U.S. patent application number 10/723342 was filed with the patent office on 2004-11-18 for refractive-diffractive spectrometer.
Invention is credited to Granger, Edward M..
Application Number | 20040227939 10/723342 |
Document ID | / |
Family ID | 25536790 |
Filed Date | 2004-11-18 |
United States Patent
Application |
20040227939 |
Kind Code |
A1 |
Granger, Edward M. |
November 18, 2004 |
Refractive-diffractive spectrometer
Abstract
A diffraction grating and a prism with the appropriate
characteristics are employed to provide a combined dispersive
characteristic that is substantially linear over the visible
spectrum. Radiation from the grating and prism is collimated by a
lens towards a detector array. The or a telecentric stop between
the grating and prism is placed at a focal point of the lens in a
telecentric arrangement so that equal magnification is achieved at
the detector array. If the detector array is replaced by a
plurality of optical channels, a multiplexer/demultiplexer is
obtained.
Inventors: |
Granger, Edward M.;
(Rochester, NY) |
Correspondence
Address: |
PARSONS HSUE & DE RUNTZ LLP
655 MONTGOMERY STREET
SUITE 1800
SAN FRANCISCO
CA
94111
US
|
Family ID: |
25536790 |
Appl. No.: |
10/723342 |
Filed: |
November 25, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10723342 |
Nov 25, 2003 |
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09991038 |
Nov 21, 2001 |
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6661513 |
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Current U.S.
Class: |
356/326 ;
356/328 |
Current CPC
Class: |
G02B 6/29373 20130101;
G01J 3/0256 20130101; G01J 3/12 20130101; G01J 3/0205 20130101;
G01J 3/0229 20130101; G01J 3/0208 20130101; G01J 3/28 20130101;
G02B 6/29311 20130101; G01J 3/0262 20130101; G01J 2003/123
20130101 |
Class at
Publication: |
356/326 ;
356/328 |
International
Class: |
G01J 003/28 |
Claims
What is claimed is:
1. An apparatus, comprising at least a first and a second element
that disperse electromagnetic radiation according to wavelength,
said at least two elements having a combined dispersive
characteristic such that they substantially linearly disperse the
electromagnetic radiation over at least a portion of an
electromagnetic spectrum.
2. The apparatus of claim 1, said at least two elements including a
refractive element and a grating.
3. The apparatus of claim 2, wherein said at least two elements
include a prism.
4. The apparatus of claim 1, wherein said portion of the spectrum
includes wavelengths in the infrared or ultraviolet range.
5. The apparatus of claim 1, wherein said apparatus provides
substantially the same magnification of the entrance slit at the
detector array at different wavelengths in the spectrum.
6. The apparatus of claim 5, wherein said at least two elements are
arranged so that the apparatus is substantially telecentric.
7. The apparatus of claim 6, further comprising a lens, said at
least two elements including a grating placed substantially at a
focal point of the lens that focuses the electromagnetic radiation
from the grating to a detector array.
8. The apparatus of claim 6, said at least two elements comprising
a lens component, and a grating placed substantially at a focal
point of the lens that focuses the electromagnetic radiation from
the grating to a detector.
9. The apparatus of claim 8, said at least two elements comprising
a prism integral with the lens component.
10. The apparatus of claim 6, further comprising a lens and an
aperture stop, said at least two elements comprising a grating,
said aperture stop being located in an optical path between the
grating and the lens, said aperture stop placed substantially at a
focal point of the lens that focuses the electromagnetic radiation
from the aperture stop to a detector.
11. The apparatus of claim 6, further comprising an aperture stop,
said at least two elements comprising a grating and a lens
component, said aperture stop being located in an optical path
between the grating and the lens, said aperture stop placed
substantially at a focal point of the lens that focuses the
electromagnetic radiation from the aperture stop to a detector.
12. The apparatus of claim 1, further comprising a lens, said at
least two elements including a prism and a grating, wherein the
prism, lens and grating are separate components.
13. The apparatus of claim 1, further comprising a lens, said at
least two elements including a prism and a grating, wherein any two
or more of the prism, lens and grating are combined to form a
unitary single optical component.
14. The apparatus of claim 13, wherein the prism, lens and grating
are combined to form a unitary single optical component.
15. The apparatus of claim 1, said at least two elements including
a prism, a grating and a lens component integral with the
prism.
16. The apparatus of claim 1, said at least two elements including
a transmissive or reflective grating.
17. The apparatus of claim 1, further comprising an array of
detectors, each detector sensitive for detecting a range of
wavelengths of electromagnetic radiation in the spectrum from the
at least two elements, and a filter corresponding to each detector
in the array, such filter filtering out at least some of the
wavelengths of electromagnetic radiation that are not within the
range of wavelengths of electromagnetic radiation of the
corresponding detector.
18. The apparatus of claim 1, further comprising an array of
detectors, wherein the electromagnetic radiation at different
wavelengths arrive at the array in substantially parallel rays.
19. The apparatus of claim 18, said array of detectors being
substantially in a plane, wherein the rays of the electromagnetic
radiation at different wavelengths arrive at the array in
directions that are substantially normal to the plane.
20. The apparatus of claim 19, wherein directions of the rays of
the electromagnetic radiation at different wavelengths arriving at
the array are at small angles to a normal direction to the plane to
avoid back reflection.
21. The apparatus of claim 1, said at least two elements comprising
a prism having a surface receiving the electromagnetic radiation
from a collimating lens, said surface being aspheric to compensate
for geometric aberration introduced by the collimating lens.
22. An optical apparatus, comprising: at least a first and a second
element that disperse electromagnetic radiation according to
wavelength, said at least two elements having a combined dispersive
characteristic such that they substantially linearly disperse the
electromagnetic radiation over at least a portion of an
electromagnetic spectrum; and input/output optical channels
conveying electromagnetic radiation signals to or from the at least
two elements, said at least two elements multiplexing or
demultiplexing the electromagnetic radiation signals.
23. The apparatus of claim 22, said at least two elements including
a refractive element and a grating.
24. The apparatus of claim 23, wherein said at least two elements
include a prism.
25. The apparatus of claim 22, wherein said portion of the spectrum
includes wavelengths in the infrared or ultraviolet range.
26. The apparatus of claim 22, wherein said apparatus provides
substantially the same relative magnification of an entrance slit
and an image thereof at the channels at different wavelengths in
the spectrum.
27. The apparatus of claim 26, wherein said at least two elements
are arranged so that the apparatus is substantially
telecentric.
28. The apparatus of claim 27, further comprising a lens, said at
least two elements including a grating placed substantially at a
focal point of the lens that focuses the electromagnetic radiation
from the grating to channels, or from the channels to the
grating.
29. The apparatus of claim 27, said at least two elements
comprising a lens component, and a grating placed substantially at
a focal point of the lens that focuses the electromagnetic
radiation from the grating to the channels, or from the channels to
the grating.
30. The apparatus of claim 29, said at least two elements
comprising a prism integral with the lens component.
31. The apparatus of claim 27, further comprising a lens and an
aperture stop, said at least two elements comprising a grating,
said aperture stop being located in an optical path between the
grating and the lens, said aperture stop placed substantially at a
focal point of the lens that focuses the electromagnetic radiation
from the aperture stop to the channels, or from the channels to the
stop.
32. The apparatus of claim 27, further comprising an aperture stop,
said at least two elements comprising a grating and a lens
component, said aperture stop being located in an optical path
between the grating and the lens, said aperture stop placed
substantially at a focal point of the lens that focuses the
electromagnetic radiation from the aperture stop to the channels,
or from the channels to the stop.
33. The apparatus of claim 22, further comprising a lens, said at
least two elements including a prism and a grating, wherein the
prism, lens and grating are separate components.
34. The apparatus of claim 22, further comprising a lens, said at
least two elements including a prism and a grating, wherein any two
or more of the prism, lens and grating are combined to form a
unitary single optical component.
35. The apparatus of claim 34, wherein the prism, lens and grating
are combined to form a unitary single optical component.
36. The apparatus of claim 22, said at least two elements including
a prism, a grating and a lens component integral with the
prism.
37. The apparatus of claim 22, said at least two elements including
a transmissive or reflective grating.
38. The apparatus of claim 22, each channel carrying a wavelength
component within a range of wavelengths of electromagnetic
radiation in the spectrum from the at least two elements, and a
filter corresponding to each channel, such filter filtering out at
least some of the wavelengths of electromagnetic radiation that are
not within the range of wavelengths of electromagnetic radiation of
the corresponding channel.
39. The apparatus of claim 22, wherein the electromagnetic
radiation at different wavelengths arrive at the channels in
substantially parallel rays.
40. The apparatus of claim 39, said channels have ends
substantially in a plane, wherein the rays of the electromagnetic
radiation at different wavelengths arrive at or emerge from the
array in directions that are substantially normal to the plane.
41. The apparatus of claim 40, wherein directions of the rays of
the electromagnetic radiation at different wavelengths arriving at
the array are at small angles to a normal direction to the plane to
avoid back reflection.
42. The apparatus of claim 41, said at least two elements
comprising a prism having a surface receiving the electromagnetic
radiation from a collimating lens, said surface being aspheric to
compensate for geometric aberration introduced by the collimating
lens.
43. An apparatus, comprising at least a first and a second element
that disperse electromagnetic radiation according to wavelength,
said at least two elements having a combined dispersive
characteristic such that they disperse the electromagnetic
radiation over at least a portion of an electromagnetic spectrum
more evenly than by only one of the two elements.
44. A method for measuring a radiation source, comprising: passing
radiation from the source to at least a first and a second element
that disperse electromagnetic radiation according to wavelength,
said at least two elements having a combined dispersive
characteristic such that they substantially linearly disperse the
electromagnetic radiation over at least a portion of an
electromagnetic spectrum; and measuring wavelength components of
the radiation that is dispersed by the elements.
45. A optical method for multiplexing or demultiplexing
electromagnetic radiation signals, comprising: providing at least a
first and a second element that disperse electromagnetic radiation
according to wavelength, said at least two elements having a
combined dispersive characteristic such that they substantially
linearly disperse the electromagnetic radiation over at least a
portion of an electromagnetic spectrum; and conveying
electromagnetic radiation signals to or from the at least two
elements, said at least two elements multiplexing or demultiplexing
the electromagnetic radiation signals.
Description
BACKGROUND OF THE INVENTION
[0001] This invention relates in general to spectrometers and, in
particular, a refractive-diffractive spectrometer.
[0002] Spectrometers or spectrophotometers are widely used devices.
They are used in digital printers and printing presses. Hand-held
spectrometers are used by graphic designers and imaging departments
at newspapers, magazines, and copy shops.
[0003] In order to analyze the spectro data from images or objects,
light from the images or objects is passed through optical elements
to a detector, such as a charged coupled device ("CCD") array. In
order to accurately measure the CIE tristimulus values of light
sources, images or objects, it would be desirable to accurately
resolve all of the wavelength components in the radiation from the
light source. Spectrometers resolve such wavelength components by
dispersing them at different angles depending on the wavelength.
Unfortunately, up to the present time, spectrometers and
spectrophotometers do not disperse the different wavelengths
linearly. This means that after being dispersed by the spectrometer
into the different wavelength components reaching the CCD array,
the dispersion of a particular wavelength component is not
proportional to the wavelength of the component. For example, if a
prism is used in the spectrometer for dispersing the wavelength
components of radiation from a source, the angle of refraction of
any wavelength component is not proportional to its wavelength.
[0004] Radiation from many light sources can have a large number of
spectral lines or wavelength components. Therefore, unless the CCD
array has the same number of detectors as the number of wavelength
components, at least some of the spectral lines or wavelength
components of the light source will be directed to positions along
the CCD array that does not fall entirely on any particular
detector, but may fall partly on one detector and partly on another
detector. Since the dispersion of the wavelength components is
nonlinear, it cannot be assumed that a linear interpolation of the
outputs of the two detectors will yield an accurate measurement of
the intensities of such wavelength components. This causes error in
measurement. Therefore, to accurately measure the CIE tristimulus
values of light sources of filters that have fine spectral detail,
spectrometers of the conventional design require higher spectral
resolution. However, high quality spectrometers are expensive.
[0005] It is therefore desirable to provide improved spectrometers
and spectrophotometers in which the above-described disadvantages
are avoided.
SUMMARY OF THE INVENTION
[0006] This invention is based on the recognition that, by
employing two optical elements having a combined dispersive
characteristic such that they substantially linearly disperse
electromagnetic radiation over at least a portion of an
electromagnetic spectrum, the above-described disadvantages of
conventional spectrometers and spectrophotometers can be avoided.
In the preferred embodiment, a refractive element such as a prism
and a diffraction grating may be employed. Preferably, the two
optical elements are arranged so that the spectrometer is
substantially telecentric; in such event, the spectrometer provides
substantially the same magnification at different wavelengths in
the spectrum. In other words, radiation energy will be dispersed
also linearly across the portion of the electromagnetic
spectrum.
[0007] Where the combined dispersive characteristic of the two
elements is substantially linear, linear interpolation of the type
described above would not introduce significant interpolation
errors, in contrast to the conventional design of spectrometers.
Therefore, even if high resolution CCD arrays are not used,
radiation sources, images and objects having a rich spectrum can
still be accurately measured. This drastically reduces the cost of
the spectrometer.
[0008] Instead of actually detecting the different wavelength
components, the wavelength components may be directed towards
different optical channels in a demultiplexing arrangement. First,
the light or radiation source may be an input optical channel
carrying radiation of different wavelength components. After
passing such wavelength components through the two optical
elements, the wavelength components are dispersed substantially
linearly. Therefore, irrespective of the wavelengths of the
wavelength components in the input optical channel, one can be
certain that a particular output channel is carrying a
corresponding particular wavelength component. This is not possible
if the combined dispersive characteristics of the two optical
elements are not substantially linear. The above demultiplexing
arrangement is bidirectional. In other words, the separate output
channels in the above demultiplexing arrangement can instead become
input channels. The wavelength components in such separate input
channels, after passing through the two elements, will emerge as a
combined beam towards the output channel (the input channel in the
demultiplexing arrangement) in a multiplexer arrangement. Again,
since the combined dispersive characteristic of the two elements is
substantially linear, the different wavelength components will be
combined into a single beam by the two elements irrespective of the
wavelengths of the different input wavelength components.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1A is a graphical plot of the natural spectral
dispersion of a diffraction grating useful for illustrating the
invention.
[0010] FIG. 1B is a graphical plot of the natural dispersion of an
optical prism useful for illustrating the invention.
[0011] FIG. 1C is a graphical plot of the dispersion of the
combination of a diffraction grating and a prism.
[0012] FIG. 2A is a schematic view of the influx optics portion of
a spectrometer to illustrate a preferred embodiment of the
invention.
[0013] FIG. 2B is a schematic view of the spectrometer section of
the embodiment of FIG. 3A.
[0014] FIG. 3A. is a schematic view of a diffraction grating, a
prism and a lens to illustrate one combination of optical elements
in the spectrometer to illustrate the invention.
[0015] FIG. 3B is a schematic view of a combined grating-prism-lens
structure in an embodiment to illustrate still another embodiment
of the invention.
[0016] FIG. 4 is a schematic view of a filter portion of the
spectrometer to illustrate another aspect of the invention.
[0017] FIG. 5A is a schematic view illustrating the relative
positions of the entrance slit image and of the exit slit or
detector to illustrate conceptually the operation of the
invention.
[0018] FIG. 5B is a graphical plot of the intercepted area of FIG.
5A versus wavelength to illustrate the operation of the
invention.
[0019] FIG. 6 is a graphical plot of the relative signal obtained
by interpolation to illustrate an aspect of the invention.
[0020] FIG. 7 is a graphical plot of the percent metameric error
versus bandwidth to illustrate the invention.
[0021] FIG. 8 is a schematic view of a demultiplexer/multiplexer to
illustrate another aspect of the invention.
[0022] For simplicity in description, identical components are
labeled by the same numerals in this application.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0023] FIG. 1A is a graphical plot of the natural spectral
dispersion of a divergent light diffraction grating. As shown in
FIG. 1A, a diffraction grating has higher dispersion of longer
wavelength components compared to the shorter wavelength components
in the visible spectrum. Thus, as shown in FIG. 1A, wavelength
components at or near the red end of the spectrum are dispersed by
a greater amount compared to wavelength components towards the blue
end of the spectrum. FIG. 1B is a graphical plot illustrating the
natural dispersion of optical prisms. As shown in FIG. 1B, the
dispersion of prisms has the opposite characteristic compared to
gratings. Prisms disperse wavelength components at or near the blue
end of the visible spectrum by a greater amount compared to other
wavelength components. Therefore, by employing both a grating and a
prism, the combined dispersive characteristic can be made to be
uniform over the entire visible spectrum, as illustrated in FIG.
1C.
[0024] The spectrometer of this invention is based on using
refraction and a transmissive (or reflective) diffraction grating
to produce an efficient and compact spectrometer. The design goal
is a linear wavelength dispersion and constant spectral bandwidth.
The goals are achieved by using a transmission grating in
conjunction with a new form of a lens-prism. A grating, which has
high dispersion in the red region of the spectrum, is combined with
a lens-prism that has high dispersion in blue spectral region
results to produce constant spectral dispersion as shown in FIG. 1C
in the same manner just as one would do to achromatize a
multi-element lens. The slit magnification is maintained by use of
a telecentric stop in the lens-prism. The stop is placed at or near
the diffraction grating. The telecentric system maintains a
constant F/# across the spectrum and therefore constant slit
magnification. The telecentric system has the additional advantage
that the detector array is illuminated normal to the array. This
configuration minimizes cross talk between array elements.
Alternatively, while the rays 30 may remain substantially normal to
the detector array, to avoid back-reflection, it may be desirable
to slightly tilt the rays or the array so that the rays are at
small angles to the normal direction to the array.
[0025] With this brief description, the system and the design will
be explained in subgroups:
[0026] Influx Optics
[0027] The influx optics 10 comprises a field lens 12, a slit 14
and a collimator 16 as shown below in FIG. 2A. The field lens is
placed just in front of the slit (slit can also be integrated with
the lens) to collect light from the target 18 and the slit is
placed substantially at a focal point of collimating lens 16. The
function of the field lens is to image the collimating lens to the
sample area or target 18. With this configuration, all of the light
from the sample area 18 that passes through the spectrometer
entrance slit also passes through the collimating lens. This
minimizes scattered light after the slit since all light leaving
the slit will be directed toward the collimating lens.
[0028] The width of slit 14 defines the spectral resolution of the
system. The slit height is chosen to fill the height of the
elements of the detector array in the spectrometer section 20 of
FIG. 2B. For a given spectral resolution, the slit width is the
product of the focal length of the collimator and angular
resolution of the grating of FIG. 2B. Once the spectral resolution
and the target area are chosen the collimator dimensions are also
defined. In one embodiment, a large slit and a long F/10.0
collimator are used. This makes both the slit and the lens easy to
manufacture.
[0029] The collimating lens and the following stops define the
field of view of the instrument at the target plane. The entrance
slit 14 is placed substantially at a focal point of collimating
lens 16 so that the collimating lens images the entrance slit to
infinity so that the light falling on the grating is collimated
(all light rays from a point are parallel). The grating could be
illuminated with diverge light. Unfortunately, divergent light
passing through the gating produces comatic aberration. The extra
aberration would increase the bandwidth of the instrument as a
function of wavelength.
[0030] The Spectrometer
[0031] The spectrometer section 20 has four parts: a grating 22, a
telecentric stop 24, a lens-prism 26 and detector array 28, such as
a CCD array. These elements are shown in FIG. 2B. The collimated
light from the front section 10 passes through and diffracted, or
is reflected and diffracted, by the grating and is dispersed into
its spectral components as shown in FIG. 2B. These rays are further
dispersed by the first surface of the lens-prism element. In one
embodiment, the grating is ruled at 600 lines/mm. The grating
frequency and the prism angle are part of the design optimization.
The lens-prism comprises a prism portion 26a and a lens portion
26b. The last variable in the optimization is the choice of which
wavelength will strike normal to the second face 26' of the prism
portion. It is this ray (the center ray 30' in FIG. 2). that is the
optical axis of lens portion 26b that makes up the second face of
the lens-prism. The grating frequency, prism angle and wavelength
of the chief ray (optical axis) are chosen to produce a system with
linear spectral dispersion. Any one of the commonly used optical
component design programs may be used to provide a precise optical
design for a system with linear spectral dispersion given the above
inputs (grating frequency etc.) so that it is not necessary to
describe the process in detail.
[0032] In one embodiment, the grating frequency is targeted to be
in the range of 500 to 600 lines/mm. The frequency is kept low to
minimize polarization efficiency differences. At higher frequencies
polarization scramblers would be required to compensate for these
polarization differences. The grating is blazed for the first
order. The blaze angle is determined by the spectral sensitivity of
the system. The wavelength of the maximum efficiency is placed
where the system has the least sensitivity. In general the optimum
solution is to have the same signal strength from each portion of
the spectrum when reading a perfect white reference.
[0033] The lens-prism 26 is designed so that the first or higher
order diffracted light is collimated and transmitted by the grating
22 and focused on the detector array 28. The length of the prism is
determined by the focal length of the final lens surface of lens
portion 26b. The face 26" of the prism portion next to the grating
is approximately at the infinity focus of the Lens-Prism. As shown
in FIG. 2B, rays 30 of light leaving a point near the grating leave
the final lens in a collimated state (parallel). This is the
telecentric condition. To achieve such condition, the telecentric
stop 24 is located at or substantially at a focal point of the lens
portion 26b. If no stop 24 is employed, the grating 22 is located
at or substantially at a focal point of the lens portion 26b. This
enables substantially equal magnification of all wavelength
components in all the rays 30. Surface 26" may be aspheric as shown
in dotted line in FIG. 2B to compensate for geometric aberration
introduced by the collimating lens 16 of FIG. 2A.
[0034] The detector array 28 is positioned to be in focus at each
wavelength and substantially perpendicular to the telecentric rays
leaving the final lens surface of lens portion 26b. This position
of the array 28 minimizes cross talk between elements and assures
constant slit magnification and therefore constant spectral
bandwidth at every detector site in the array.
[0035] While in the preferred embodiment, a lens-prism 26 is
employed, it is also possible to use a separate prism and a
separate lens instead, as illustrated in FIG. 3A. In such event,
the telecentric stop 24 is placed at a focal point of lens 34.
Where no stop 24 is used, grating 22 is placed at a focal point of
lens 34. In the same manner as illustrated above in reference to
FIG. 2A, 2B, grating 22 of FIG. 3A may act as a transmissive or
reflective grating. In other words, light (preferably collimated)
from the target may pass through and diffracted by grating 22 and
proceed towards prism 32 and lens 34, or is reflected and
diffracted by the grating. In any event, the first or higher order
diffraction passes through prism 32 and lens 34 and is incident on
a detector array such as array 28 (not shown). In still another
arrangement, all three elements: the grating, the prism and the
lens may be combined into a single optical element 40 as shown in
FIG. 3B. In such event, the grating surface 40' is located
substantially at a focal point of the lens portion 40" of the
element.
[0036] FIG. 4 is a schematic view illustrating a filter placed in
front of the detector array 28 to further reduce cross-talk in the
spectrometer of this invention. As shown in FIG. 4, the rays (such
as rays 30 of FIG. 2B) that are directed towards the detector array
are first passed through corresponding filter elements 50 before
the filtered rays are then directed towards the detector array 28.
While only seven filters 50 are shown in FIG. 4, comprising blue,
blue-green, green, yellow, orange, red-orange and red filters, it
will be understood that more or fewer filters may be employed,
which is within the scope of the invention.
[0037] Explained below is the reason why the new Grating-Prism-Lens
(GPL) Spectrometer of this invention has the colorimetric accuracy
of a spectrometer with a much smaller bandwidth. A 1 mn bandwidth
conventional system is compared to a 10 nm GPL system.
[0038] The GPL spectrometer (such as system 20 of FIG. 2B) has been
designed to have two unique features. The first is that by using a
prism combined with a grating, the dispersion of the system is made
linear or substantially linear over the visual wavelength region of
400 nm to 700 nm. By using a prism combined with a grating, the
dispersion of the system can also be made linear or substantially
linear over a portion of the spectrum that includes wavelengths in
the infrared or ultraviolet range. Thus, the spacing between 10 nm
samples occurs at equal distances in the image plane. Second, the
use of the telecentric condition produces a system that has
constant magnification of the slit for all wavelengths. Therefore,
an array detector with 10 nm spacing between detectors will be just
filled with light by a line source that is at the center wavelength
of the detector.
[0039] FIG. 5A illustrates how the image of the entrance slits,
from wavelengths differing from the center wavelength of the
detector element, move across the array element. The detector
element acts as the exit slit of the system. FIG. 5A shows how much
of the light is intercepted for each of the line spectra. The
images 14' of the slit 14 of FIG. 2B on the exit slit (detector)
are shown for wavelength differences of -6 nm, -3 nm, 0.0 nm, 3 nm
and 6 nm. The amount of energy intercepted by the exit slit is
directly proportional to the difference between the center
wavelength of the exit slit position and the wavelength of the
entering light. Therefore, if the wavelength difference is zero,
all the light from the entrance slit will fall on the exit slit. As
is shown in the plot on FIG. 5B, the amount of light intercepted by
the exit slit is a linear function of the difference between
wavelengths. The amount of light intercepted by the exit slit is
zero for differences of 10 nm or greater. The amount of light
falling on a detector is a triangular function of the difference in
wavelength between the center wavelength and the wavelength of the
entering light.
[0040] The GPL is different from other spectrometer configurations.
All others have some form of uncorrected dispersion. As such, none
of them exhibit the natural interpolation abilities of the GPL
spectrometer. All other spectrometers require higher spectral
resolution to accurately measure the CIE tristimulus values of
source or filters that have fine spectral detail. The GPL
spectrometer can determine the CIE tristimulus values of line
spectra without the need to resolve the line spectra. The next
section illustrates the ability of the GPL system.
[0041] GPL CIE Tristimulus Determination
[0042] Spectrometers in use today require a resolution of 1 nm to
determine the tristimulus values of sources that have line spectra
included in a continuum spectrum. Fluorescent lamps and monitor
phosphors are good examples of problem sources that normally
require high spectral resolution. The GPL spectrometer has the
ability of obtaining accurate CIE tristimulus values without the
need to resolve the spectral lines. Since all radiation is just the
sum of an infinite number of spectral line sources, the GPL will
yield accurate tristimulus values for all light distributions. The
following discourse will illustrate the ability of the GPL system
to produce exact CIE tristimulus values for an infinitesimal width
spectral line source.
[0043] FIG. 6 shows the spectral response functions of two adjacent
detectors in an array of detectors. An arbitrary and perfect line
source is received by the GPL system that has a wavelength that is
between these detectors. The source wavelength is assumed to be
placed at a distance a times the spectral distance between the
adjacent detectors.
[0044] A perfect spectrometer with a small enough bandwidth is
assumed to resolve the source given above. One would then know the
exact center wavelength of the source and the energy of the source,
Es. The tristimulus value of the source would be computed by linear
interpolation. The known source wavelength lies between two
wavelengths where the CIE color mixing functions have been
tabulated. The tristimulus value is given by linear
interpolation:
T=M1*Es*(1-.alpha.)+M2*Es*.alpha. (1)
[0045] where M1 is the color mixing function at the lower
wavelength and M2 at the upper wavelength. The source wavelength
lays a proportionate distance .alpha. from the lower
wavelength.
[0046] FIG. 6 shows how the source is seen by the GPL spectrometer.
The original energy passing through the entrance slit falls on both
detectors. Detector 1 receives E1 amount of energy and detector 2
receives E2. The tristimulus value would be calculated as
follows:
T=W1*E1+W2*E2 (2)
[0047] From FIG. 6, one can see that the triangular band pass of
GPL devise splits the energy, Es, as follows:
E1=Es*(1-.alpha.) (3)
and
E2=Es*.alpha. (4)
[0048] Now if equations 3 and 4 are substituted for E1 and E2 in
equation 2, we obtain:
T=W1*Es*(1-.alpha.)+W2*Es*.alpha. (5)
[0049] This is the same result obtained by the spectrometer with
infinite resolution. Therefore, if the use of the spectrometer is
to determine the tristimulus values of a source, the GPL
spectrometer will give the proper result. If the purpose is to
accurately resolve the spectral components of the source, then the
broad band GPL is not the appropriate tool.
[0050] Bandwidth Considerations
[0051] The final question in the design of the GPL device is the
wavelength spacing of the samples. The choice was made to use 10 nm
spacing. This choice is a compromise between accuracy and
sensitivity. The sensitivity of the instrument increases with
increase of bandwidth. Unfortunately the metamerism error in the
computation of tristimulus values increases with spectral
bandwidth. Triangular filtering a 1 nm table of color mixing
functions to a 3, 10 and 20 nm bandwidth simulated the optical
actions of each spectrometer. The metameric error is calculated by
subtracting the linear interpolated data from the true 1 nm color
mixing functions. FIG. 7 displays the increase of standard
deviation of metameric error as a function of spectral bandwidth. A
spectral resolution of 10 nm is chosen as optimum compromise
between sensitivity and metameric error. Note that the error
difference between a 3 nm and a 10 nm bandwidth is small as
compared with an instrument with a 20 nm bandwidth.
[0052] The GPL spectrometer has been designed to have linear
dispersion and constant slit magnification over the spectral region
of 400 to 700 nm. As a result the instrument can measure the CIE
Tristimulus values of sources that contain very spiky spectral
components. An analysis is made of the metameric error in the
weighting functions as a result of using the triangular spectral
band pass as an interpolator. It is found that 10 nm was the upper
limit of the allowed spectral band pass to limit metameric error to
a value of 0.001639 RMS of the true value of the color mixing
functions. This value is only slightly larger that a system with a
3 nm bandwidth.
[0053] Multiplexer/Demultiplexer
[0054] The above-described diffraction grating and prism may also
be used in optical multiplexers and demultiplexers as illustrated
in FIG. 8. Thus, in reference to FIGS. 2A and 2B, if the radiation
or light collected by field lens 12 originates from an optical
channel such as an optical fiber, such radiation is collected by
lens 12 in the same manner as that described above. Radiation from
collimator 16 then undergoes diffraction and other optical
operations in FIG. 2B, except that instead of being detected by a
detector array 28, each of the rays 30 is collected by a
corresponding output optical channel. In other words, the different
wavelength components from an input optical channel is dispersed
into its different wavelength components where each wavelength
component is then collected by a corresponding output optical
channel, thereby functioning as an optical demultiplexer.
[0055] Thus, as shown in FIG. 8, each of the three arrows 102 is an
input optical channel. For each input optical channel 102, there is
a corresponding optical system comprising lens 12, slit 14,
collimator 16, grating 22, stop 24, lens-prism 26 and the separated
wavelength components are collected by a plurality of three output
optical channels. While only three output optical channels 104 are
shown collecting the wavelength components originating from each
input optical channel 102, fewer or more output optical channels
may be employed and is within the scope of the invention. Thus,
output optical channels 104' are used to collect rays 30 that
originate from input optical channel 102', and direct these optical
signals to corresponding receivers (not shown). The same advantages
of linear dispersion and equal magnification can advantageously be
used in the demultiplexer 100. Since the dispersion is linear, it
would be easy to identify the spacing and location of the output
optical channels 104, if the expected wavelengths of the input
radiation is known. It would then be much simpler to design the
demultiplexer 100. Since system 100 provides substantially the same
magnification for all wavelength components, there would be little
or no distortion or unequal reduction of intensity of the
wavelength components between the different wavelength components
in the different output channels.
[0056] As shown in FIG. 8, where the input and output optical
channels are optical fibers, a GRIN lens (not shown) may be used as
an optical interface for each of the optical channels in FIG.
8.
[0057] The passage of radiation in system 100 is bidirectional.
This means that system 100 may also function as a multiplexer by
converting each of the input optical channels 102 into output
optical channels and the output optical channels 104 into input
optical channels. In such event, the different wavelength
components carried by the input optical channels 104' would then be
combined and directed towards the output optical channel 102' in
such multiplexer. Again, if the optical channels are optical
fibers, GRIN lenses may be employed as optical interfaces.
[0058] While the invention has been described above by reference to
various embodiments, it will be understood that changes and
modifications may be made without departing from the scope of the
invention, which is to be defined only by the appended claims and
their equivalent. For example, while it is preferred to employ a
refractive element and a grating so that their combined dispersion
is substantially linear, it may be adequate for some applications
where the combined dispersion over at least a portion of an
electromagnetic spectrum is not linear, but nevertheless more even
than by only one of the two elements. All references referred to
herein are incorporated by reference in their entireties.
* * * * *