferometers. In some embodiments, the spatial
position of the interferometers 110 in the second plurality of
interferometers vis a vis the interferometers 110 in the first
plurality of interferometers may vary without impacting operation
of spectrometer 100.
[0139] The second plurality of self-interfering signals can be used
to generate a low-resolution spectrum from the input light signal
120. The low-resolution spectrum can be used to identify
low-resolution spectral components in the received input light
signal 120. The low-resolution spectral components may interfere
with the compressive sensing techniques used to reconstruct the
emitted spectrum from samples of the input light signal. The
low-resolution spectral components may then be used to determine a
pre-processed discrete interference pattern from the first
plurality of self-interfering signals 122 to facilitate
reconstruction of the emitted spectrum.
[0140] The second plurality of interferometers may be configured to
acquire a low-resolution set of interferometric samples of the
input light signal 120 across the spectral bandwidth B. The
low-resolution set of interferometric samples can satisfy the
Nyquist criterion for a lower spectral resolution.
[0141] The lower resolution spectrum may be a low-resolution
spectrum having the spectral bandwidth B and a low-resolution
spectral resolution of .DELTA..lamda..sub.low where
.DELTA..lamda..sub.low>.DELTA..lamda.. The number of
interferometers and the phase delays of the interferometers 110 in
the second plurality of interferometers can be selected, to
generate a low-resolution spectrum of the input signal 120 over the
spectral bandwidth B with a second/low-resolution spectral
resolution .DELTA..lamda..sub.low>>.DELTA..lamda.. In some
cases, as described below, a subset of the interferometers in the
second plurality of interferometers may be used to generate the
low-resolution spectrum.
[0142] For example, the low-resolution spectral resolution may be
less than half the resolution of the emitted signal spectrum being
reconstructed (i.e. the steps between adjacent samples may be
.DELTA..lamda..sub.low>2.DELTA..lamda.). The number of
interferometers in the second plurality of interferometers can be
not less than the number of interferogram samples required to
satisfy the Nyquist criterion for reconstructing the low resolution
spectrum of the input light signal.
[0143] The phase shifts for the second plurality of interferometers
can be determined in order to satisfy the Nyquist criterion based
on the spectral bandwidth B and the low-resolution spectral
resolution .DELTA..lamda..sub.low as explained above. That is, the
interferometric samples required to satisfy the Nyquist criterion
for the spectral bandwidth B and the spectral resolution of
.DELTA..lamda..sub.low may correspond to a second plurality of
Nyquist phase shifts, and the phase shifts of the interferometers
110 in the second plurality of interferometers can be selected to
correspond to the second plurality of Nyquist phase shifts.
[0144] In general, the second plurality of interferometers can
include fewer interferometers 110 than the first plurality of
interferometers. In some embodiments, the number of interferometers
110 in the second plurality of interferometers can comprise fewer
than 50% of the number of interferometers 110 in the first
plurality of interferometers. In some embodiments, the number of
interferometers 110 in the second plurality of interferometers can
comprise fewer than 25% of the number of interferometers 110 in the
first plurality of interferometers. In some embodiments, the number
of interferometers 110 in the second plurality of interferometers
may even comprise fewer than 10% of the number of 110
interferometers in the first plurality of interferometers.
[0145] Depending on the expected operating conditions of
spectrometry system 100, the configuration of the interferometer
array 108 may differ. For instance, a system 100 in which no
background or fluorescent contamination is expected (i.e. the input
light signal is a sparse emission signal) may not require the
second plurality of interferometers. The number of interferometers
in the second plurality of interferometers may also depend on the
expected operational conditions of the system 100.
[0146] In some cases, the low-resolution (i.e. background or slowly
varying signal components) may be identifiable from only 3-4
low-resolution samples. However, more complex background signals
may require additional interferometers for the second plurality of
interferometers.
[0147] In embodiments of system 100 employing the second plurality
of interferometers, the second plurality of interferometers may
include about 10 interferometers or more. In some embodiments, the
number of interferometers in the second plurality of
interferometers may be in the range of about 30-40
interferometers.
[0148] In general, the array of interferometers 108 can include
fewer interferometers 110 than the number of samples required for
the Nyquist criterion to be satisfied, even when both the first
plurality of interferometers and the second plurality of
interferometers are included.
[0149] The detector array 112 can be optically coupled to the
interferometer array 108. The detector array 112 can detect a first
plurality of self-interfering signals 122 from the signal outputs
of the interferometers 110 in the first plurality of
interferometers. The first plurality of self-interfering signals
122 can include the self-interfering signal 122 from the signal
output of each of the interferometers 110 in the first plurality of
interferometers. The first plurality of self-interfering signals
122 from the signal outputs of the interferometers 110 in the first
plurality of interferometers may be referred to as an emitted
spectrum set of self-interfering signals.
[0150] The detector array 112 may also detect a second plurality of
self-interfering signals 122 from the signal outputs of the
interferometers 110 in the second plurality of interferometers. The
second plurality of self-interfering signals 122 can include the
self-interfering signal 122 from the signal output of each of the
interferometers 110 in the second plurality of interferometers. The
second plurality of self-interfering signals 122 may be referred to
as a low-resolution set of self-interfering signals.
[0151] The first plurality of self-interfering signals 122 from the
signal outputs of the interferometers 110 in the first plurality of
interferometers may be combined into an interference pattern
corresponding to the input signal. The interference pattern may be
a discrete interference pattern that is built up based on the first
plurality of self-interfering signals 122 from the signal outputs
of the interferometers 110 in the first plurality of
interferometers.
[0152] Similarly, the second plurality of self-interfering signals
from the signal outputs of the interferometers 110 in the second
plurality of interferometers may be combined into a low-resolution
interference pattern corresponding to the input signal 120.
[0153] The detector array 112 may include a plurality of detector
elements. Each interferometer 110 in the array of interferometers
108 may have a corresponding detector element in the detector array
112. Each detector element may be used to detect the
self-interfering signal 122 from the signal output of the
corresponding interferometer 110.
[0154] The detector array 112 may be aligned with the signal
outputs of the interferometers 110 in the interferometer array 108.
The signal outputs from the interferometers 110 may be aligned with
a row of the detector array 112. For example, the detector array
112 may be a charge-coupled device or CMOS-based detector. An
electronically gated scientific camera may also be used.
[0155] In some cases, the detector array 112 may provide
time-resolved detection of the self-interfering signals 122
corresponding to the input signal 120. The detector array 112 may
provide periodic detection with a defined period or frequency. For
example, the detector array 112 may be a charge-coupled device with
a shift register to provide time-resolved spectra at the timing of
the line shift (e.g. 1 MHz). The detector array 112 may be provided
as an ROIC circuit. A CMOS ROIC may be provided with a periodic
(e.g. 1 MHz) transfer into an output capacitor. This may also
provide for time-resolved detection of the self-interfering signals
122.
[0156] Time-resolved signal detection may facilitate applications
operating during daylight or in higher light conditions. The
time-resolved signal detection may also facilitate identification
and removal of background fluorescence and luminescence signals
from the emitted signal components that may be present only in
response to a pulse emitted from light source 118.
[0157] In some embodiments, the detector array 112 may include an
Electron Multiplying CCD. This may provide improved signal to noise
for a faint emitted signal (that has been multiplexed into a
plurality of waveguides 106). The EMCCD may be configured to
operate in a high gain analog mode. This may provide a detector
array 112 with a gain of upwards to 1000.times.. The EMCCD may also
be configured to provide frame transfers for time-resolved
detection.
[0158] An example data collection process may now be described for
a detector array 112 synchronized with a light source 118. The data
collection process may begin by flushing the detector array 112 to
remove any residual signal values from previous data
collection.
[0159] The controller 116 may transmit a trigger pulse to the light
source 118 and detector array 112. The trigger pulse may provide
synchronization between the detector array 118 and light source
118. The trigger pulse can trigger the transmission of an
excitation light pulse 124 from light source 118 to the sample of
interest 126. The detector array 122 may be synchronized to the
emitted laser pulses, e.g. with a 1 MHz transfer rate.
[0160] The detector array 112 may then detect self-interfering
signals 122 output from the array of interferometers 108. As
explained above, the detected self-interfering signals 122 may
include a first plurality of self-interfering signals from the
interferometers 110 in the first plurality of interferometers. The
detected self-interfering signals 122 may also include a second
plurality of self-interfering signals 122 from the interferometers
110 in the second plurality of interferometers in embodiments using
the second plurality of interferometers. The detected
self-interfering signals 122 can be transferred (e.g. using a frame
transfer for CCD or a CTIA charge transfer for ROIC) and then
stored in memory 114.
[0161] The detection and storage of self-interfering signals 122
may be repeated multiple times. For example, the data collection
process may be repeated until a reduced fluorescence state is
identified. To identify a reduced fluorescence state, the intensity
levels of the self-interfering signals 122 from the interferometers
110 in the second plurality of interferometers may be monitored.
When the intensity levels are identified to have dropped a
threshold amount, it may be determined that the fluorescence has
been reduced.
[0162] In some cases, the data collection process may be repeated
while adjusting the phase delays of interferometers 110 in the
first plurality of interferometers. For example, in some
embodiments thermo-optic heaters may be coupled to each (or a
subset) of the interferometers 110 in the first plurality of
interferometers. The controller 116 may randomly adjust the phase
delays of the interferometers 110 using the thermo-optic heaters
(e.g. using a random number generator). This may provide multiple
measurements with different samples of the time-series. In other
embodiments, active electro-optic phase shifting elements may be
used.
[0163] The repeated data collection process may permit a plurality
of distinct discrete interference patterns to be generated for a
particular emitted spectrum. This may allow the emitted spectrum to
be reconstructed a plurality of times, and the reconstructions may
be averaged to determine the emitted spectrum. This may suppress
noise in the reconstructed signal.
[0164] As mentioned, the array of interferometers 108 may be
provided on a spectrometer chip. The detector array 112 may be
provided as a separate detector chip. The spectrometer chip may be
bonded onto the detector chip with no air gap using an optical
adhesive. The spectrometer chip may be bonded horizontally onto the
detector chip with a 90 degree out-of-plane mirror bend at the
output facet to allow the spectrometer chip to sit flat on the
detector chip when bonded thereto.
[0165] Memory 114 may generally be a computer-readable storage
medium. The memory 114 can be coupled to the detector array 112.
The memory 114 may be used to store at least one interferometric
output signal based on the plurality of self-interfering signals
122 output from the interferometers 110 in the first plurality of
interferometers detected by the detector array 112. For instance,
the at least one interferometric output signal may be stored as the
plurality of self-interfering signals 122 or as an interference
pattern. The memory 114 may also be used to store at least one low
resolution output signal based on the second plurality of
self-interfering signals 122 output from the interferometers 110 in
the second plurality of interferometers detected by the detector
array 112.
[0166] In some cases, the controller 116 may be implemented using a
computer processor, such as a general purpose microprocessor. In
some other cases, controller may be a field programmable gate
array, application specific integrated circuit, microcontroller, or
other suitable computer processor, or controller. The controller
116 may be configured to provide control and/or synchronization
between various components of spectrometer 100.
[0167] The controller 116 may be configured to perform various
aspects of a process for reconstructing an emitted spectrum, such
as methods 200 and 300 described below. In other cases, the
spectrometry system 100 may be communicatively coupled to a remote
processor that may perform aspects of a process for reconstructing
an emitted spectrum, such as methods 200 and 300 described
below.
[0168] Optionally, a light source 118 can be included in the
spectrometry system 100. Typically, the light source 118 can be
included where the spectrometry system 100 is used to excite a
sample or location of interest 126 using an excitation light signal
124 such as a laser pulse. The light source 118 can be configured
to transmit an excitation light signal 124 with a known wavelength
towards the location of interest 126. The excitation light 124 can
be used to excite the location of interest 126 to cause emissions
which may be reconstructed from the input light signal 120.
[0169] For example, spectrometry system 100 may be used in laser
induced breakdown spectrometry. The light source 118 may be a laser
light source configured to emit a pulse of laser light 124. The
laser light pulse 124 may induce the sample of interest 126 to emit
scattered light signals, including the input light signal 120.
[0170] The wavelength of the light source 118 may vary depending on
the wavelength of interest in the particular application of the
spectrometry system 100. In some cases, the light source 118 may be
a Raman laser. Various embodiments may use Raman lasers with
wavelengths such as <250 nm, 325 nm, 532 nm, 633 nm, 785 nm,
1064 nm.
[0171] For example, the light source 118 may be a 532 nm Raman
laser with a linewidth and spectral drift <the desired spectral
resolution .DELTA..lamda.. The light source 118 may be
approximately 100 mW power in some cases. The light source 118 may
be pulsed with a defined frequency using transistor-transistor
logic. The light source pulse 124 can be synchronized with the
detector array 112. The light source 118 may be hybridized to the
same chip carrier as the detector array 112 and the waveguides 106
and interferometer array 108.
[0172] In some cases, the spectrometer system 100 may include a
light source 118 with a transmission/reception head at the
wavelength of interest. This may be configured to direct the
received scattered light signal 120 into the waveguides 106 at high
etendue. The outgoing laser pulse 124 from the light source 118 can
be transferred using a multi-mode fiber (MMF). For example, where
the light source 118 emits a 532 nm laser pulse a MMF with a 100
micron core may be used. The outgoing laser pulse 124 may be
focused on the sample of interest 126 using an objective lens. For
example, the objective lens may be an oversized objective lens
positioned with an approximately 1 cm standoff.
[0173] In some embodiments, the input aperture 102 may receive the
input light signal 120 using optical components used to emit the
excitation signal 124 from light source 118. The scattered signal
emitted by the sample 126 may be hemispherically scattered in
response to the excitation signal 124. The objective lens may
collimate the received scattered signal 120. The collimated
scattered signal 120 may then be split onto a return path to the
input aperture 102 using a dichroic. In some cases, the laser
return signal may be blocked using a notch filter.
[0174] The received scattered signal 120 may initially be
transmitted using a multi-mode fiber. In some cases, the input
aperture 102 and optical coupling 104 may include mode conversion
optics to convert the multi-mode fiber to a plurality of
single-mode fibers. That is, the mode conversion optics may convert
the received light signal 120 from transmission using a multi-mode
fiber to provide single-mode transmission that may be suitable for
a plurality of single-mode fibers, such as may be used for
waveguides 106.
[0175] In general, the mode conversion optics may be configured to
convert a multimode fiber comprising a plurality of distinct modes
of light (e.g. 50 distinct modes) into an array of single-mode
fibers. For example, in some cases the mode conversion optics may
include a photonic lantern. In some cases, the mode conversion
optics may include mode converters etched directly into the
waveguides.
[0176] In some embodiments, the optical coupling 104 may include a
mirror array with a plurality of mirrors. Each of the mirrors in
the mirror array may correspond to one of the waveguides 106. Each
of the input waveguides 106 in the input waveguide region may have
a corresponding mirror in the mirror array. The mirror
corresponding to each input waveguide 106 can be angled to direct
the input light signal from the input aperture 102 along that input
waveguide 106.
[0177] In some embodiments, the spectrometry system/device 100 may
include a planar spectrometer surface. Each of the input waveguides
106 may be positioned on the spectrometer surface. For example,
each input waveguide 106 may be a substantially planar waveguide.
Planar waveguides 106 may be etched into the planar spectrometer
surface.
[0178] Each mirror in the mirror array may also be mounted on the
spectrometer surface. Each mirror can be mounted at an angle to the
spectrometer surface to direct the input light signal incident on
the mirror from the input aperture 102 along the corresponding
waveguide 106.
[0179] The input aperture 102 may be secured to the spectrometer
surface (but there may be a gap between the input aperture 102 and
the spectrometer surface) with an aperture output facing towards
the surface. The input aperture 102 may direct the input light
signal 120 towards the spectrometer surface through the aperture
output. Each mirror may re-direct the light that is incident on the
spectrometer surface from the aperture output (above the surface)
along a waveguide 106 that is substantially in the plane of the
spectrometer surface.
[0180] For example, the plurality of waveguides 106 may be formed
on the surface of a planar waveguide chip. The upper surface of the
planar waveguide chip may define the spectrometer surface. The
plurality of waveguides 106 can be etched into the surface of the
waveguide chip. The mirror array can be secured on the surface of
the waveguide chip so that light incident on the surface of the
waveguide chip can be re-directed along the waveguides 106.
[0181] In some embodiments, the input aperture 102 may include a
plurality of lenses. For example, the lenses may be provided using
gradient-index (GRIN) lenses. The plurality of lenses may define
the input aperture 102. For example, the lenses may be arranged
into a grid of lenses.
[0182] In some cases, the plurality of lenses may direct the
received input signal to a circular bundle of waveguides. The
circular bundle of waveguides may then fan-out into an array (e.g.
a V-groove array) matched to the spacing of the input waveguide
region. This may provide input coupling between the input aperture
102 and the plurality of waveguides 106.
[0183] In embodiments using a micro-mirror array, the circular
bundle of waveguides may not be required. The plurality of lenses
can include a lens corresponding to each of the mirrors in the
mirror array. Each lens can be used to direct the input light
signal 120 toward the corresponding mirror in the mirror array.
That mirror may then re-direct the light signal from the
corresponding lens along the corresponding waveguide 106.
[0184] The plurality of waveguides 106 may be spatially distributed
or arrayed. Similarly, the mirrors in the mirror array can be
spatially distributed so as to be aligned with the corresponding
waveguides 106. As a result, there may be gaps between neighboring
mirrors in the mirror array. The plurality of lenses in the input
aperture 102 can be arranged to direct substantially all of the
input light signal 120 to the mirrors in the mirror array (and in
turn to the waveguides 106). That is, the lenses in the plurality
of lenses may be directed and focused to avoid directing the input
light signal 120 towards the gaps between mirrors in the mirror
array.
[0185] The mirror array may be provided as a circular array of
micro-mirrors directly etched into the surface of the spectrometer
chip. The mirrors can be positioned and angled to direct the
received input signal from the back focus of the plurality of
lenses into plurality of waveguides 106 on the chip.
[0186] The angle of the mirrors may be adjusted based on the angle
of the incident light from the input aperture 102. For example,
where the input aperture 102 is placed directly above the
spectrometer surface (i.e. the input light signal 120 is directed
towards the spectrometer surface substantially perpendicular to the
plane of the spectrometer surface), the mirrors may be angled at
approximately 45 degrees to direct the received input signal along
the waveguides 106.
[0187] As mentioned, the plurality of lenses can be focused to
direct the received light signal 120 into the waveguides 106. The
back focal point of each lens may be focused to coincide with the
corresponding waveguide 106 after reflection by the corresponding
mirror in the mirror array. The f-number of the lenses in the
plurality of lenses can be matched to the acceptance cones of the
waveguides 106 as defined by their numerical aperture. Each lens
may focus a portion of the received light signal into the
corresponding waveguide 106.
[0188] The plurality of lenses may be provided as a single
component. For example, the plurality of lenses may be provided as
a micro-lens array. Similarly, the plurality of waveguides 106 can
be provided on the spectrometer surface/chip as a single component.
The plurality of lenses may be aligned so the focal point of each
lens (after reflection by the mirrors in the mirror array) is
focused on a corresponding waveguide 106. The plurality of lenses
may then be secured to the spectrometer in the aligned
position.
[0189] For example, an adhesive layer may be applied between the
plurality of lenses (e.g. the micro-lens array) and the
spectrometer surface. In some cases, the adhesive layer may be a
ball-loaded adhesive to maintain a uniform adhesive layer
thickness. A test light signal can be directed through the
plurality of lenses, and the position of the lenses can be adjusted
while monitoring output light from each waveguide 106. When light
is detected from all of the waveguides, the adhesive layer can be
set.
[0190] It should be understood that spectrometer system/device 100
is merely exemplary, and a spectrometer device 100 may include
various additional components not shown in FIG. 1. For instance,
the spectrometer 100 may include various user interface components
such as input devices, output devices, display devices etc. The
spectrometer 100 may also include various communication components
that may permit transmission and reception of control commands and
data between the spectrometer 100 and other devices, e.g. using
wired or wireless communication protocols.
[0191] In some embodiments, a multi-unit spectrometry device/system
may be provided. The multi-unit spectrometer may include two or
more spectrometry devices such as those shown by system 100.
[0192] In some cases, the spectrometry devices may be substantially
identical (i.e. reconstructing an emitted spectrum over the same
bandwidth and spectral resolution. The discrete interference
patterns (and corresponding reconstructed emitted signal) may then
be used as independent results to improve the signal to noise ratio
of the spectrometer.
[0193] A multi-unit spectrometer may be used to improve the
time-resolution of spectrometer system 100. For example, each
spectrometry device in the multi-unit spectrometer may have an
associated signal collection time. The signal collection time for
each spectrometry device in the multi-unit spectrometer may be
different (i.e. the signals collected by the spectrometry devices
in the multi-unit spectrometer may be offset in time). The
multi-unit spectrometer may then collect multiple input signals
(and corresponding discrete interference patterns) in the span of a
single data collection period. This may provide improved time
resolution of the reconstructed emitted spectra. This may also
facilitate the measurement and observation of processes that occur
rapidly and may otherwise have emissions that occur outside the
collection time of a single-unit spectrometer.
[0194] In some cases, the spectrometry devices in the multi-unit
spectrometer may be different. Each spectrometry device in a
multi-unit spectrometer may have a different bandwidth. For
example, each spectrometry device in the multi-unit spectrometer
may collect signals corresponding to a portion of a bandwidth of
interest. The plurality of spectrometry devices in the multi-unit
spectrometer may then combine to provide a multi-unit spectrometer
with expanded bandwidth and/or improved resolution.
[0195] In some cases, the spectrometry system 100 may require an
initial calibration. One technique to calibrate the spectrometry
system 100 can include experimentally determining the DCT matrix
corresponding to Equation (2). This DCT matrix can be
experimentally determined using a tunable laser. Monochromatic
light of a known wavenumber can be used as the input to the device.
The output of each interferometer 110 can be detected and stored as
the tunable laser is swept across the full spectral range of the
spectrometer 100. The stored outputs can then be used to determine
the DCT matrix.
[0196] Referring now to FIG. 2, shown therein is an example process
200 for determining an emitted spectrum from an input light signal
in accordance with an example embodiment. Process 200 may be used
to determine an emitted spectrum having a spectral bandwidth B and
a spectral resolution .DELTA..lamda.. Process 200 is an example of
a process that may be used to reconstruct an emitted spectrum with
fewer samples than would be required by the Nyquist criterion.
Process 200 may be implemented using a spectrometry device or
system such as spectrometer 100.
[0197] At 210, an input light signal can be received by the
spectrometer. The input light signal may typically be received from
a location or sample of interest, such as sample 126. The input
light signal may be received by an aperture, such as aperture
102.
[0198] The input light signal may include scattered signal
components emitted in response to an excitation light signal or
pulse (e.g. light pulse 124 from a light source such as light
source 118). For example, the input light signal may include Raman
scattering signal components emitted by a sample of interest in
response to a laser light pulse.
[0199] At 220, the input light signal received at 210 may be
directed to an array of interferometers such as array 108. For
example, the input light signal may be directed along a plurality
of waveguides (e.g. waveguides 106) leading to the array of
interferometers.
[0200] As explained above, the input light signal may be coupled,
e.g. using various optical components such as aperture 102 and
optical coupling 104 described herein above.
[0201] At 230, a plurality of self-interfering signal can be
detected from the array of interferometers, e.g. using a detector
array such as detector array 112. The plurality of self-interfering
signals may be detected substantially simultaneously or
concurrently. The plurality of self-interfering signals can include
a first plurality of self-interfering signals from a first
plurality of interferometers in the interferometer array.
[0202] The number of self-interfering signals in the first
plurality of self-interfering signals can be fewer than the number
of samples required to satisfy the Nyquist criterion to reconstruct
the emitted spectrum (with spectral bandwidth B and spectral
resolution .DELTA..lamda.). As explained above, the number of
self-interfering signals may be determined based on the
undersampling coefficient of a particular compressive sensing
process in the same manner as determining the number of
interferometers required.
[0203] In some cases, the number of self-interfering signals in the
plurality of self-interfering signals can be equal to or less than
half the number of samples required to satisfy the Nyquist
criterion for the spectrum of the input light signal. In some
cases, the number of self-interfering signals in the plurality of
self-interfering signals can be equal to or less than 1/4 the
number of samples required to satisfy the Nyquist criterion for the
spectrum of the input light signal.
[0204] The array of interferometers can include a first plurality
of interferometers with known phase shifts. The phase shifts of the
interferometers in the first plurality of interferometers may all
be different. As explained herein above, the first plurality of
interferometers can include fewer, and often substantially fewer,
interferometers than would be required to satisfy the Nyquist
criterion. The number and phase shifts of the interferometers in
the first plurality of interferometers may be determined based on
the spectral bandwidth B, the spectral resolution .DELTA..lamda.
and an undersampling coefficient as described above.
[0205] At 240, the emitted light spectrum can be reconstructed from
the plurality of self-interfering signals detected at 230. The
emitted light spectrum may be reconstructed using compressive
sensing.
[0206] A discrete interference pattern may be determined from the
plurality of self-interfering signals detected at 230. The emitted
light spectrum may be reconstructed from the discrete interference
pattern. Reconstruction of the emitted light spectrum using
compressive sensing may involve a minimization process.
[0207] At least one potential emitted spectrum may be identified.
Typically, a plurality of potential emitted spectra can be
identified. A distance value can be determined for each potential
emitted spectrum. The distance value can be determined based on the
discrete interference pattern and defined signal acquisition
properties of the spectrometer. For example, the distance value may
be determined using a rectilinear distance or l.sub.1-norm.
[0208] The spectrometer may have defined signal acquisition
properties indicating how an input signal may be transformed and
sampled during a data collection process. Such signal acquisition
properties may be pre-defined for the spectrometer. In some cases,
the signal acquisition properties may be determined during an
initial calibration process. In general, however, the signal
acquisition properties for the spectrometer can be pre-defined for
the acquisition of a particular input signal at the time of
acquisition of that input signal.
[0209] A lowest distance potential emitted spectrum can be
identified. The lowest distance potential emitted spectrum can be
identified as the potential emitted spectrum corresponding to the
lowest distance value. The lowest distance potential emitted
spectrum may be identified as part of a process for minimizing the
l.sub.1-norm. The emitted light spectrum may then be reconstructed
as the lowest distance potential emitted spectrum.
[0210] The output from the plurality of self-interfering signals
(i.e. the discrete interference pattern) can correspond to samples
y of the representation of the input signal in the cosine
transformation basis. Signal acquisition parameters of the
spectrometer, such as the cosine transformation basis matrix .PSI.
and the sensing matrix .PHI. can be defined.
[0211] A theoretical or potential cosine transformation basis
matrix .PSI. may be defined by the phase shifts of the
interferometers used to generate the self-interfering signals. In
some cases, the cosine transformation basis matrix .PSI. can be
determined in an initial calibration of the device. In an initial
calibration, the phase-shift of each interferometer can be
determined either individually or in parallel. In some cases, the
phase shifts defining the cosine transform matrix .PSI. may vary
with temperature. The temperature of the spectrometer may be
determined at the time of measurement and used to determine
correction factors. The correction factors can be used to adjust
the reconstruction of the emitted spectrum to account for changes
in interferometer phase shifts. For example, the correction factors
may be determined using a detected reference laser signal of known
wavelength as explained herein.
[0212] The sensing matrix .PHI. can be determined from the phase
shifts of the interferometers in the first plurality of
interferometers. In general, the sensing matrix .PHI. acts on the
cosine transformation matrix to "select" or identify the components
of the cosine transform that are actually measured/detected. In
some cases, variations in coupling efficiency may provide
non-uniform illumination and throughput. These variations can be
calibrated initially and may be incorporated into the sensing
matrix.
[0213] Using the output from the plurality of self-interfering
signals and signal acquisition parameters of the spectrometer, the
emitted light spectrum can be determined or reconstructed using a
minimization process to solve Equation (9) set out above.
Minimizing the l.sub.1-norm can provide a stable solution to
Equation (9), as discussed above.
[0214] In some cases, the input light signal received at 210 may be
a sparse signal. In such cases, method 200 may proceed directly
from 230 to 240 reconstruct the emitted light spectrum. However, in
some cases the input signal may not be sparse (e.g. it may be
contaminated by background light or fluorescence). In such cases, a
pre-processing process, such as method 300 described below may be
used to pre-process the discrete interference pattern prior to
reconstructing the emitted light spectrum.
[0215] In some cases, additional pre-processing may also be
performed prior to reconstructing the emitted light spectrum at
240. For example, the additional pre-processing may include the
removal of signal components corresponding to detector artifacts,
dark current, gain non-linearities and the like.
[0216] A pre-processed discrete interference pattern may then be
generated. The emitted light spectrum can be reconstructed from the
pre-processed discrete interference pattern. For example, rather
than using the discrete interference pattern in the reconstruction
process described at 240 above, the pre-processed discrete
interference pattern can be used in its place. This may provide a
sparse signal that may be more likely to result in an accurate
reconstruction of the emitted light spectrum, even in the presence
of other contaminating signal components.
[0217] Referring now to FIG. 3, shown therein is an example process
300 that can be used to generate a pre-processed discrete
interference pattern. Process 300 may be used to remove signal
components to provide a sparse signal for reconstruction using
compressive sensing. Process 300 may remove signal components that
may be considered to contaminate the emitted light spectrum of
interest, such as background or fluorescent signals. Process 300
may be implemented using a spectrometer system or device such as
spectrometer 100.
[0218] At 310, a second plurality of self-interfering signals can
be detected. The second plurality of self-interfering signals can
be detected from the outputs of a second plurality of
interferometers in the array of interferometers. The second
plurality of self-interfering signals may be detected substantially
simultaneously or concurrently.
[0219] The second plurality of self-interfering signals may
correspond to samples of the same spectral bandwidth B as the first
plurality of self-interfering signals, but with a lower spectral
resolution .DELTA..lamda..sub.low. The second plurality of
self-interfering signals may provide a fully Nyquist sampled set of
low-resolution samples for the spectral bandwidth B. Typically, the
number of self-interfering signals in the second plurality of
self-interfering signals can be lower than the number of signals in
the first plurality of self-interfering signals (e.g. 50%, 25% or
even 10%).
[0220] The second plurality of self-interfering signals may be
generated using embodiments of the second plurality of
interferometers described herein above. For example, the number and
phase shifts of the interferometers in the second plurality of
interferometers can be selected to provide a fully Nyquist sampled
set of low-resolution samples.
[0221] At 320, a low resolution spectrum of the input light signal
may be determined from the second plurality of self-interfering
signals detected at 310. The low resolution spectrum may represent
a reconstruction of the input light signal with the spectral
bandwidth B and a spectral resolution of .DELTA..lamda..sub.low.
The low-resolution spectrum may be reconstructed by applying a
Fourier transform to the second plurality of self-interfering
signals detected at 310.
[0222] In some cases, a low-resolution spectrum reconstructed using
all the self-interfering signals in the second plurality of
self-interfering signals may incorporate some signal components
that may be of interest for reconstruction of the input signal
spectrum. For instance, where the input light signal has a simple,
consistent background/contaminant signal component some of the
self-interfering signals may include Raman signal components.
[0223] Accordingly, in some embodiments the low-resolution spectrum
may be reconstructed using only a subset of the self-interfering
signals in the second plurality of self-interfering signals. This
may avoid excluding some of the emitted signal components of
interest that may be detected in the full set of self-interfering
signals in the second plurality of self-interfering signals.
[0224] A first low-resolution spectrum may be reconstructed using
all the self-interfering signals in the second plurality of
self-interfering signals. A second low-resolution spectrum may also
be reconstructed using a subset of the self-interfering signals in
the second plurality of self-interfering signals. For example,
where the second plurality of self-interfering signals includes 40
low-resolution self-interfering signals, the second low-resolution
spectrum may be reconstructed using only 10 of those low-resolution
self-interfering signals.
[0225] The first low-resolution spectrum and second low-resolution
spectrum may be compared to determine a low-resolution spectrum
difference. Based on the low-resolution spectrum difference, the
first low-resolution spectrum and second low-resolution spectrum
may be selected as the low-resolution spectrum.
[0226] In general, the low-resolution spectrum may contain
information from Raman peaks of interest. In the low-resolution
spectrum this effect can manifest as spectral leakage components.
For example, spectral leakage components from a single Raman peak
can manifest as a sinc function overlaid on top of the broadband
spectrum. Such spectral leakage components may be identified in
various ways.
[0227] For example, an initial emitted spectrum may be determined
(i.e. via compressive-sensing retrieval) after subtracting the
low-resolution spectral components corresponding to a first
low-resolution spectrum (which may contain the aforementioned
distortions caused by spectral leakage). The initial emitted
spectrum may include an initial plurality of negative components.
Such negative components may represent compensation by the
compressive sensing process for the spectral leakage components. A
negative component threshold may be defined to determine that the
initial emitted spectrum may be suitable for reconstruction while
subtracting fewer low-resolution spectral components.
[0228] For example, the negative component threshold may be defined
based on a ratio of the minimum (or maximally negative)
reconstructed signal component in the initial emitted spectrum to
the standard deviation of the initial emitted spectrum. If ratio of
the minimum (or maximally negative) reconstructed signal component
in the initial emitted spectrum to the standard deviation of the
initial emitted spectrum is greater than the negative component
threshold, it can be determined that fewer low-resolution spectral
components should be subtracted, and a subsequent emitted spectrum
may be reconstructed with fewer low-resolution spectral components
subtracted. This process may be repeated iteratively until the
negative component threshold is satisfied.
[0229] In another example, the local maxima of the spectral leakage
components (e.g. sinc function) may overlap with Raman components
in an initial reconstructed emitted spectrum. This may occur
because strong Raman components can cause the spectral leakage
components. The local maxima of the spectral leakage components can
be identified (e.g. using a "findpeaks" routine in MATLAB). A peak
overlap threshold can be defined to identify reconstructed emitted
spectra with multiple local maxima in the low-resolution spectrum
that overlap with the highest intensity emitted components in the
reconstructed emitted spectrum. Such reconstructed emitted spectra
can be flagged for reconstruction with fewer low-resolution
spectral components subtracted.
[0230] At 330, low-resolution spectral components can be identified
from the low resolution spectrum determined at 320. For example,
the entire low-resolution spectrum may be used to define the
plurality of low-resolution spectral components.
[0231] As mentioned, the input light signal may be contaminated
with signals such as fluorescence, Planck emissions and other
background signals. Such signals may tend to be slowly-varying.
Accordingly, such signal components may be identifiable by the
low-resolution spectrum.
[0232] In contrast, emitted signal components of interest such as
Raman spectral signals for example tend to have a few, separated
peaks. These spectral signal components may thus not be identified
in the low-resolution spectrum determined at 320.
[0233] At 340, a pre-processed discrete interference pattern can be
generated. The pre-processed discrete interference pattern may be
generated by removing the low-resolution spectral components
identified at 330 from the discrete interference pattern.
[0234] The low-resolution spectral components may be determined
using the discrete cosine transform at the phase shift of each
interferometer in the array. In other words, equation (2) set out
above can be used to determine low-resolution spectral components
corresponding to the self-interfering signals output from each
interferometer in the first plurality of interferometers by
substituting the determined low-resolution spectrum for
p.sup.in(.sigma.), and substituting the phase shift of each
interferometer for 2.pi.n.sub.effL.sub.i. These low-resolution
spectral components can then be subtracted from the
self-interfering signals detected from each interferometer in the
first plurality of interferometers to provide pre-processed
self-interfering signals. A pre-processed discrete interference
pattern can be determined from the pre-processed self-interfering
signals.
[0235] In some cases, the spectrum of the input signal may be
considered as a linear combination of background or low-resolution
components indicated by b and emitted signal components of
interest, such as Raman components, indicated by r (see, for
example, FIG. 4 below). For example, the spectrum of an input
signal s may be represented according to Equation (11):
s=b+r (11)
[0236] The first plurality of self-interfering signals (e.g. the
self-interfering signals output by the first plurality of
interferometers) may be considered to correspond to the cosine
transform of the data given by:
F ( i ) = .delta. .sigma. k = 1 .DELTA. .sigma. _ / .delta. .sigma.
_ s ( .sigma. ) cos ( 2 .pi. .sigma. n eff L i ) ( 12 ) = .delta.
.sigma. k = 1 .DELTA. .sigma. _ / .delta. .sigma. _ [ b ( .sigma. )
+ r ( .sigma. ) ] cos ( 2 .pi. .sigma. n eff L i ) ( 13 ) = .delta.
.sigma. k = 1 .DELTA. .sigma. _ / .delta. .sigma. _ b ( .sigma. )
cos ( 2 .pi. .sigma. n eff L i ) + ( 14 ) .delta. .sigma. k = 1
.DELTA. .sigma. _ / .delta. .sigma. _ r ( .sigma. ) cos ( 2 .pi.
.sigma. n eff L i ) ##EQU00012##
[0237] An initial low-resolution or background signal spectrum b'
can be determined from the second plurality of self-interfering
signals (e.g. the self-interfering signals output by the second
plurality of interferometers) by:
p ( .sigma. ' ) = 2 .delta. L neff N F ( i ) cos ( 2 .pi. .sigma. '
n eff L i ) ( 15 ) ##EQU00013##
where .sigma.' indicates that the resolution of b' is much lower
than that of r.
[0238] The initial low-resolution or background signal spectrum b'
may also be determined by inverting a different discrete cosine
transform matrix, .PSI.', corresponding to the phase shifts of the
interferometers in the second plurality of interferometers.
[0239] The initial low-resolution or background signal spectrum b'
may then be smoothed to provide a smoothed low-resolution spectrum
b. The smoothed low-resolution spectrum b may have a comparable
resolution to r and s, although it generated using low-resolution
sampling. The smoothed low-resolution spectrum may be referred to
as a background spectrum or slowly-varying spectrum (similarly, the
initial low-resolution spectrum may be referred to as an initial
background spectrum or an initial slowly-varying spectrum). For
example, the initial low-resolution spectrum b' may be curvefitted
to a sum of sines to provide the smoothed low-resolution spectrum
b. Alternatively, interpolation may be used to smooth the initial
low-resolution spectrum b' to provide the smoothed low-resolution
spectrum b.
[0240] The low-resolution spectral signal components F'(i) of the
spectrum b, may then be obtained by substituting b for p in
equation (2). These components may then be subtracted from the
first plurality of self-interfering signals F(i) in equation (12)
to provide a first plurality of pre-processed self-interfering
signals. The first plurality of pre-processed self-interfering
signals may then correspond primarily to the emitted signal
components of interest r (such as Raman components, Laser-induced
breakdown spectroscopy (LIBS) emissions, atomic emissions,
molecular emissions and the like). A pre-processed discrete
interference pattern may then be determined from the first
plurality of pre-processed self-interfering signals.
[0241] The pre-processed discrete interference pattern may then be
used to reconstruct the emitted light spectrum. The pre-processed
discrete interference pattern can be used to reconstruct the
emitted light spectrum as explained herein above, for example in
relation to step 240 of process 200.
[0242] In some cases, a source spectral component may be identified
in the reconstructed emitted light spectrum. The source spectral
component may correspond to the wavelength of an emitted light
signal from a light source with a known wavelength. That is, the
source spectral component may be identified at a wavelength
position near to the known wavelength of the light source.
[0243] The source spectral component may represent a portion of the
excitation laser signal. The source spectral component may be used
to identify and calibrate thermo-optical shifts of the
spectrometer. This may provide improved robustness of the
spectrometer with respect to its local environment.
[0244] In some cases, the source spectral component may be
identified at a wavelength position different from the known
wavelength of the light source. For example, the source spectral
component may be expected to be 532 nm but may be identified at 534
nm. This may indicate the presence of a thermo-optic shift in the
spectrometer.
[0245] At least one correction factor may be determined based on
the identified source spectral component and the known wavelength
of the emitted light signal. The at least one correction factor may
include a plurality of correction factors, with one correction
factor for each interferometer in the interferometer array. The
correction factor may be determined based on a thermo-optic
coefficient of the waveguide material used to implement the
interferometers in the interferometer array. The correction factor
may also be determined taking into account the actual optical path
for each interferometer.
[0246] The at least one correction factor may be used to adjust the
reconstructed emitted light spectrum. The correction factors may be
used to adjust or correct the signal acquisition properties of the
spectrometer. The adjusted signal acquisition properties may then
be used to perform the reconstruction of the emitted light
spectrum. For instance, the phase shifts associated with each
interferometer (and in turn the cosine transformation matrix) may
be adjusted based on the corresponding correction factor.
[0247] Referring now to FIG. 4, shown therein is an example graph
plotting an input light spectrum. The input light spectrum shown in
FIG. 4 was generated experimentally. The input light spectrum was
then analyzed using an instrument model of a Raman waveguide
spectrometer designed in accordance with embodiments described
herein.
[0248] As shown in FIG. 4, the spectrum of the input signal may be
decomposed into Raman signal components and background or broadband
signal components (which may correspond to a low-resolution
spectrum).
[0249] The background signal components shown in FIG. 4 were
determined using a spline fit, with Raman components identified and
removed manually. As FIG. 4 illustrates, the spectrum of an input
signal may be considered a linear combination of broadband
"background" signal components and sparse Raman signal
components.
[0250] Referring now to FIG. 5, shown therein is an example graph
plotting Raman signal components from the input light spectrum
shown in FIG. 4. The graph shown in FIG. 5 also illustrates the
determination of the Raman signal components from the Raman
spectrum shown in FIG. 4 using a compressive sensing process.
[0251] The compressive sensing process used in the instrument model
to determine the reconstructed Raman signal components in FIG. 5
had an undersampling rate of 5.2.times. (undersampling coefficient
of 1/5.2), meaning that 5.2.times. fewer samples were required to
identify the reconstructed Raman signal components than the Nyquist
criterion would require. As FIG. 5 illustrates, by removing a
low-resolution or background spectrum from the input signal, the
resulting pre-processed signal is a sparse signal that is
appropriate for reconstruction using compressive sensing.
[0252] Referring now to FIG. 6, shown therein is a graph plotting
an example reconstruction from the input signal spectrum of FIG. 4
according to the Nyquist criterion (using 1879 Mach-Zehnder
interferometers) and an example reconstruction from the input
signal spectrum of FIG. 4 using sub-Nyquist sampling (400
Mach-Zehnder interferometers) in a compressive sensing process in
accordance with an example embodiment.
[0253] In the reconstruction shown in FIG. 6, the low-resolution or
background spectrum was removed using an example embodiment of the
process 300 for pre-processing the input signal described herein.
In the instrument model used to reconstruct the input signal
spectrum in a compressive sensing process in accordance with an
example embodiment, the first plurality of interferometers included
360 interferometers while the second plurality of interferometers
included 40 interferometers. In other words, the low-resolution
spectrum (used to determine the low-resolution spectral components
to be removed) was determined based on self-interfering signals
from 40 interferometers. The plurality of self-interfering signals
used to reconstruct the emitted signal spectrum had
self-interfering signals from 360 interferometers.
[0254] As shown by FIG. 6, in embodiments described herein the
emitted light spectrum may be reconstructed using substantially
fewer interferometers (400 vs. 1879) while generating a
reconstructed spectrum with good accuracy, i.e. a low error level.
In the example reconstruction shown in FIG. 6 in accordance with
embodiments described herein, a normalized root mean square error
of 1.12% was achieved.
[0255] Referring now to FIG. 7, shown therein is another graph
plotting the example reconstructions shown in FIG. 6 as well as an
example reconstruction from the input signal without removal of the
low-resolution or background spectrum. As FIG. 7 demonstrates, if
the background or low-resolution signal components are not removed
the compressive sensing process may not provide an accurate
reconstruction of the emitted light spectrum. However, once the
background or low-resolution signal components are removed using an
embodiment of the process 300, the emitted light spectrum can be
reconstructed accurately with substantially fewer interferometers
than would be required by the Nyquist criterion.
[0256] Referring now to FIG. 8, shown therein is a graph plotting
an example reconstruction from a second input signal spectrum
according to the Nyquist criterion (using 1879 Mach-Zehnder
interferometers) and an example reconstruction from the second
input signal spectrum using sub-Nyquist sampling (400 Mach-Zehnder
interferometers) in a compressive sensing process in accordance
with an example embodiment. In the example shown in FIG. 8, the
compressive sensing process has an undersampling rate of 4.7 (or
undersampling coefficient of 1/4.7)
[0257] The second input signal spectrum includes Raman signal
components as well as a more complex or varied
low-resolution/background spectrum as compared to the input signal
spectrum of FIG. 4. Nonetheless, the reconstruction of the emitted
light spectrum using an example of an embodiment described herein
with pre-processing to remove low-resolution signal components
provides an accurate, i.e. low-error reconstruction. In the example
reconstruction shown in FIG. 8 in accordance with embodiments
described herein, a normalized root mean square error of 0.38% was
achieved.
[0258] Referring now to FIG. 9, shown therein is an example graph
plotting the reconstructions shown in FIG. 8 as well as a
conventional reconstruction using only 400 Mach-Zehnder
interferometers. As FIG. 9 illustrates, the emitted light spectrum
is not accurately reconstructed using conventional inverse DFT
techniques with sub-Nyquist sampling while the reconstruction using
an embodiment of the described compressive sensing process provides
an accurate reconstruction.
[0259] Referring now to FIG. 10, shown therein is another graph
plotting the example reconstructions shown in FIG. 8 as well as an
example reconstruction of the input signal without removal of the
low-resolution or background spectrum. As FIG. 10 demonstrates, if
the background or low-resolution signal components are not removed,
the compressive sensing process may not provide an accurate
reconstruction of the emitted light spectrum. However, once the
background or low-resolution signal components in accordance with
an embodiment of the process 300, the emitted light spectrum can be
reconstructed accurately with substantially fewer interferometers
than would be required by the Nyquist criterion.
[0260] Embodiments of the devices, systems and methods described
herein may permit reconstruction of an emitted light spectrum using
fewer samples than would be required by the Nyquist sampling
criterion. Embodiments described herein may thus provide
spectrometers using interferometer arrays with fewer
interferometers than may otherwise be required. Minimization
processes and compressive sensing techniques may be applied to
reconstruct the emitted light spectrum from an input light signal
with fewer samples where the sampled signal is a sparse signal.
[0261] Embodiments described herein may also provide pre-processing
of a sampled input light signal to provide a sparse sampled signal.
Low-resolution signal components can be identified in the input
light signal. The low-resolution signal components can be removed
to provide a sparse sampled set suitable for reconstruction using
compressive sensing.
[0262] Embodiments described herein may also provide optical
coupling of an input light signal to a plurality of waveguides. A
plurality of lenses may be used to focus the input light signal
along the waveguides using a corresponding plurality of mirrors.
The plurality of mirrors may be arrayed in the same plane as the
waveguides, but angled to reflect the input light signal along the
waveguides. Embodiments of the optical coupling may thus provide
for accurate distribution of input light signal to the waveguides,
while avoiding gaps between adjacent waveguides.
[0263] While the above description provides examples of the
embodiments, it will be appreciated that some features and/or
functions of the described embodiments are susceptible to
modification without departing from the spirit and principles of
operation of the described embodiments. Accordingly, what has been
described above has been intended to be illustrative and
non-limiting and it will be understood by persons skilled in the
art that other variants and modifications may be made without
departing from the scope of the invention as defined in the claims
appended hereto.
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