U.S. patent application number 10/765368 was filed with the patent office on 2004-12-23 for apparatus and method for joint measurements of conjugated quadratures of fields of reflected/scattered and transmitted beams by an object in interferometry.
This patent application is currently assigned to Zetetic Institute. Invention is credited to Hill, Henry Allen.
Application Number | 20040257577 10/765368 |
Document ID | / |
Family ID | 32829806 |
Filed Date | 2004-12-23 |
United States Patent
Application |
20040257577 |
Kind Code |
A1 |
Hill, Henry Allen |
December 23, 2004 |
Apparatus and method for joint measurements of conjugated
quadratures of fields of reflected/scattered and transmitted beams
by an object in interferometry
Abstract
An interferometery system for making interferometric
measurements of an object, the system including: a beam generation
module which during operation delivers an output beam that includes
a first beam at a first frequency and a second beam at a second
frequency that is different from the first frequency, the first and
second beams within the output beam being coextensive, the beam
generation module including a beam conditioner which during
operation introduces a sequence of different shifts in a selected
parameter of each of the first and second beams, the selected
parameter selected from a group consisting of phase and frequency;
a detector assembly having a detector element; and an
interferometer constructed to receive the output beam at least a
part of which represents a first measurement beam at the first
frequency and a second measurement beam at the second frequency,
the interferometer further constructed to image both the first and
second measurement beams onto a selected spot on the object to
produce therefrom corresponding first and second return measurement
beams, and to then simultaneously image the first and second return
measurement beams onto said detector element.
Inventors: |
Hill, Henry Allen; (Tucson,
AZ) |
Correspondence
Address: |
Henry Allen Hill
340 S. Avenida de Palmas
Tucson
AZ
85716
US
|
Assignee: |
Zetetic Institute
Tucson
AZ
|
Family ID: |
32829806 |
Appl. No.: |
10/765368 |
Filed: |
January 27, 2004 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60442858 |
Jan 27, 2003 |
|
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60442892 |
Jan 28, 2003 |
|
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Current U.S.
Class: |
356/450 |
Current CPC
Class: |
G01B 9/04 20130101; G01B
9/02007 20130101; G02B 27/108 20130101; G01B 9/02002 20130101; G02B
27/143 20130101; G02B 27/144 20130101; G01B 9/0201 20130101; G01B
9/02079 20130101; G02B 21/14 20130101; G02B 21/0056 20130101; A45D
8/006 20210101; G01B 9/02042 20130101; G02B 27/126 20130101; G02B
27/017 20130101; G01B 9/02022 20130101; G01B 9/02014 20130101; G02B
27/145 20130101; G01B 2290/70 20130101 |
Class at
Publication: |
356/450 |
International
Class: |
G01B 009/02 |
Claims
What is claimed is:
1. An interferometery system for making interferometric
measurements of an object, said system comprising: a beam
generation module which during operation delivers an output beam
that includes a first beam at a first frequency and a second beam
at a second frequency that is different from said first frequency,
said first and second beams within the output beam being
coextensive, said beam generation module including a beam
conditioner which during operation introduces a sequence of
different shifts in a selected parameter of each of the first and
second beams, said selected parameter selected from a group
consisting of phase and frequency; a detector assembly having a
detector element; and an interferometer constructed to receive the
output beam at least a part of which represents a first measurement
beam at the first frequency and a second measurement beam at the
second frequency, said interferometer further constructed to image
both the first and second measurement beams onto a selected spot on
the object to produce therefrom corresponding first and second
return measurement beams, and to then simultaneously image the
first and second return measurement beams onto said detector
element.
2. The interferometer system of claim 1 wherein the beam generation
module further comprises a beam source which during operation
generates a single input beam at a predetermined frequency, and
wherein the beam conditioner comprises an optical element that
derives the first and second beams from the single input beam.
3. The interferometer system of claim 2 wherein said optical
element is an acousto-optic modulator.
4. The interferometer system of claim 1 wherein each of said first
and second beams includes a first component and a second component
that is orthogonal to the first component, and wherein the beam
conditioner is constructed to introduce a first sequence of
different discrete phase shifts into a relative phase difference
between the first and second components of the first beam and
concurrently therewith a second sequence of different discrete
phase shifts into the relative phase difference between the first
and second components of the second beam.
5. The interferometer system of claim 4 wherein the beam
conditioner includes a first phase shifter for introducing the
first sequence of different discrete phase shifts into the relative
phase difference between the first and second components of the
first beam and a second phase shifter for introducing the second
sequence of different discrete phase shifts into the relative phase
difference between the first and second components of the second
beam.
6. The interferometer system of claim 4 wherein the interferometer
is characterized by a measurement beam optical path length and a
reference beam optical path length and wherein the difference
between those two optical path lengths is nominally zero.
7. The interferometer system of claim 4 wherein the interferometer
is constructed to generate the first measurement beam from the
first component of the first beam and the second measurement beam
from the first component of the second beam.
8. The interferometer system of claim 7 wherein the interferometer
is further constructed to generate a first reference beam from the
second component of the first beam and a second reference beam from
the second component of the second beam.
9. The interferometer system of claim 8 wherein the first phase
shifter introduces the first sequence of different discrete phase
shifts into the second component of the first beam and the second
phase shifter introduces the second sequence of different discrete
phase shifts into the second component of the second beam.
10. The interferometer system of claim 1 wherein the beam
conditioner is constructed to introduce a first sequence of
different frequency shifts into the frequency of the first beam and
concurrently therewith a second sequence of different frequency
shifts into the frequency of the second beam.
11. The interferometer system of claim 10 wherein the beam
conditioner includes a first set of acousto-optic modulators for
introducing the first sequence of different frequency shifts into
the frequency of the first beam and a second set of acousto-optic
modulators for introducing the second sequence of different
frequency shifts into the frequency of the second beam.
12. The interferometer system of claim 10 wherein the
interferometer is characterized by a measurement beam optical path
length and a reference beam optical path length and wherein the
difference between those two optical path lengths is nominally a
non-zero value.
13. The interferometer system of claim 1 further comprising a
controller which controls the beam conditioner and causes said beam
conditioner to introduce the first and second sequences of
different shifts in the selected parameter of each of the first and
second beams.
14. The interferometer system of claim 13 wherein the controller is
programmed to acquire from the detector assembly measured values
for a set of interference signals resulting from introducing the
first and second sequences of different shifts in the selected
parameters of each of the first and second beams and further
programmed to compute first and second components of conjugated
quadratures of the fields of beams from said selected spot.
15. The interferometer system of claim 11 wherein said detector
element is characterized by a frequency bandwidth and wherein the
first and second frequencies are separated by an amount that is
larger than the frequency bandwidth of the detector.
16. The interferometer system of claim 1 wherein the interferometer
is a scanning interferometric far-field confocal microsope.
17. The interferometer system of claim 1 wherein the interferometer
is a scanning interferometric far-field non-confocal microsope.
18. The interferometer system of claim 1 wherein the interferometer
is a scanning interferometric near-field confocal microsope.
19. The interferometer system of claim 1 wherein the interferometer
is a scanning interferometric near-field non-confocal
microsope.
20. The interferometer system of claim 1 wherein the interferometer
is a linear displacement interferometer.
21. An interferometery system for making interferometric
measurements of an object, said system comprising: a beam
generation module which during operation delivers an output beam
that includes a first beam at a first frequency and a second beam
at a second frequency that is different from said first frequency,
said first and second beams within the output beam being
coextensive; a detector assembly having a detector element that is
characterized by a frequency bandwidth, wherein the first and
second frequencies are separated by an amount that is larger than
the frequency bandwidth of the detector; and an interferometer
constructed to receive the output beam, at least a part of which
represents within the interferometer a first measurement beam at
the first frequency and a second measurement beam at the second
frequency, said interferometer further constructed to
simultaneously image both the first and second measurement beams
onto a selected spot on or in the object to produce therefrom
corresponding first and second return measurement beams, and then
to simultaneously image the first and second return measurement
beams onto said detector element.
22. The interferometer system of claim 21 wherein said first beam
includes a first component and a second component that is
orthogonal to the first component and said second beam also
includes a first component and a second component that is
orthogonal to the first component, and wherein the beam conditioner
is constructed to introduce a first sequence of different discrete
phase shifts into a relative phase difference between the first and
second components of the first beam and concurrently therewith a
second sequence of different discrete phase shifts into the
relative phase difference between the first and second components
of the second beam.
23. The interferometer system of claim 22 wherein the beam
conditioner includes a first phase shifter for introducing the
first sequence of different discrete phase shifts into the relative
phase difference between the first and second components of the
first beam and a second phase shifter for introducing the second
sequence of different discrete phase shifts into the relative phase
difference between the first and second components of the second
beam.
24. The interferometer system of claim 21 wherein the beam
conditioner is constructed to introduce a first sequence of
different frequency shifts into the frequency of the first beam and
concurrently therewith a second sequence of different frequency
shifts into the frequency of the second beam.
25. A source beam assembly comprising a beam generation module
which during operation delivers an output beam that includes a
first beam at a first frequency and a second beam at a second
frequency that is different from said first frequency, said first
and second beams within the output beam being coextensive, said
beam generation module including a beam conditioner which during
operation introduces a sequence of different shifts in a selected
parameter of each of the first and second beams, said selected
parameter selected from a group consisting of phase and
frequency.
26. The source beam assembly of claim 25 wherein said first beam
includes a first component and a second component that is
orthogonal to the first component and said second beam also
includes a first component and a second component that is
orthogonal to the first component, and wherein the beam conditioner
is constructed to introduce a first sequence of different discrete
phase shifts into a relative phase difference between the first and
second components of the first beam and concurrently therewith a
second sequence of different discrete phase shifts into the
relative phase difference between the first and second components
of the second beam.
27. The source beam assembly of claim 26 wherein the beam
conditioner includes a first phase shifter for introducing the
first sequence of different discrete phase shifts into the relative
phase difference between the first and second components of the
first beam and a second phase shifter for introducing the second
sequence of different discrete phase shifts into the relative phase
difference between the first and second components of the second
beam.
28. The source beam assembly of claim 25 wherein the beam
conditioner is constructed to introduce a first sequence of
different frequency shifts into the frequency of the first beam and
concurrently therewith a second sequence of different frequency
shifts into the frequency of the second beam.
29. A method of performing measurements of an object using an
interferometer, said method comprising: generating an input beam
for the interferometer, said input beam including a first beam at a
first frequency and a second beam at a second frequency that is
different from the first frequency, said first and second beams
being coextensive and sharing the same temporal window; and by
using the interferometer and the input beam supplied to the
interferometer, jointly measuring two orthogonal components of
conjugated quadratures of fields of reflected, scattered, or
transmitted beams from a selected spot in and/or on the object.
30. The method of claim 29, wherein the jointly measuring
comprises: deriving a first measurement beam from the first beam;
deriving a second measurement beam from the second beam, wherein
the first and second measurement beams are coextensive within the
interferometer; and imaging both the first and second measurement
beams on said selected spot.
31. The method of claim 30, wherein imaging both the first and
second measurement beams on said selected spot generates a first
return measurement beam at the first frequency and a second return
measurement beam at the second frequency and wherein the jointly
measuring further comprises producing a combined interference
signal by interfering the first return measurement beam with a
first reference beam that is at the first frequency and by
interfering the second return measurement beam with a second
reference beam that is at the second frequency.
32. The method of claim 29, wherein the jointly measuring further
comprises, for each of a plurality of successive time intervals,
introducing a corresponding different shift in a selected parameter
of the first beam and introducing a different corresponding shift
in the selected parameter of the second beam, said selected
parameters are selected from a group consisting of phase and
frequency.
33. The method of claim 32, wherein the jointly measuring further
comprises: for each of the plurality of successive time intervals,
measuring a value of the combined interference signal; and from the
measured values of the combined interference signal for the
plurality of successive time internals, computing the two
orthogonal components of conjugated quadratures.
34. The method of claim 32, wherein each of said first and second
beams includes a first component and a second component that is
orthogonal to the first component, wherein the selected parameter
of the first beam is the phase of the second component, and wherein
the selected parameter of the second beam is the phase of the
second component.
35. The method of claim 32, wherein the selected parameter of the
first beam is the frequency of the first beam, and wherein the
selected parameter of the second beam is the frequency of the
second beam.
36. A method of performing measurements of an object using an
interferometer, said method comprising: generating a source beam
for the interferometer, said source beam including a first input
beam at a first frequency and a second input beam at a second
frequency that is different from the first frequency, said first
and second input beams being coextensive and sharing the same
temporal window function; by using the source beam supplied to the
interferometer, making a sequence of measurements of an
interference signal for a selected spot on or in the object,
wherein the making of the sequence of measurements involves, for
each measurement of the sequence of measurements, introducing a
corresponding different shift in a selected parameter of the first
input beam and a corresponding different shift in the selected
parameter of the second input beam, wherein selected parameter is
selected from the group consisting of phase and frequency, and
wherein each of said sequence of measurements simultaneously
captures information for both conjugated quadratures of fields of
reflected, scattered, or transmitted beams from the selected
spot.
37. A method of claim 36 wherein the making of the sequence of
measurements comprises: deriving a first measurement beam from the
first input beam; deriving a second measurement beam from the
second input beam; imaging the first and second measurement beams
on a selected spot on or in the object to produce corresponding
first and second return measurement beams; interfering the first
and second return measurement beams with respective first and
second reference beams to produce a combined interference signal;
and making a sequence of measurements of the combined interference
signal.
38. A method of generating an source beam, said method comprising:
generating an output beam that includes a first beam at a first
frequency and a second beam at a second frequency that is different
from said first frequency, said first and second beams within the
output beam being coextensive; and introducing a sequence of
different shifts in a selected parameter of each of the first and
second beams, said selected parameter selected from a group
consisting of phase and frequency.
39. A method of performing measurements of an object using a
scanning confocal interferometer in which there is an array of
pinholes, said method comprising: generating an input beam for the
scanning interferometer, said input beam including a first beam at
a first frequency and a second beam at a second frequency that is
different from the first frequency, said first and second beams
being coextensive and sharing the same temporal window function;
causing an image of the array of pinholes to scan across the object
so that each pinhole of a conjugate set of pinholes among the array
of pinholes becomes conjugate to a selected spot on or in the
object at successive times during the scan; for each pinhole of the
conjugate set of pinholes, measuring an interference signal value
for a selected spot on or in the object, wherein the measured
interference signal value for each pinhole of the conjugate set of
pinholes simultaneously captures information for two orthogonal
components of conjugated quadratures of fields of reflected,
scattered, or transmitted beams from the selected spot.
40. The method of claim 39 further comprising, from the measured
interference signal values for all of the conjugate set of
pinholes, computing each of the two orthogonal components of the
conjugated quadratures of fields.
41. The method of claim 39 wherein generating the input beam
further comprises, for each of a plurality of successive time
intervals, introducing a corresponding different shift in a
selected parameter of the first beam and introducing a different
corresponding shift in the selected parameter of the second beam,
said selected parameters are selected from a group consisting of
phase and frequency, and wherein each of said sequence of time
intervals corresponds to a time at which a different corresponding
one of said conjugate set of pinholes is conjugate with said
spot.
42. The method of claim 41, wherein each of said first and second
beams includes a first component and a second component that is
orthogonal to the first component, wherein the selected parameter
of the first beam is the phase of the second component, and wherein
the selected parameter of the second beam is the phase of the
second component.
43. The method of claim 41, wherein the selected parameter of the
first beam is the frequency of the first beam, and wherein the
selected parameter of the second beam is the frequency of the
second beam.
44. A method of performing measurements of an object using a
scanning confocal interferometer in which there is an array of
pinholes, said method comprising: generating an input beam for the
scanning interferometer, said input beam including a first beam at
a first frequency and a second beam at a second frequency that is
different from the first frequency, said first and second beams
being coextensive and sharing the same temporal window function;
causing an image of the array of pinholes to scan across the object
so that each detector element of a conjugate set of detector
elements among an array of detector elements becomes conjugate to a
selected spot on or in the object at successive times during the
scan; for each detector of the conjugate set of detectors,
measuring an interference signal value for a selected spot on or in
the object, wherein the measured interference signal value for each
detector of the conjugate set of detectors simultaneously captures
information for two orthogonal components of conjugated quadratures
of fields of reflected, scattered, or transmitted beams from the
selected spot.
45. The method of claim 44 further comprising, from the measured
interference signal values for all of the conjugate set of
detectors, computing each of the two orthogonal components of the
conjugated quadratures of fields.
46. The method of claim 44 wherein generating the input beam
further comprises, for each of a plurality of successive time
intervals, introducing a corresponding different shift in a
selected parameter of the first beam and introducing a different
corresponding shift in the selected parameter of the second beam,
said selected parameters are selected from a group consisting of
phase and frequency, and wherein each of said sequence of time
intervals corresponds to a time at which a different corresponding
one of said conjugate set of detectors is conjugate with said
spot.
47. The method of claim 46, wherein each of said first and second
beams includes a first component and a second component that is
orthogonal to the first component, wherein the selected parameter
of the first beam is the phase of the second component, and wherein
the selected parameter of the second beam is the phase of the
second component.
48. The method of claim 46, wherein the selected parameter of the
first beam is the frequency of the first beam, and wherein the
selected parameter of the second beam is the frequency of the
second beam.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/442,858, filed Jan. 27, 2003 (ZI-47); and U.S.
Provisional Application No. 60/442,892, filed Jan. 28, 2003
(ZI-45), both of which are incorporated herein by reference.
[0002] This application also incorporates by reference: U.S. patent
application Ser. No. ______ entitled "Interferometric Confocal
Microscopy Incorporating A Pinhole Array Beam-Splitter," filed on
Jan. 27, 2004 (ZI-45).
TECHNICAL FIELD
[0003] This invention relates to the measurement of conjugated
quadratures of fields of reflected, scattered and transmitted beams
by an object in interferometry.
BACKGROUND OF THE INVENTION
[0004] Over the years people have developed various sophisticated
confocal interferometric techniques. Examples of the variety of the
available technologies are the following.
[0005] There is interferometric, confocal far-field and near-field
microscopy using heterodyne techniques and a detector having a
single detector element or having a relatively small number of
detector elements.
[0006] There is also interferometric confocal far-field and
near-field microscopy using a step and stare method with a
single-homodyne detection method for acquiring conjugated
quadratures of fields of reflected and/or scattered beams when a
detector is used that includes a large number of detector elements.
The respective conjugated quadrature of a field is
.vertline..alpha..vertline.sin .phi. when the quadrature x(.phi.)
of a field is expressed as .vertline..alpha..vertline.cos .phi..
The step and stare method and single-homodyne detection method have
been used in order to obtain for each detector element a set of at
least four electrical interference signal values with a substrate
that is stationary with respect to the respective interferometric
microscope during the stare portion of the step and stare method.
The set of at least four electrical interference signal values are
required to obtain for each detector element conjugated quadratures
of fields of a measurement beam comprising a reflected and/or
scattered far-field or near-field from a spot in or on a substrate
that is conjugate to the each detector element.
[0007] There are heterodyne and single-homodyne detection methods
to obtain phase information in linear and angular displacement
interferometers.
[0008] And there is a double homodyne detection method based on use
of four detectors wherein each detector generates an electrical
interference signal value used to determine a corresponding
component of a conjugated quadratures of a field such as described
in Section IV of the article by G. M D'ariano and M G. A. Paris
entitled "Lower Bounds On Phase Sensitivity In Ideal And Feasible
Measurements," Phys. Rev. A 49, 3022-3036 (1994).). The four
detectors generate the four electrical interference signal values
simultaneously and each electrical interference signal value
contains information relevant to one conjugated quadratures
component.
[0009] High speed, high resolution imaging with high
signal-to-noise ratios is required, for example, in inspection of
masks and wafers in microlithography. Two techniques that have been
used for obtaining high resolution imaging with high
signal-to-noise ratios are interferometric far-field and near-field
confocal microscopy of the types described above. However, the
acquisition of high signal-to-noise ratios with the high resolution
imaging generally limits data rates in part by the necessity to
acquire conjugated quadratures of fields of a reflected and/or
scattered beam for each spot in and/on a substrate being imaged.
The determination of conjugated quadratures requires the
measurement of at least four electrical interference signal values
for the each spots in and/or on the substrate being imaged.
Acquisition of the at least four interference signal values for the
each spots places tight restrictions on how large a rate of scan
can be employed in generation of a one-dimensional, a
two-dimensional or three-dimensional image of the substrate having
artifacts down to of the order of 100 nm in size or smaller.
SUMMARY OF THE INVENTION
[0010] The bi-homodyne and quad-homodyne detection methods
described herein relax the tight restrictions and permit
significantly increased throughput in high resolution imaging that
has high signal-to-noise ratios for each spot being imaged. The
tight restrictions are relaxed as a consequence of a joint
measurement of conjugated quadratures of fields using a conjugate
set of four pixels for each spot being imaged wherein the temporal
window function for the measured four electrical interference
signal values used in the determination of one component of
conjugated quadratures of fields is the same as the temporal window
function for the measured four interference signal values used in
the determination of the second component of the conjugated
quadratures of the fields, i.e., the two sets of four interference
signal values are the same.
[0011] With the bi-homodyne detection method, the two temporal
window functions are made the same by using one frequency component
of an input beam for the determination of one component of the
conjugated quadratures of the fields and using a second frequency
component of the input beam for the determination of the second
component of the conjugated quadratures of the fields. The two
frequency components of the input beam are coextensive in spatial
and temporal coordinates, i.e., coextensive in space and have the
same temporal window functions in the interferometer system.
[0012] With the quad-homodyne detection method, the two temporal
window functions are made the same by using two frequency
components of an input beam for the determination of one component
of the conjugated quadratures of the fields and using two other
frequency components of the input beam for the determination of the
second component of the conjugated quadratures of the fields. The
four frequency components of the input beam are coextensive in
spatial and temporal coordinates, i.e., coextensive in space and
have the same temporal window functions in the interferometer
system.
[0013] At least some of the bi-homodyne and quad-homodyne detection
methods described herein obtain four electrical interference signal
values wherein each measured value of an electrical interference
signal contains simultaneously information about two orthogonal
components of a conjugated quadratures.
[0014] The bi-homodyne detection method uses a single detector
element for each electrical interference signal value obtained and
an input beam to an interferometer system comprising two frequency
components with a frequency difference large compared to the
frequency bandwidth of the detector for a joint measurement of the
conjugated quadratures. One frequency component is used to generate
an electrical interference signal component corresponding to a
first component of conjugated quadratures of a field of a
corresponding measurement beam comprising either a reflected and/or
scattered or transmitted far-field or near-field from a spot in or
on a measurement object that is conjugate to the detector element.
The second frequency component is used to generate a second
electrical interference signal component corresponding to a
respective second component of the conjugated quadratures of the
field. Information about the first and second components of the
conjugated quadratures are obtained jointly as a consequence of the
two frequency components being coextensive in space and having the
same temporal window function in the interferometer system. The
temporal window function when operating in a scanning mode
corresponds to the window function of a respective set of pulses of
the input beam to the interferometer system.
[0015] When operating in the scanning mode and using either the
bi-homodyne or quad-homodyne detection methods described herein,
conjugate sets of detector elements are defined and used. A
conjugate set of detector elements comprises the pixels of the
detector conjugate to the spot on or in the substrate at the times
that the measurements are made of a corresponding set of the four
electrical interference signal values.
[0016] For each of the two frequency components of the input beam
used in the bi-homodyne detection method, reference and measurement
beams are generated. In certain of the embodiments that use the
bi-homodyne detection method, different phase shift combinations
are introduced between the respective reference and measurement
beam components by shifting the frequencies of one or both of the
two frequency components for acquiring a set of four electrical
interference signal values for each spot in or on the measurement
object that is imaged. In certain other of the embodiments that use
the bi-homodyne detection method, different phase shift
combinations are introduced between the respective reference and
measurement beam components by a phase-shifter for each of the two
frequency components for acquiring a set of the four electrical
interference signal values for each spot in and/or on a measurement
object or substrate that is imaged. In the certain of the
embodiments, the difference in optical path of the reference and
measurement beams is a non-zero value.
[0017] The quad-homodyne detection method uses two detectors and an
input beam to an interferometer system comprising four coextensive
measurement beams and corresponding reference beams in the
interferometer system simultaneously to obtain four electrical
signal values wherein each measured value of an electrical
interference signal contains simultaneously information about two
orthogonal components of a conjugated quadratures for a joint
measurement of conjugated quadratures of a field of a beam either
reflected and/or scattered or transmitted by a spot on or in a
substrate. One detector element is used to obtain two electrical
interference signal values and the second detector element is used
to obtain two other of the four electrical interference signal
values. The four coextensive measurement beams and corresponding
reference beams are generated in the interferometer system
simultaneously by using an input beam that comprises four frequency
components wherein each frequency component corresponds to a
measurement and corresponding reference beam. The frequency
differences of the four frequency components are such that the four
frequency components are resolved by an analyzer into two beams
incident on the two different detector elements wherein each of the
two beams comprises two different frequency components and the
frequency differences are large compared to the frequency bandwidth
of the detector. One of the two frequency components incident on a
first detector element is used to generate an electrical
interference signal component corresponding to a first component of
conjugated quadratures of a field of a corresponding measurement
beam comprising either a reflected and/or scattered or transmitted
far-field or near-field from a spot in or on a measurement object
that is conjugate to a detector element. The second of the two
frequency components incident on the first detector element is used
to generate a second electrical interference signal component
corresponding to a respective second component of the conjugated
quadratures of the field. The description for the second detector
element with respect to frequency components and components of
conjugated quadratures is the same as the corresponding description
with respect to the first detector element. Information about the
first and second components of the conjugated quadratures are
accordingly obtained jointly as a consequence of the four frequency
components being coextensive in space and having the same temporal
window function in the interferometer system. The temporal window
function when operating in a scanning mode corresponds to the
window function of a respective set of two pulses or pulse
sequences of the input beam to the interferometer system.
[0018] In general, according to one aspect of the invention, in
interferometric far-field and near-field confocal and non-confocal
microscopy respective at least four electrical interference signal
values are acquired when operating in a relatively fast scanning
mode wherein each of the at least four electrical interference
signal values correspond to the same respective spot on or in a
substrate and contain information that can be used for
determination of joint measurements of conjugated quadratures of
fields in both spatial and temporal coordinates.
[0019] In general, according to another aspect of the invention,
joint measurements are made of conjugated quadratures of fields of
beams reflected from a measurement object in single or
multiple-wavelength linear and angular displacement
interferometers.
[0020] In general, according to still another aspect of the
invention, scanning interferometric far-field and near-field
confocal and non-confocal microscopy, employing either a
bi-homodyne or a quad-homodyne detection method, is used to obtain
joint measurements of conjugated quadratures of fields either
reflected and/or scattered or transmitted by a substrate with a
detector having a large number of detector elements. For each spot
in and/or on the substrate that is imaged, a corresponding set of
four electrical interference signal values is obtained. Each of the
set of four electrical interference signal values contains
information for determination of a joint measurement of respective
conjugated quadratures of fields.
[0021] In general, according to yet another aspect of the
invention, in linear and angular displacement interferometry, joint
measurements are made of conjugated quadratures of fields of beams
reflected from a measurement object.
[0022] In general, in one aspect, the invention features an
interferometery system for making interferometric measurements of
an object. The system includes a beam generation module which
during operation delivers an output beam that includes a first beam
at a first frequency and a second beam at a second frequency that
is different from said first frequency, wherein the first and
second beams within the output beam being coextensive, and the beam
generation module included a beam conditioner which during
operation introduces a sequence of different shifts in a selected
parameter of each of the first and second beams, the selected
parameter selected from a group consisting of phase and frequency.
The system also includes a detector assembly having a detector
element, and an interferometer constructed to receive the output
beam at least a part of which represents a first measurement beam
at the first frequency and a second measurement beam at the second
frequency, said interferometer further constructed to image both
the first and second measurement beams onto a selected spot on the
object to produce therefrom corresponding first and second return
measurement beams, and to then simultaneously image the first and
second return measurement beams onto said detector element.
[0023] Other embodiments include one or more of the following
features. The beam generation module further includes a beam source
which during operation generates a single input beam at a
predetermined frequency, and the beam conditioner includes an
optical element that derives the first and second beams from the
single input beam. The optical element is an acousto-optic
modulator. Each of the first and second beams includes a first
component and a second component that is orthogonal to the first
component, and the beam conditioner is constructed to introduce a
first sequence of different discrete phase shifts into a relative
phase difference between the first and second components of the
first beam and concurrently therewith a second sequence of
different discrete phase shifts into the relative phase difference
between the first and second components of the second beam.
[0024] In some embodiments, the beam conditioner includes a first
phase shifter for introducing the first sequence of different
discrete phase shifts into the relative phase difference between
the first and second components of the first beam and a second
phase shifter for introducing the second sequence of different
discrete phase shifts into the relative phase difference between
the first and second components of the second beam. In at least
some of those cases, the interferometer is characterized by a
measurement beam optical path length and a reference beam optical
path length and wherein the difference between those two optical
path lengths is nominally zero. Also, the interferometer is
constructed to generate the first measurement beam from the first
component of the first beam and the second measurement beam from
the first component of the second beam. And the interferometer is
further constructed to generate a first reference beam from the
second component of the first beam and a second reference beam from
the second component of the second beam. The first phase shifter
introduces the first sequence of different discrete phase shifts
into the second component of the first beam and the second phase
shifter introduces the second sequence of different discrete phase
shifts into the second component of the second beam.
[0025] In other embodiments, the beam conditioner is constructed to
introduce a first sequence of different frequency shifts into the
frequency of the first beam and concurrently therewith a second
sequence of different frequency shifts into the frequency of the
second beam. The beam conditioner includes a first set of
acousto-optic modulators for introducing the first sequence of
different frequency shifts into the frequency of the first beam and
a second set of acousto-optic modulators for introducing the second
sequence of different frequency shifts into the frequency of the
second beam. In at least some of those cases, the interferometer is
characterized by a measurement beam optical path length and a
reference beam optical path length and wherein the difference
between those two optical path lengths is nominally a non-zero
value.
[0026] In addition, in other embodiments, the interferometer system
further includes a controller which controls the beam conditioner
and causes the beam conditioner to introduce the first and second
sequences of different shifts in the selected parameter of each of
the first and second beams. The controller is programmed to acquire
from the detector assembly measured values for a set of
interference signals resulting from introducing the first and
second sequences of different shifts in the selected parameters of
each of the first and second beams and further programmed to
compute first and second components of conjugated quadratures of
the fields of beams from said selected spot. The detector element
is characterized by a frequency bandwidth and the first and second
frequencies are separated by an amount that is larger than the
frequency bandwidth of the detector.
[0027] The interferometer can be any one of a wide variety of types
of interferometer, including without limitation, a scanning
interferometric far-field confocal microsope, a scanning
interferometric far-field non-confocal microsope, a scanning
interferometric near-field confocal microsope, a scanning
interferometric near-field non-confocal microsope, and a linear
displacement interferometer.
[0028] In general, in another aspect, the invention features an
interferometery system for making interferometric measurements of
an object. The system includes a beam generation module which
during operation delivers an output beam that includes a first beam
at a first frequency and a second beam at a second frequency that
is different from the first frequency, and the first and second
beams within the output beam being coextensive. The interferometry
system also includes a detector assembly having a detector element
that is characterized by a frequency bandwidth, wherein the first
and second frequencies are separated by an amount that is larger
than the frequency bandwidth of the detector; and an interferometer
constructed to receive the output beam, at least a part of which
represents within the interferometer a first measurement beam at
the first frequency and a second measurement beam at the second
frequency. The interferometer is further constructed to
simultaneously image both the first and second measurement beams
onto a selected spot on or in the object to produce therefrom
corresponding first and second return measurement beams, and then
to simultaneously image the first and second return measurement
beams onto the detector element.
[0029] In general, in still another aspect, the invention features
a source beam assembly including a beam generation module which
during operation delivers an output beam that includes a first beam
at a first frequency and a second beam at a second frequency that
is different from the first frequency, and wherein the first and
second beams within the output beam are coextensive. The beam
generation module included a beam conditioner which during
operation introduces a sequence of different shifts in a selected
parameter of each of the first and second beams, wherein the
selected parameter selected from a group consisting of phase and
frequency.
[0030] In general, in still yet another aspect, the invention
features a method of performing measurements of an object using an
interferometer. The method includes generating an input beam for
the interferometer, wherein the input beam includes a first beam at
a first frequency and a second beam at a second frequency that is
different from the first frequency, and wherein the first and
second beams are coextensive and share the same temporal window.
The method further includes, using the interferometer and the input
beam supplied to the interferometer, to jointly measure two
orthogonal components of conjugated quadratures of fields of
reflected, scattered, or transmitted beams from a selected spot in
and/or on the object.
[0031] In general, another aspect, the invention features a method
of performing measurements of an object using an interferometer
wherein the method includes generating a source beam for the
interferometer, therein the source beam included a first input beam
at a first frequency and a second input beam at a second frequency
that is different from the first frequency, and using the source
beam supplied to the interferometer, to make a sequence of
measurements of an interference signal for a selected spot on or in
the object. The first and second input beams are coextensive and
share the same temporal window function. The making of the sequence
of measurements involves, for each measurement of the sequence of
measurements, introducing a corresponding different shift in a
selected parameter of the first input beam and a corresponding
different shift in the selected parameter of the second input beam,
wherein selected parameter is selected from the group consisting of
phase and frequency. Each measurement of the sequence of
measurements simultaneously captures information for both
conjugated quadratures of fields of reflected, scattered, or
transmitted beams from the selected spot.
[0032] In general, in still yet another aspect, the invention
features a method of generating an source beam, that includes
generating an output beam that includes a first beam at a first
frequency and a second beam at a second frequency that is different
from the first frequency, wherein the first and second beams within
the output beam being coextensive; and introducing a sequence of
different shifts in a selected parameter of each of the first and
second beams, wherein the selected parameter is selected from a
group consisting of phase and frequency.
[0033] In general, in another aspect, the invention features a
method of performing measurements of an object using a scanning
confocal interferometer in which there is an array of pinholes. The
method includes generating an input beam for the scanning
interferometer, wherein the input beam included a first beam at a
first frequency and a second beam at a second frequency that is
different from the first frequency, and wherein the first and
second beams are coextensive and share the same temporal window
function. The method also includes causing an image of the array of
pinholes to scan across the object so that each pinhole of a
conjugate set of pinholes among the array of pinholes becomes
conjugate to a selected spot on or in the object at successive
times during the scan; for each pinhole of the conjugate set of
pinholes, measuring an interference signal value for a selected
spot on or in the object, wherein the measured interference signal
value for each pinhole of the conjugate set of pinholes
simultaneously captures information for two orthogonal components
of conjugated quadratures of fields of reflected, scattered, or
transmitted beams from the selected spot.
[0034] In general, in yet another aspect, the invention features a
method of performing measurements of an object using a scanning
confocal interferometer in which there is an array of pinholes. In
this case, the method includes generating an input beam for the
scanning interferometer, wherein the input beam included a first
beam at a first frequency and a second beam at a second frequency
that is different from the first frequency, and wherein the first
and second beams are coextensive and share the same temporal window
function. The method also includes causing an image of the array of
pinholes to scan across the object so that each detector element of
a conjugate set of detector elements among an array of detector
elements becomes conjugate to a selected spot on or in the object
at successive times during the scan; for each detector of the
conjugate set of detectors, measuring an interference signal value
for a selected spot on or in the object, wherein the measured
interference signal value for each detector of the conjugate set of
detectors simultaneously captures information for two orthogonal
components of conjugated quadratures of fields of reflected,
scattered, or transmitted beams from the selected spot.
[0035] An advantage of at least one embodiment of the present
invention is that a one-dimensional, two-dimensional or
three-dimensional image of a substrate may be obtained in
interferometric confocal or non-confocal far-field and near-field
microscopy when operating in a scanning mode with a relatively fast
scan rate. The image comprises a one-dimensional array, a
two-dimensional array or a three-dimensional array of conjugated
quadratures of reflected and/or scattered or transmitted
fields.
[0036] Another advantage of at least one embodiment of the present
invention is that information used in the determination of a
conjugated quadratures of reflected and/or scattered or transmitted
fields by a substrate is obtained jointly, i.e.,
simultaneously.
[0037] Another advantage of at least one embodiment of the present
invention is that the conjugated quadratures of fields that are
obtained jointly when operating in the scanning mode and using
either the bi-homodyne or quad-homodyne detection methods have
reduced sensitivity to effects of pinhole-to-pinhole variations in
the properties of a conjugate set of pinholes used in a confocal
microscopy system that are conjugate to a spot in or on the
substrate being imaged at different times during the scan.
[0038] Another advantage of at least one embodiment of the present
invention is that the conjugated quadratures of fields that are
obtained jointly when operating in the scanning mode and using
either the bi-homodyne or the quad-homodyne detection methods have
reduced sensitivity to effects of pixel-to-pixel variation of
properties within a set of conjugate pixels that are conjugate to a
spot in or on the substrate being imaged at different times during
the scan.
[0039] Another advantage of at least one embodiment of the present
invention is that the conjugated quadratures of fields that are
obtained jointly when operating in the scanning mode and using
either the bi-homodyne or the quad-homodyne detection methods have
reduced sensitivity to effects of pulse to pulse variations of a
respective set of pulses or pulse sequences of the input beam to
the interferometer system.
[0040] Another advantage of at least one embodiment of the present
invention is an increased throughput for an interferometric
far-field or near-field confocal or non-confocal microscope with
respect to the number of spots in and/or on a substrate imaged per
unit time.
[0041] Another advantage of at least one embodiment of the present
invention is reduced systematic errors in a one-dimensional, a
two-dimensional or a three-dimensional image of a substrate
obtained in interferometric far-field and near-field confocal and
non-confocal microscopy.
[0042] Another advantage of at least one embodiment of the present
invention is reduced sensitivity to vibrations in generating
one-dimensional, two-dimensional or three-dimensional images of a
substrate by interferometric far-field and near-field confocal and
non-confocal microscopy.
[0043] Another advantage of at least one embodiment of the present
invention is reduced sensitivity to an overlay error of a spot in
or on the substrate that is being imaged and a conjugate image of a
conjugate pixel of a multi-pixel detector during the acquisition of
the four electrical interference values for each spot in and/or on
a substrate imaged using interferometric far-field and/or
near-field confocal and non-confocal microscopy. Overlay errors are
errors in the set of four conjugate images of a respective set of
conjugate detector pixels relative to the spot being imaged for
either the bi-homodyne quad-homodyne detection methods.
[0044] Another advantage of at least one embodiment of the present
invention is that the phase of an input beam component does not
affect values of measured conjugated quadratures when operating in
frequency-shift mode of either the bi-homodyne or quad-homodyne
detection methods.
BRIEF DESCRIPTION OF THE DRAWINGS
[0045] FIG. 1a is a diagram of an interferometric system that uses
the bi-homodyne and quad-homodyne detection methods.
[0046] FIG. 1b is a schematic diagram of a beam-conditioner
configured to operate in a two-frequency generator and phase
shifter.
[0047] FIG. 1c is a schematic diagram of a beam-conditioner
configured to operate in a two-frequency generator and
frequency-shifter.
[0048] FIG. 2a is a schematic diagram of a confocal microscope
system.
[0049] FIG. 2b is a schematic diagram of catadioptric imaging
system.
[0050] FIG. 2c is a schematic diagram of a pinhole array used in a
confocal microscope system.
DETAILED DESCRIPTION
[0051] Apparatus and methods are described herein for joint
measurements of conjugated quadratures of fields of reflected
and/or scattered and/or transmitted beams in interferometry such as
scanning interferometric far-field and near-field confocal and
non-confocal microscopy and in interferometric based metrology such
as linear displacement interferometers. A bi-homodyne detection
method and a quad-homodyne detection method are used to obtain
measurements of quantities subsequently used in determination of
joint measurements of the conjugated quadratures of fields. The
prefixes bi- and quad- refer to the number of different coextensive
measurement and corresponding reference beams present in an
interferometer system simultaneously, i.e., 2 and 4,
respectively.
[0052] With respect to information content and signal-to-noise
ratios, the conjugated quadratures of fields obtained jointly in a
microscopy system that is operating in a scanning mode and using
either the bi-homodyne or quad-homodyne detection methods are
substantially equivalent to conjugated quadratures of fields
obtained when operating the microscopy system in a step and stare
mode, i.e., a non-scanning mode. The conjugated quadratures of
fields obtained jointly when operating in the scanning mode and
using either the bi-homodyne or the quad-homodyne detection methods
have reduced sensitivity to pinhole-to-pinhole variations in
properties of a conjugate set of pinholes used in a confocal
microscopy system and reduced sensitivity to pixel-to-pixel
variation of properties within a set of conjugate pixels of a
multipixel detector in confocal and non-confocal microscopy
systems.
[0053] The conjugated quadratures of fields obtained jointly when
operating in the scanning mode and using either the bi-homodyne or
the quad-homodyne detection method have reduced sensitivity to
pulse to pulse variations of the input beam used in generating the
conjugated quadratures of fields, reduced sensitivity to vibrations
of a substrate, and reduced sensitivity to a relative motion of a
substrate being imaged during the acquisition of joint measurements
of the conjugated quadratures of fields. The reduced sensitivity is
relative to conjugated quadratures of fields obtained when
operating in a single-homodyne detection mode and for operating in
either a scanning or non-scanning mode. In microscopy applications,
conjugated quadratures of fields are obtained for each spot in
and/or on a substrate that is imaged.
[0054] The conjugated quadratures of fields that are obtained
jointly in a single or multiple wavelength linear displacement
interferometer operating in a scanning mode and using either the
bi-homodyne or the quad-homodyne detection methods have a reduced
phase redundancy problem and have reduced sensitivity to vibrations
as compared to a single or multiple wavelength linear or angular
displacement interferometer operating in a scanning mode and using
a single-homodyne detection method.
[0055] Several embodiments are described that comprise
interferometric confocal and non-confocal far-field and near-field
microscopy systems and a linear displacement interferometer, e.g.,
such as used in wavelength monitors, refractivity of gas monitors,
monitors of the reciprocal dispersive power .GAMMA. of a gas, and
dispersion interferometry. In the first embodiment, the difference
in the optical path length of a reference beam and a measurement
beam in a interferometric far-field confocal microscope is a
relatively large non-zero value, e.g., 0.2 m, and in the second
embodiment, the difference in the optical path length of the
reference beam and the measurement beam in a interferometric
confocal far-field microscope is nominally zero. The difference in
the optical path length of the reference and measurement beams in
interferometric measurements is normally kept a minimum value.
However, in certain interferometric far-field confocal microscopes
the difference in the optical path length of the reference and
measurement beams is a relatively large value such as described in
U.S. Provisional Patent Application No. 60/442,982 [ZI-45] entitled
"Interferometric Confocal Microscopy Incorporating Pinhole Array
Beam-Splitter" by Henry A. Hill, the contents of which are herein
incorporated in their entirety by reference.
[0056] A general description of embodiments incorporating various
aspects of the present invention will first be given wherein the
bi-homodyne and the quad-homodyne detection methods are used in
interferometer systems for measuring conjugated quadratures of
fields of beams reflected and/or scattered and of beams transmitted
by a substrate. Referring to FIG. 1a, an interferometer system is
shown diagrammatically comprising an interferometer generally shown
as numeral 10 for measuring beams reflected and/or scattered and
beams transmitted by a measurement object 60, a source 18, a
beam-conditioner 22, detector 70, and an electronic processor and
controller 80. Source 18 is a pulsed source that generates input
beam 20 comprising either one, two, or four frequency components.
Beam 20 is incident on and exits beam-conditioner 22 as input beam
24 that has either two or four frequency components. The
measurement beam components of the two or four frequency components
of input beam 24 are coextensive in space and have the same
temporal window function and the corresponding reference beam
components are coextensive in space and have the same temporal
window function.
[0057] Reference and measurement beams may be generated in either
beam-conditioner 22 from a set of beams or in interferometer 10 for
each of the two or four frequency components of input beam 24.
Measurement beam 30A generated in either beam-conditioner 22 or in
interferometer 10 is incident on substrate 60. Measurement beam 30B
is a return measurement beam generated as either a portion of
measurement beam 30A reflected and/or scattered by substrate 60 or
a portion of measurement beam 30A transmitted by substrate 60.
Return measurement beam 30B is combined with the reference beam in
interferometer 10 to form output beam 32.
[0058] Output beam 32 is detected by detector 70 to generate either
one or two electrical interference signals per source pulse or
pulse sequence for the bi-homodyne or quad-homodyne detection
methods, respectively, and transmitted as signal 72. Detector 70
may comprise an analyzer to select common polarization states of
the reference and return measurement beam components of beam 32 to
form a mixed beam. Alternatively, interferometer 10 may comprise an
analyzer to select common polarization states of the reference and
return measurement beam components such that beam 32 is a mixed
beam.
[0059] In practice, known phase shifts are introduced between the
reference and measurement beam components of output beam 32 by two
different techniques. In one technique, phase shifts are introduced
between the reference and measurement beam components for each of
the two or four frequency components of input beam 24 by
beam-conditioner 22 as controlled by signal 74 from electronic
processor and controller 80. In the second technique, phase shifts
are introduced between corresponding reference and measurement beam
components for each of the two or four frequency components of
output beam 32 as a consequence of a non-zero optical path
difference between the reference and measurement beam paths in
interferometer 10 and corresponding frequency shifts introduced to
the two or four frequency components of input beam 24 by
beam-conditioner 22 and/or source 18 as controlled by signal 74
from electronic processor and controller 80.
[0060] There are different ways to configure source 18 and
beam-conditioner 22 to meet the input beam requirements of
different embodiments described herein. Reference is made to FIG.
1b where beam-conditioner 22 is configured as a two-frequency
generator and a phase-shifter and source 18 is configured to
generate beam 20 with one frequency component. The two-frequency
generator and phase-shifter configuration comprises acousto-optic
modulators 1020, 1026, 1064 and 1068; polarizing beam-splitters
1030, 1042, 1044, and 1056; phase-shifters 1040 and 1052; half wave
phase retardation plates 1072 and 1074; non-polarizing
beam-splitter 1070; and mirrors 1036, 1038, 1050, and 1054.
[0061] Input beam 20 is incident on acousto-optic modulator 1020
with a plane of polarization parallel to the plane of FIG. 1b. A
first portion of beam 20 is diffracted by acousto-optic modulator
1020 as beam 1022 and then by acousto-optic modulator 1026 as beam
1028 having a polarization parallel to the plane of FIG. 1b. A
second portion of beam 20 is transmitted as a non-diffracted beam
1024 having a plane of polarization parallel to the plane of FIG.
1b. The acoustic power to acousto-optic modulator 1020 is adjusted
such that beams 1022 and 1024 have nominally the same
intensity.
[0062] Acousto-optic modulators 1020 and 1026 may be of either the
non-isotropic Bragg diffraction type or of the isotropic Bragg
diffraction type. The frequency shifts introduced by acousto-optic
modulators 1020 and 1026 are of the same sign and equal to 1/4 of
the desired frequency shift between the two frequency components of
input beam 24. Also the direction of propagation of beam 1028 is
parallel to the direction of propagation of beam 1024.
[0063] Beam 1024 is diffracted by acousto-optic modulators 1064 and
1068 as beam 1082 having a polarization parallel to the plane of
FIG. 1b. Acousto-optic modulators 1064 and 1068 may be of either
the non-isotropic Bragg diffraction type or of the isotropic Bragg
diffraction type. The frequency shifts introduced by acousto-optic
modulators 10640 and 1068 are of the same sign and equal to 1/4 of
the desired frequency shift between the two frequency components of
input beam 24. Also the direction of propagation of beam 1082 is
parallel to the direction of propagation of beam 1024.
[0064] Beams 1028 and 1082 are incident on half-wave phase
retardation plates 1072 and 1074, respectively, and transmitted as
beams 1076 and 1078, respectively. Half-wave phase retardation
plates 1072 and 1074 are oriented such that the planes of
polarization of beams 1076 and 1078 are at 45 degrees to the plane
of FIG. 1b. The components of beams 1076 and 1078 polarized
parallel to the plane of FIG. 1b will be used as the measurement
beam components in interferometer 10 and the components of beams
1076 and 1078 polarized orthogonal to the plane of FIG. 1b will be
used as the reference beam components in interferometer 10.
[0065] Continuing with reference to FIG. 1b, beam 1076 is incident
on polarizing beam-splitter 1044 and the respective measurement and
reference beam components transmitted and reflected, respectively,
as beams 1046 and 1048, respectively. Measurement beam component
1046 is transmitted by polarizing beam-splitter 1056 as a
measurement beam component of beam 1058 after reflection by mirror
1054. Reference beam component 1048 is reflected by polarizing
beam-splitter 1056 as reference beam component of beam 1058 after
reflection by mirror 1050 and transmission by phase-shifter 1052.
Beam 1058 is incident on beam-splitter 1070 and a portion thereof
is reflected as a component of beam 24.
[0066] Beam 1078 is incident on polarizing beam-splitter 1030 and
the respective measurement and reference beam components
transmitted and reflected, respectively, as beams 1032 and 1034,
respectively. Measurement beam component 1032 is transmitted by
polarizing beam-splitter 1042 as a measurement beam component of
beam 1060 after reflection by mirror 1036. Reference beam component
1034 is reflected by polarizing beam splitter 1042 as reference
beam component of beam 1060 after reflection by mirror 1038 and
transmission by phase-shifter 1040. Beam 1060 is incident on
beam-splitter 1070 and a portion thereof is transmitted as a
component of beam 24 after reflection by mirror 1056.
[0067] Phase-shifters 1052 and 1040 introduce phase shifts between
respective reference and measurement beams according to signal 74
from electronic processor and controller 80 (see FIG. 1a). The
schedule of the respective phase shifts is described in the
subsequent discussion of Equation (1). Phase-shifters 1052 and 1040
may be for example of the optical-mechanical type comprising for
example prisms or mirrors and piezoelectric translators or of the
electro-optical modulator type.
[0068] Beam 24 that exits beam-conditioner 22 comprises one
reference beam and measurement beam having one frequency, a second
reference beam and measurement beam having a second frequency, and
relative phases of the reference beams and the measurement beams
that are controlled by electronic processor and controller 80
through control signal 74.
[0069] Continuing with a description of different ways to configure
source 18 and beam-conditioner 22 to meet the input beam
requirements of different embodiments described herein, reference
is made to FIG. 1c where beam-conditioner 22 is configured as a
two-frequency generator and a frequency shifter. The two-frequency
generator and frequency-shifter configuration comprises
acousto-optic modulators 1120, 1126, 1130, 1132, 1142, 1146, 1150,
1154, 1058, and 1062; beam-splitter 1168; and mirror 1166.
[0070] Source 18 is configured to generate beam 20 with a single
frequency component. Beam 20 is incident on acousto-optic modulator
1120 with a plane of polarization parallel to the plane of FIG. 1c.
A first portion of beam 20 is diffracted by acousto-optic modulator
1120 as beam 1122 and then by acousto-optic modulator 1126 as beam
1128 having a polarization parallel to the plane of FIG. 1c. A
second portion of beam 20 is transmitted as a non-diffracted beam
1124 having a plane of polarization parallel to the plane of FIG.
1c. The acoustic power to acousto-optic modulator 1120 is adjusted
such that beams 1122 and 1124 have nominally the same
intensity.
[0071] Acousto-optic modulators 1120 and 1126 may be of either the
non-isotropic Bragg diffraction type or of the isotropic Bragg
diffraction type. The frequency shifts introduced by acousto-optic
modulators 1120 and 1126 are of the same sign and equal to 1/2 of a
frequency shift .DELTA.f that will generate in interferometer 10 a
relative .pi./2 phase shift between a corresponding reference beam
and a measurement beam that have a relative change in frequency
equal to the frequency shift .DELTA.f. The direction of propagation
of beam 1128 is parallel to the direction of propagation of beam
1124.
[0072] Continuing with FIG. 1c, beam 1128 is incident on
acousto-optic modulator 1132 and is either diffracted by
acousto-optic modulator 1132 as beam 1134 or transmitted by
acousto-optic modulator 1132 as beam 1136 according to control
signal 74 (see FIG. 1a) from electronic processor and controller
80. When beam 1134 is generated, beam 1134 is diffracted by
acousto-optic modulators 1142, 1146, and 1150 as a
frequency-shifted beam component of beam 1152. The frequency shifts
introduced by acousto-optic modulators 1132, 1142, 1146, and 1150
are all in the same direction and equal in magnitude to .DELTA.f/2.
Thus the net frequency shift introduced by acousto-optic modulators
1132, 1142, 1146, and 1150 is .+-.2.DELTA.f and will generate a
relative .pi. phase between the respective reference and
measurement beams in interferometer 10. The net frequency shift
introduced by acousto-optic modulators 1120, 1126, 1132, 1142,
1146, and 1150 is .DELTA.f.+-.2.DELTA.f and will generate a
respective relative phase shift of .pi./2.+-.7 between the
respective reference and measurement beams in interferometer
10.
[0073] When beam 1136 is generated, beam 1136 is transmitted by
acousto-optic modulator 1150 according to control signal 74 from
electronic processor and controller 80 as a non-frequency shifted
beam component of beam 1152 with respect to beam 1128. The net
frequency shift introduced by acousto-optic modulators 1120, 1126,
1132, and 1150 is .DELTA.f which will generate a respective
relative phase shift of .pi./2 between the respective reference and
measurement beams in interferometer 10.
[0074] Beam 1124 is incident on acousto-optic modulator 1130 and is
either diffracted by acousto-optic modulator 1130 as beam 1140 or
transmitted by acousto-optic modulator 1130 as beam 1138 according
to control signal 74 from electronic processor and controller 80.
When beam 1140 is generated, beam 1140 is diffracted by
acousto-optic modulators 1154, 1158, and 1162 as a
frequency-shifted beam component of beam 1164. The frequency shifts
introduced by acousto-optic modulators 1130, 1154, 1158, and 1162
are all in the same direction and equal to .+-..DELTA.f/2. Thus the
net frequency shift introduced by acousto-optic modulators 1130,
1154, 1158, and 1162 is .+-.2.DELTA.f and will generate a relative
phase shift of .pi. between the respective reference and
measurement beams on transit through interferometer 10. The net
frequency shift introduced by acousto-optic modulators 1120, 1130,
1154, 1158, and 1162 is .+-.2.DELTA.f and will generate a
respective relative phase shift of .+-..pi. between the respective
reference and measurement beams on transit through interferometer
10
[0075] When beam 1138 is generated, beam 1138 is transmitted by
acousto-optic modulator 1162 according to control signal 74 from
electronic processor and controller 80 as a non-frequency shifted
beam component of beam 1164. The frequency shift introduced by
acousto-optic modulators 1120, 1130, and 1162 is 0 and will
generate a respective relative phase shift of 0 between the
respective reference and measurement beams on transit through
interferometer 10.
[0076] Beams 1152 and 1164 may be used directly as input beam 24
when an embodiment requires spatially separated reference and
measurement beams for an input beam. When an embodiment requires
coextensive reference and measurement beams as an input beam, beam
1152 and 1164 are combined by beam-splitter 1168 to form beam 24.
Acousto-optic modulators 1120, 1126, 1130, 1132, 1142, 1146, 1150,
1154, 1058, and 1062 may be either of the non-isotropic Bragg
diffraction type or of the isotropic Bragg diffraction type. Beams
1152 and 1164 are both polarized in the plane of FIG. 1c for either
non-isotropic Bragg diffraction type or of the isotropic Bragg
diffraction type and beam-splitter 1168 is of the non-polarizing
type.
[0077] With a continuation of the description of different ways to
configure source 18 and beam-conditioner 22 to meet the input beam
requirements of different embodiments, source 18 will preferably
comprise a pulse source. There are a number of different ways for
producing a pulsed source [see Chapter 11 entitled "Lasers",
Handbook of Optics, 1, 1995 (McGraw-Hill, New York) by W.
Silfvast]. Each pulse of source 18 may comprise a single pulse or a
train of pulses such as generated by a mode locked Q-switched
Nd:YAG laser. A single pulse train is referenced herein as a pulse
sequence and a pulse and a pulse sequence are used herein
interchangeably.
[0078] Source 18 may be configured in certain embodiments to
generate two or four frequencies by techniques such as described in
a review article entitled "Tunable, Coherent Sources For
High-Resolution VUV and XUV Spectroscopy" by B. P. Stoicheff, J. R.
Banic, P. Herman, W. Jamroz, P. E. LaRocque, and R. H. Lipson in
Laser Techniques for Extreme Ultraviolet Spectroscopy, T. J.
McIlrath and R. R. Freeman, Eds., (American Institute of Physics) p
19 (1982) and references therein. The techniques include for
example second and third harmonic generation and parametric
generation such as described in the articles entitled "Generation
of Ultraviolet and Vacuum Ultraviolet Radiation" by S. E. Harris,
J. F. Young, A. H. Kung, D. M. Bloom, and G. C. Bjorklund in Laser
Spectroscopy I, R. G. Brewer and A. Mooradi, Eds. (Plenum Press,
New York) p 59, (1974) and "Generation of Tunable Picosecond VUV
Radiation" by A. H. Kung, Appl. Phys. Lett. 25, p 653 (1974). The
contents of the three cited articles are herein incorporated in
their entirety by reference.
[0079] The output beams from source 18 comprising two or four
frequency components may be combined in beam-conditioner 22 by
beam-splitters to form coextensive measurement and reference beams
that are either spatially separated or coextensive as required in
various embodiments. When source 18 is configured to furnish two or
four frequency components, the frequency shifting of the various
components required in certain embodiments may be introduced in
source 18 for example by frequency modulation of input beams to
parametric generators and the phase shifting of reference beams
relative to measurement beams in beam-conditioner 22 may be
achieved by phase shifters of the optical-mechanical type
comprising for example prisms or mirrors and piezoelectric
translators or of the electro-optical modulator type.
[0080] The general description is continued with reference to FIG.
1a. Input beam 24 is incident on interferometer 10 wherein
reference beams and measurement beams are present in input beam 24
or are generated from input beam 24 in interferometer 10. The
reference beams and measurement beams comprise two arrays of
reference beams and two arrays of measurement beams wherein the
arrays may comprise arrays of one element. The arrays of
measurement beams are incident on or focused on and/or in substrate
60 and arrays of return measurement beams are generated by
reflection and/or scattering or transmission by the substrate. In
the case of single element arrays for the reference beams and
measurement beams, the measurement beams are generally reflected or
transmitted by substrate 60. The arrays of reference beams and
return measurement beams are combined by a beam-splitter to form
two arrays of output beam components. The arrays of output beam
components are mixed with respect to state of polarization either
in interferometer 10 or in detector 70. The arrays of output beams
are subsequently focused to spots on pixels of a multi-pixel or
single pixel detector as required and detected to generate
electrical interference signal 72.
[0081] The conjugated quadratures of fields of return measurement
beams are obtained by making a set of four measurements of the
electrical interference signal 72. In single homodyne detection,
for each of the four measurements of the electrical interference
signal 72, a known sequence of phase shifts is introduced between
the reference beam component and the return measurement beam
component of the output beam 32. A sequence of phase shifts
comprise 0, .pi./4, .pi./2, and 3.pi./2. For reference, the
subsequent data processing procedure used to extract the conjugated
quadratures of the reflected/scattered fields for an input beam
comprising a single frequency component is described for example in
U.S. Pat. No. 6,445,453 (ZI-14) entitled "Scanning Interferometric
Near-Field Confocal Microscopy" by Henry A. Hill, the contents of
which are incorporated herein in their entirety by reference.
[0082] Referring to the bi-homodyne detection method used in
various embodiments, a set of four electrical interference signal
values are obtained for each spot on and/or in substrate 60 being
imaged. The set of four electrical interference signal values
S.sub.j, j=1, 2, 3, 4, used for obtaining conjugated quadratures of
fields for a single a spot on and/or in a substrate being imaged is
represented for the bi-homodyne detection within a scale factor by
the formula 1 S j = P j { j 2 A 1 2 + j 2 B 1 2 + j 2 C 1 2 + j j 2
B 1 C 1 cos B 1 C 1 j + j j 2 A 1 ; B 1 cos A 1 B 1 j + j j j 2 A 1
C 1 cos A 1 C 1 + j 2 A 2 2 + j 2 B 2 2 + j 2 C 2 2 + j j 2 B 2 C 2
cos B 2 C 2 j + j j 2 A 2 B 2 cos A 2 B 2 j + j j j 2 A 2 C 2 cos A
2 C 2 } ( 1 )
[0083] where coefficients A.sub.1 and A.sub.2 represent the
amplitudes of the reference beams corresponding to the first and
second frequency components of the input beam; coefficients B.sub.1
and B.sub.2 represent the amplitudes of background beams
corresponding to reference beams A.sub.1 and A.sub.2, respectively;
coefficients C.sub.1 and C.sub.2 represent the amplitudes of the
return measurement beams corresponding to reference beams A.sub.1
and A.sub.2, respectively; P.sub.j represents the integrated
intensity of the first frequency component of the input beam in
pulse j of the pulse sequence; and the values for .epsilon..sub.j
and .gamma..sub.j are listed in Table 1. The change in the values
of .epsilon..sub.j and .gamma..sub.j from 1 to -1 or from -1 to 1
correspond to changes in relative phases of respective reference
and measurement beams. The coefficients .xi..sub.j, .zeta..sub.j,
and .eta..sub.j represent effects of variations in properties of a
conjugate set of four pinholes such as size and shape if used in
the generation of the spot on and/or in substrate 60 and the
sensitivities of a conjugate set of four detector pixels
corresponding to the spot on and/or in substrate 60 for the
reference beam, the background beam, and the return measurement
beam, respectively.
1 TABLE 1 j .epsilon..sub.j .gamma..sub.j
.epsilon..sub.j.gamma..sub.j 1 1 1 1 2 -1 -1 1 3 -1 1 -1 4 1 -1
-1
[0084] It is assumed in Equation (1) that the ratio of
.vertline.A.sub.2.vertline./.vertline.A.sub.1.vertline. is not
dependent on j or on the value of P.sub.j. In order to simplify the
representation of S.sub.j so as to project the important features
without departing from either the scope or spirit of the present
invention, it is also assumed in Equation (1) that the ratio of the
amplitudes of the return measurement beams corresponding to A.sub.2
and A.sub.1 is not dependent on j or on the value of P.sub.j.
However, the ratio
.vertline.C.sub.2.vertline./.vertline.C.sub.1.vertline. will be
different from the ratio
.vertline.A.sub.2.vertline./.vertline.A.sub.1.vertline. when the
ratio of the amplitudes of the measurement beam components
corresponding to A.sub.2 and A.sub.1 are different from the ratio
.vertline.A.sub.2.vertline./.vertline.A.sub.1.vertline..
[0085] Noting that cos
.phi..sub.A.sub..sub.2.sub.C.sub..sub.2=.+-.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 by the control of the
relative phase shifts between corresponding reference and return
measurement beam components in beam 32, Equation (1) may be
rewritten as 2 S j = P j { j 2 ( A 1 2 + A 2 2 ) + j 2 ( B 1 2 + B
2 2 ) + j 2 ( C 1 2 + C 2 2 ) + 2 j j ( A 1 B 1 cos A 1 B 1 j + A 2
B 2 cos A 2 B 2 j ) + 2 j j [ j A 1 C 1 cos A 1 C 1 + j ( A 2 A 1 )
( C 2 C 1 ) A 1 C 1 sin A 1 C 1 ] + 2 j j ( j B 1 C 1 cos B 1 C 1 1
+ j B 2 C 2 cos B 2 C 2 j ) } ( 2 )
[0086] where the relationship cos
.phi..sub.A.sub..sub.2.sub.C.sub..sub.2=- sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 has been used without
departing from either the scope or spirit of the present
invention.
[0087] The change in phase
.phi..sub.A.sub..sub.1.sub.B.sub..sub.1.sub..ep- silon..sub..sub.j
for a change in .epsilon..sub.j and the change in phase
.phi..sub.A.sub..sub.2.sub.B.sub..sub.2.sub..gamma..sub..sub.j for
a change in .gamma..sub.j may be different from ir in embodiments
depending on where and how the background beam is generated. It may
be of value in evaluating the effects of the background beams to
note that the factor cos
.phi..sub.B.sub..sub.1.sub.C.sub..sub.1.sub..gamma..sub..sub.j may
be written as
cos[.phi..sub.A.sub..sub.1.sub.C.sub..sub.1+(.phi..sub.B.sub..-
sub.1.sub.C.sub..sub.1.sub..epsilon..sub.j-.phi..sub.A.sub..sub.1.sub.C.su-
b..sub.1)] where the phase difference
(.phi..sub.B.sub..sub.1.sub.C.sub..s-
ub.1.sub..epsilon..sub.j-.phi..sub.A.sub..sub.1.sub.C.sub..sub.1)
is the same as the phase
.phi..sub.A.sub..sub.1.sub.B.sub..sub.1.sub..epsilon..s- ub..sub.j,
i.e., cos .phi..sub.B.sub..sub.1.sub.C.sub..sub.1.sub..epsilon.-
.sub..sub.j=cos(.phi..sub.A.sub..sub.1.sub.C.sub..sub.1+.phi..sub.A.sub..s-
ub.1.sub.B.sub..sub.1.sub..epsilon..sub..sub.j).
[0088] It is evident from inspection of Equation (2) that the term
in Equation (2) corresponding to the component of conjugated
quadratures .vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 is a rectangular function
that has a mean value of zero and is symmetric about j=2.5 since
.epsilon..sub.j is symmetric about j=2.5. In addition the term in
Equation (2) corresponding to the component of conjugated
quadratures .vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.s- ub..sub.1 in Equation (2) is a
rectangular function that has a mean value of zero and is
antisymmetric about j=2.5 since .gamma..sub.j is a antisymmetric
function about j=2.5. Another important property by the design of
the bi-homodyne detection method is that the conjugated quadratures
.vertline.C.sub.1.vertline.cos .phi..sub.A.sub..sub.1.sub.C.s-
ub..sub.1 and .vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.- sub..sub.1 terms are orthogonal over
the range of j=1, 2, 3, 4 since .epsilon..sub.j and .gamma..sub.j
are orthogonal over the range of j=1, 2, 3, 4, i.e.,
.SIGMA..sub.j=1.sup.4.epsilon..sub.j.gamma..sub.j=0.
[0089] Information about conjugated quadratures
.vertline.C.sub.1.vertline- .cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertlin- e.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 are obtained using the
symmetric and antisymmetric properties and orthogonality property
of the conjugated quadratures terms in Equation (2) as represented
by the following digital filters applied to the signal values
S.sub.j: 3 F 1 ( S ) = j = 1 4 j S j P j ' j '2 = ( A 1 2 + A 2 2 )
j = 1 4 j ( P j P j ' ) ( j 2 j '2 ) + ( B 1 2 + B 2 2 ) j = 1 4 j
( P j P j ' ) ( j 2 j '2 ) + ( C 1 2 + C 2 2 ) j = 1 4 j ( P j P j
' ) ( j 2 j '2 ) + 2 A 1 C 1 cos A 1 C 1 j = 1 4 ( P j P j ' ) ( j
j j '2 ) + 2 ( A 2 A 1 ) ( C 2 C 1 ) A 1 C 1 sin A 1 C 1 j = 1 4 j
j ( P j P j ' ) ( j j j '2 ) + 2 A 1 B 1 j = 1 4 j ( P j P j ' ) (
j j j '2 ) cos A 2 B 2 j + 2 A 2 B 2 j = 1 4 j ( P j P j ' ) ( j j
j '2 ) cos A 2 B 2 j + 2 B 1 C 1 j = 1 4 ( P j P j ' ) ( j j j '2 )
cos B 1 C 1 j + 2 B 2 C 2 j = 1 4 j j ( P j P j ' ) ( j j j '2 )
cos B 2 C 2 j , ( 3 ) F 2 ( S ) = j = 1 4 j S j P j ' j '2 = ( A 1
2 + A 2 2 ) j = 1 4 j ( P j P j ' ) ( j 2 j '2 ) + ( B 1 2 + B 2 2
) j = 1 4 j ( P j P j ' ) ( j 2 j '2 ) + ( C 1 2 + C 2 2 ) j = 1 4
j ( P j P j ' ) ( j 2 j '2 ) + 2 A 1 C 1 cos A 1 C 1 j = 1 4 j j (
P j P j ' ) ( j j j '2 ) + 2 ( A 2 A 1 ) ( C 2 C 1 ) A 1 C 1 sin A
1 C 1 j = 1 4 ( P j P j ' ) ( j j j '2 ) + 2 A 1 B 1 j = 1 4 j ( P
j P j ' ) ( j j j '2 ) cos A 1 B 1 j + 2 A 2 B 2 j = 1 4 j ( P j P
j ' ) ( j j j '2 ) cos A 2 B 2 j + 2 B 1 C 1 j = 1 4 j j ( P j P j
' ) ( j j j '2 ) cos B 1 C 1 j + 2 B 2 C 2 j = 1 4 ( P j P j ' ) (
j j j '2 ) cos B 2 C 2 j ( 4 )
[0090] where .xi..sub.j' and P.sub.j' are values used in the
digital filters to represent .xi..sub.j and P.sub.j.
[0091] The parameter 4 [ ( A 2 A 1 ) ( C 2 C 1 ) ] ( 5 )
[0092] in Equations (3) and (4) needs to be determined in order
complete the determination of a conjugated quadratures. The
parameter given in Equation (5) can be measured for example by
introducing .pi./2 phase shifts into the relative phase of the
reference beam and the measurement beam and repeating the
measurement for the conjugated quadratures. The ratio of the
amplitudes of the conjugated quadratures corresponding to (sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1/cos
.phi..sub.A.sub..sub.1.s- ub.C.sub..sub.1) from the first
measurement divided by the ratio of the amplitudes of the
conjugated quadratures corresponding to (sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1/cos
.phi..sub.A.sub..sub.1.sub.C.- sub..sub.1) from the second
measurement is equal to 5 [ ( A 2 A 1 ) ( C 2 C 1 ) ] 2 . ( 6 )
[0093] Note that certain of the factors in Equations (3) and (4)
have nominal values of 4 within a scale factor, e.g., 6 j = 1 4 ( P
j P j ' ) ( j j j '2 ) 4 , j = 1 4 ( P j P j ' ) ( j j j '2 ) 4. (
7 )
[0094] The scale factors correspond to the average values for the
ratios of .xi..sub.j'/.eta..sub.j and .xi..sub.j'/.zeta..sub.j,
respectively, assuming that the average value of
P.sub.j/P.sub.j'.congruent.1. Certain other of the factors in
Equations (3) and (4) have nominal values of zero, e.g., 7 j = 1 4
j ( P j P j ' ) ( j 2 j '2 ) 0 , j = 1 4 j ( P j P j ' ) ( j 2 j '2
) 0 , j = 1 4 j ( P j P j ' ) ( j 2 j '2 ) 0 , j = 1 4 j ( P j P j
' ) ( j 2 j '2 ) 0 , j = 1 4 j ( P j P j ' ) ( j 2 j '2 ) 0 , j = 1
4 j ( P j P j ' ) ( j 2 j '2 ) 0 , j = 1 4 j j ( P j P j ' ) ( j j
j '2 ) 0. ( 8 )
[0095] The remaining factors, 8 j = 1 4 j ( P j P j ' ) ( j j j '2
) cos A 1 B 1 j , j = 1 4 j ( P j P j ' ) ( j j j '2 ) cos A 2 B 2
j , j = 1 4 ( P j P j ' ) ( j j j '2 ) cos B 1 C 1 j , j = 1 4 j j
( P j P j ' ) ( j j j '2 ) cos B 2 C 2 j , j = 1 4 j ( P j P j ' )
( j j j '2 ) cos A 1 B 1 j , j = 1 4 j ( P j P j ' ) ( j j j '2 )
cos A 2 B 2 j , j = 1 4 j j ( P j P j ' ) ( j j j '2 ) cos B 1 C 1
j , j = 1 4 ( P j P j ' ) ( j j j '2 ) cos B 2 C 2 j , ( 9 )
[0096] will have nominal magnitudes ranging from approximately zero
to approximately 4 times a cosine factor and either the average
value of factor
(P.sub.j/P.sub.J')(.xi..sub.j.zeta..sub.j/.xi..sub.j'.sup.2) or
(P.sub.j/P.sub.J')(.zeta..sub.j.eta..sub.j)/.xi..sub.j'.sup.2)
depending on the properties respective phases. For the portion of
the background with phases that do not track to a first
approximation the phases of the respective measurement beams, the
magnitudes of all of the terms listed in the Equation (9) will be
approximately zero. For the portion of the background with phases
that do track to a first approximation the phases of the respective
measurement beams, the magnitudes of the terms listed in Equation
(9) will be approximately 4 times a cosine factor and either the
average value of factor
(P.sub.j/P.sub.J')(.xi..sub.j.zeta..sub.j/.xi- ..sub.j'.sup.2) and
or factor (P.sub.j/P.sub.J')(.zeta..sub.j.eta..sub.j/.-
xi..sub.j'.sup.2).
[0097] The two largest terms in Equations (3) and (4) are generally
the terms that have the factors
(.vertline.A.sub.1.vertline..sup.2+.vertline.-
A.sub.2.vertline..sup.2) and
(.vertline.B.sub.1.vertline..sup.2+.vertline.-
B.sub.2.vertline..sup.2). However, the corresponding terms are
substantially eliminated in various embodiments by selection of
.xi..sub.j' values for the terms that have
(.vertline.A.sub.1.vertline..s-
up.2+.vertline.A.sub.2.vertline..sup.2) as a factor and by the
design of .zeta..sub.j values for the terms that have
(.vertline.B.sub.1.vertline..- sup.2+B.sub.2.vertline..sup.2) as a
factor as shown in Equation (8).
[0098] The largest contribution from effects of background is
represented by the contribution to the interference term between
the reference beam and the portion of the background beam generated
by the measurement beam 30A. This portion of the effect of the
background can be measured by measuring the corresponding
conjugated quadratures of the portion of the background with the
return measurement beam component of beam 32 set equal to zero,
i.e., measuring the respective electrical interference signals
S.sub.j with substrate 60 removed and with either
.vertline.A.sub.2.vertline.=0 or .vertline.A.sub.1.vertline.=0 and
visa versa. The measured conjugated quadratures of the portion of
the effect of the background can then be used to compensate for the
respective background effects beneficially in an end use
application if required.
[0099] Information about the largest contribution from effects of
background amplitude
2.xi..sub.j.zeta..sub.j.vertline.A.sub.1.vertline..v-
ertline.B.sub.1.vertline. and phase
.phi..sub.A.sub..sub.1.sub.B.sub..sub.- 1.sub..epsilon..sub..sub.j,
i.e., the interference term between the reference beam and the
portion of background beam generated by the measurement beam 30A,
may be obtained by measuring S.sub.j for j=1, 2, 3, 4 as a function
of relative phase shift between reference beam and the measurement
beam 30A with substrate 60 removed and either
.vertline.A.sub.2.vertline.=0 or .vertline.A.sub.1.vertline.=0 and
visa versa and Fourier analyzing the measured values of S.sub.j.
Such information can be used to help identify the origin of the
respective background.
[0100] Other techniques may be incorporated into embodiments to
reduce and/or compensate for the effects of background beams
without departing from either the scope or spirit of the present
invention such as described in commonly owned U.S. Pat. No.
5,760,901 entitled "Method And Apparatus For Confocal Interference
Microscopy With Background Amplitude Reduction and Compensation,"
U.S. Pat. No. 5,915,048 entitled "Method and Apparatus for
Discrimination In-Focus Images from Out-of-Focus Light Signals from
Background and Foreground Light Sources," and U.S. Pat. No.
6,480,285 B1 wherein each of three patents are by Henry A. Hill.
The contents of each of the three cited patents are herein
incorporated in their entirety by reference.
[0101] The selection of values for .xi..sub.j' is based on
information about coefficients .xi..sub.j for j=1, 2, 3, 4 that may
be obtained by measuring the S.sub.j for j=1, 2, 3, 4 with only the
reference beam present in the interferometer system. In certain
embodiments, this may correspond simply blocking the measurement
beam components of input beam 24 and in certain other embodiments,
this may correspond to simply measuring the S.sub.j for j=1, 2, 3,
4 with substrate 60 removed. A test of the correctness of a set of
values for .xi..sub.j' is the degree to which the
(.vertline.A.sub.1.vertline..sup.2+.vertline.A.sub.2.vertline..-
sup.2) terms in Equations (3) and (4) are zero.
[0102] Information about coefficients .xi..sub.j.eta..sub.j for
j=1, 2, 3, 4 may be obtained by scanning an artifact past the spots
corresponding to the respective four conjugate detector pixels with
either .vertline.A.sub.2.vertline.=0 or
.vertline.A.sub.1.vertline.=0 and measuring the conjugated
quadratures component 2.vertline.A.sub.1.vertlin-
e..vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 or
2.vertline.A.sub.1.vertline..vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1, respectively. A change in
the amplitude of the
2.vertline.A.sub.1.vertline..vertline.C.sub.1.vertline.c- os
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 or
2.vertline.A.sub.1.vertline.- .vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 term corresponds to a
variation in .xi..sub.j.eta..sub.j as a function of j. Information
about the coefficients .xi..sub.j.eta..sub.j for j=1, 2, 3, 4 may
be used for example to monitor the stability of one or more
elements of interferometer system 10.
[0103] The bi-homodyne detection method described herein is a
robust technique for the determination of conjugated quadratures of
fields. First, the conjugated quadratures
.vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertline.si- n
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 are the primary terms in
the digitally filtered values F.sub.1 (S) and F.sub.2 (S),
respectively, as expressed by Equations (3) and (4), respectively,
since as noted in the discussion with respect to Equation (8), the
terms with the factors
(.vertline.A.sub.1.vertline..sup.2+.vertline.A.sub.2.vertline..sup.2)
and
(.vertline.B.sub.1.vertline..sup.2+.vertline.B.sub.2.vertline..sup.2)
are substantially zero.
[0104] Secondly, the coefficients of .vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.2.vertline.si- n
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 terms in Equations (3) and
(4) are identical. Thus highly accurate measurements of the
interference terms between the return measurement beam and the
reference beam with respect to amplitudes and phases, i.e., highly
accurate measurements of conjugated quadratures of fields can be
measured wherein first order variations in .xi..sub.j and first
order errors in normalizations such as (P.sub.j/P.sub.j') and
(.xi..sub.j.sup.2/.xi..sub.j'.sup.2) enter in only second or higher
order. This property translates into a significant advantage. Also,
the contributions to each component of the conjugated quadratures
.vertline.C.sub.1.vertline.cos .phi..sub.A.sub..sub.1.sub.C.s-
ub..sub.1 and .vertline.C.sub.2.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.- sub..sub.1 from a respective set of
four electrical interference signal values have the same window
function and thus are obtained as jointly determined values.
[0105] Other distinguishing features of the bi-homodyne technique
described herein are evident in Equations (3) and (4): the
coefficients of the conjugated quadratures
.vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertline.si- n
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 in Equations (3) and (4),
respectively, corresponding to the first equation of Equations (7)
are identical independent of errors in assumed values for
.xi..sub.j'; the coefficients of the conjugated quadratures
.vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertline.co- s
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 in Equations (3) and (4),
respectively, corresponding to the fourth equation of Equations (8)
are identical independent of errors in assumed values for
.xi..sub.j'. Thus highly accurate values of the phases
corresponding to conjugated quadratures can be measured with first
order variations in .xi..sub.j and first order errors in
normalizations such as (P.sub.j/P.sub.j') and
(.xi..sub.j.sup.2/.xi..sub.j'.sup.2) enter in only through some
high order effect.
[0106] It is also evident that since the conjugated quadratures of
fields are obtained jointly when using the bi-homodyne detection
method, there is a significant reduction in the potential for an
error in tracking phase as a result of a phase redundancy unlike
the situation possible in single-homodyne detection of conjugated
quadratures of fields.
[0107] There are a number of advantages of the bi-homodyne
detection method described herein as a consequence of the
conjugated quadratures of fields being jointly acquired quantities.
One advantage is a reduced sensitivity the effects of an overlay
error of a spot in or on the substrate that is being imaged and a
conjugate image of conjugate pixel of a multi-pixel detector during
the acquisition of four electrical interference signal values of
each spot in and/or on a substrate imaged using interferometric
far-field and/or near-field confocal and non-confocal microscopy.
Overlay errors are errors in the set of four conjugate images of a
respective set of conjugate detector pixels relative to the spot
being imaged.
[0108] Another advantage is that when operating in the scanning
mode there is a reduced sensitivity to effects of
pinhole-to-pinhole variations in properties of a conjugate set of
pinholes used in a confocal microscopy system that are conjugate to
a spot in or on the substrate being imaged at different times
during the scan.
[0109] Another advantage is that when operating in the scanning
mode there is a reduced sensitivity to effects of pixel-to-pixel
variation of properties within a set of conjugate pixels that are
conjugate to a spot in or on the substrate being imaged at
different times during the scan.
[0110] Another advantage is that when operating in the scanning
mode there is reduced sensitivity to effects of pulse sequence to
pulse sequence variations of a respective conjugate set of pulse
sequences of the input beam 24 to the interferometer system.
[0111] The pinholes and pixels of a multi-pixel detector of a set
of conjugate pinholes and conjugate pixels of a multi-pixel
detector may comprise contiguous pinholes of an array of pinholes
and/or contiguous pixels of a multi-pixel detector or may comprise
selected pinholes from an array of pinholes and/or pixels from an
array of pixels wherein the separation between the selected
pinholes is an integer number of pinhole spacings and the
separation between an array of respective pixels corresponds to an
integer number of pixel spacings without loss of lateral and/or
longitudinal resolution and signal-to-noise ratios. The
corresponding scan rate would be equal to the integer times the
spacing of spots on the measurement object 60 conjugate to set of
conjugate pinholes and/or set of conjugate pixels divided by the
read out rate of the multi-pixel detector. This property permits a
significant increase in throughput for an interferometric far-field
or near-field confocal or non-confocal microscope with respect to
the number of spots in and/or on a substrate imaged per unit
time.
[0112] Referring to the quad-homodyne detection method used in
various embodiments described herein, a set of four electrical
interference signal values are obtained for each spot on and/or in
substrate 60 being imaged with two pulse sequences from source 18
and beam-conditioner 22. The set of four electrical interference
signal values S.sub.j, j=1, 2, 3, 4 used for obtaining conjugated
quadratures of fields for a single a spot on and/or in a substrate
being imaged is represented for the quad-homodyne detection within
a scale factor by the formulae 9 S 1 = P 1 { 1 2 A 1 2 + 1 2 B 1 2
+ 1 2 C 1 2 + 1 1 2 B 1 C 1 cos B 1 C 1 1 + 1 1 2 A 1 B 1 cos A 1 B
1 1 + 1 1 1 2 A 1 C 1 cos A 1 C 1 + 1 2 A 2 2 1 2 B 2 2 + 1 2 C 2 2
+ 1 1 2 B 2 C 2 cos B 2 C 2 1 + 1 1 2 A 2 B 2 cos A 2 B 2 1 + 1 1 1
2 A 2 C 2 cos A 2 C 2 } , ( 10 ) S 2 = P 1 { 2 2 A 3 2 + 2 2 B 3 2
+ 2 2 C 3 2 + 2 2 2 B 3 C 3 cos B 3 C 3 2 + 2 2 2 A 3 B 3 cos A 3 B
3 2 + 2 2 2 2 A 3 C 3 cos A 3 C 3 + 2 2 A 4 2 2 2 B 4 2 + 2 2 C 4 2
+ 2 2 2 B 4 C 4 cos B 4 C 4 2 + 2 2 2 A 4 B 4 cos A 4 B 4 2 + 2 2 2
2 A 4 C 4 cos A 4 C 4 } , ( 11 ) S 3 = P 2 { 1 2 A 1 2 + 1 2 B 1 2
+ 1 2 C 1 2 + 1 1 2 B 1 C 1 cos B 1 C 1 3 + 1 1 2 A 1 B 1 cos A 1 B
1 3 + 3 1 1 2 A 1 C 1 cos A 1 C 1 + 1 2 A 2 2 1 2 B 2 2 + 1 2 C 2 2
+ 1 1 2 B 2 C 2 cos B 2 C 2 3 + 1 1 2 A 2 B 2 cos A 2 B 2 3 + 3 1 1
2 A 2 C 2 cos A 2 C 2 } , ( 12 ) S 4 = P 2 { 2 2 A 3 2 + 2 2 B 3 2
+ 2 2 C 3 2 + 2 2 2 B 3 C 3 cos B 3 C 3 4 + 2 2 2 A 3 B 3 cos A 3 B
3 4 + 4 2 2 2 A 3 C 3 cos A 3 C 3 + 2 2 A 4 2 2 2 B 4 2 + 2 2 C 4 2
+ 2 2 2 B 4 C 4 cos B 4 C 4 4 + 2 2 2 A 4 B 4 cos A 4 B 4 4 + 4 2 2
2 A 4 C 4 cos A 4 C 4 } , ( 13 )
[0113] where coefficients A.sub.1, A.sub.2, A.sub.3, and A.sub.4
represent the amplitudes of the reference beams corresponding to
the first, second, third, and fourth frequency components,
respectively, of input beam 24; coefficients B.sub.1, B.sub.2,
B.sub.3, and B.sub.4 represent the amplitudes of background beams
corresponding to reference beams A.sub.1, A.sub.2, A.sub.3, and
A.sub.4, respectively; coefficients C.sub.1, C.sub.2, C.sub.3, and
C.sub.4 represent the amplitudes of the return measurement beams
corresponding to reference beams A.sub.1, A.sub.2, A.sub.3, and
A.sub.4, respectively; P.sub.1 and P.sub.2 represent the integrated
intensities of the first frequency component in the first and
second pulse sequences, respectively, of the input beam 24; and the
values for .epsilon..sub.j and .gamma..sub.j are listed in Table 1.
The description of the coefficients .xi..sub.j, .zeta..sub.j, and
.eta..sub.j for the quad-homodyne detection method is the same as
the corresponding portion of the description given for .xi..sub.j,
.zeta..sub.j, and .eta..sub.j of the bi-homodyne detection
method.
[0114] It is assumed in Equations (10), (11), (12), and (13) that
the ratios of
.vertline.A.sub.2.vertline./.vertline.A.sub.1.vertline. and
.vertline.A.sub.4.vertline./.vertline.A.sub.3.vertline. are not
dependent on j or the value of P.sub.j. In order to simplify the
representation of S.sub.j so as to project the important features
without departing from either the scope or spirit of the present
invention, it is also assumed in Equations (10), (11), (12), and
(13) that the ratios of the amplitudes of the return measurement
beams corresponding to .vertline.A.sub.2.vertli-
ne./.vertline.A.sub.1.vertline. and
.vertline.A.sub.4.vertline./.vertline.- A.sub.3.vertline. are not
dependent on j or the value of P.sub.j. However, the ratios
.vertline.C.sub.2.vertline./.vertline.C.sub.1.vertline. and
.vertline.C.sub.4.vertline./.vertline.C.sub.3.vertline. will be
different from the ratios
.vertline.A.sub.2.vertline./.vertline.A.sub.1.vertline. and
.vertline.A.sub.4.vertline./.vertline.A.sub.3.vertline.,
respectively, when the ratio of the amplitudes of the measurement
beam components corresponding to
.vertline.A.sub.2.vertline./.vertline.A.sub.1- .vertline. and
.vertline.A.sub.4.vertline./.vertline.A.sub.3.vertline.,
respectively, are different from the ratios
.vertline.A.sub.2.vertline./.- vertline.A.sub.1.vertline. and
.vertline.A.sub.4.vertline./.vertline.A.sub- .3.vertline.,
respectively.
[0115] Noting that cos
.phi..sub.A.sub..sub.2.sub.C.sub..sub.2=.+-.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 by the control of the
relative phase shifts between corresponding reference and
measurement beam components in beam 32, Equations (10), (11), (12),
and (13) may be written, respectively, as 10 S 1 = P 1 { 1 2 ( A 1
2 + A 2 2 ) + 1 2 ( B 1 2 + B 2 2 ) + 1 2 ( C 1 2 + C 2 2 ) + 2 1 1
[ B 1 ; C 1 cos B 1 C 1 1 + B 2 ; C 2 cos B 2 C 2 1 ] + 2 1 1 [ 1 A
1 ; C 1 cos A 1 C 1 + 1 ( A 2 A 1 ) ( C 2 C 1 ) A 1 ; C 1 sin A 1 C
1 ] + 2 1 1 [ A 1 ; B 1 cos A 1 B 1 1 + A 2 ; B 2 cos A 2 B 2 1 ] }
, ( 14 ) S 2 = P 1 { 2 2 ( A 3 2 + A 4 2 ) + 2 2 ( B 3 2 + B 4 2 )
+ 2 2 ( C 3 2 + C 4 2 ) + 2 2 2 [ B 3 ; C 3 cos B 3 C 3 2 + B 4 ; C
4 cos B 4 C 4 2 ] + 2 2 2 ( A 3 A 1 ) ( C 3 C 1 ) [ 2 A 1 ; C 1 cos
A 1 C 1 + 2 ( A 4 A 3 ) ( C 4 C 3 ) A 1 ; C 1 sin A 1 C 1 ] + 2 2 2
[ A 3 ; B 3 cos A 3 B 3 2 + A 4 ; B 4 cos A 4 B 4 2 ] } , ( 15 ) S
3 = P 2 { 1 2 ( A 1 2 + A 2 2 ) + 1 2 ( B 1 2 + B 2 2 ) + 1 2 ( C 1
2 + C 2 2 ) + 2 1 1 [ B 1 ; C 1 cos B 1 C 1 3 + B 2 ; C 2 cos B 2 C
2 3 ] + 2 1 1 [ 3 A 1 ; C 1 cos A 1 C 1 + 3 ( A 2 A 1 ) ( C 2 C 1 )
A 1 ; C 1 sin A 1 C 1 ] + 2 1 1 [ A 1 ; B 1 cos A 1 B 1 3 + A 2 ; B
2 cos A 2 B 2 3 ] } , ( 16 ) S 4 = P 2 { 2 2 ( A 3 2 + A 4 2 ) + 2
2 ( B 3 2 + B 4 2 ) + 2 2 ( C 3 2 + C 4 2 ) + 2 2 2 [ B 3 ; C 3 cos
B 3 C 3 4 + B 4 ; C 4 cos B 4 C 4 4 ] + 2 1 1 [ 1 A 1 ; C 1 cos A 1
C 1 + 2 2 2 ( A 3 A 1 ) ( C 3 C 1 ) [ 4 A 1 ; C 1 cos A 1 C 1 + 4 (
A 4 A 3 ) ( C 4 C 3 ) A 1 ; C 1 sin A 1 C 1 ] + 2 2 2 [ A 3 ; B 3
cos A 3 B 3 4 + A 4 ; B 4 cos A 4 B 4 4 ] } , ( 17 )
[0116] where the relationship cos
.phi..sub.A.sub..sub.2.sub.C.sub..sub.2=- sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 has been used without
departing from either the scope or spirit of the present
invention.
[0117] Information about the conjugated quadratures
.vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertline.sin
.phi..sub.A.sub..sub.1.sub.C.sub..sub.- 1 are obtained using the
symmetric and antisymmetric properties and orthogonality property
of the conjugated quadratures as represented by the following
digital filters applied to the signal values S.sub.j: 11 F 3 ( S )
= ( 1 P 1 ' ) ( S 1 1 '2 - S 2 2 '2 ) - ( 1 P 2 ' ) ( S 3 1 '2 - S
4 2 '2 ) , ( 18 ) F 4 ( S ) = ( 1 P 1 ' ) ( S 1 1 '2 - S 2 2 '2 ) +
( 1 P 2 ' ) ( S 3 1 '2 - S 4 2 '2 ) . ( 19 )
[0118] The description of .xi..sub.j' and P.sub.j' for the
quad-homodyne detection method is the same as the corresponding
description given for .xi..sub.j' and P.sub.j' in the bi-homodyne
detection method. Using Equations (14), (15) (16), (17), (18), and
(19), the following expressions are obtained for the filtered
quantities containing components of the conjugated quadratures
.vertline.C.sub.1.vertline.cos
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1 and
.vertline.C.sub.1.vertline.si- n
.phi..sub.A.sub..sub.1.sub.C.sub..sub.1: 12 F 3 ( S ) = ( P 1 P 1 '
- P 2 P 2 ' ) [ ( A 1 2 + A 2 2 ) ( 1 2 1 '2 ) - ( A 3 2 + A 4 2 )
( 2 2 2 '2 ) ] + ( P 1 P 1 ' - P 2 P 2 ' ) [ ( B 1 2 + B 2 2 ) ( 1
2 1 '2 ) - ( B 3 2 + B 4 2 ) ( 2 2 2 '2 ) ] + ( P 1 P 1 ' - P 2 P 2
' ) [ ( C 1 2 + C 2 2 ) ( 1 2 1 '2 ) - ( C 3 2 + C 4 2 ) ( 2 2 2 '2
) ] + 2 ( P 1 P 1 ' + P 2 P 2 ' ) [ ( 1 1 1 '2 ) + ( 2 2 2 '2 ) ( A
3 A 1 ) ( C 3 C 1 ) A 1 ; C 1 cos A 1 C 1 + 2 ( P 1 P 1 ' + P 2 P 2
' ) ( A 2 A 1 ) ( C 2 C 1 ) [ ( 1 1 1 '2 ) + ( 2 2 2 '2 ) ( A 4 A 2
) ( C 4 C 2 ) ] A 1 ; C 1 sin A 1 C 1 + 2 ( P 1 P 1 ' cos A 1 B 1 1
- P 2 P 2 ' cos A 1 B 1 3 ) 1 1 1 '2 A 1 ; B 1 - 2 ( P 1 P 1 ' cos
A 3 B 3 2 - P 2 P 2 ' cos A 3 B 3 4 ) 2 2 2 '2 A 3 ; B 3 + 2 ( P 1
P 1 ' cos A 2 B 2 1 - P 2 P 2 ' cos A 2 B 2 3 ) 1 1 1 '2 A 2 ; B 2
- 2 ( P 1 P 1 ' cos A 4 B 4 2 - P 2 P 2 ' cos A 4 B 4 4 ) 2 2 2 '2
A 4 ; B 4 + 2 ( P 1 P 1 ' cos B 1 C 1 1 - P 2 P 2 ' cos B 1 C 1 3 )
1 1 1 '2 B 1 ; C 1 - 2 ( P 1 P 1 ' cos B 3 C 3 2 - P 2 P 2 ' cos B
3 C 3 4 ) 2 2 2 '2 B 3 ; C 3 + 2 ( P 1 P 1 ' cos B 2 C 2 1 - P 2 P
2 ' cos B 2 C 2 3 ) 1 1 1 '2 B 2 ; C 2 - 2 ( P 1 P 1 ' cos B 4 C 4
2 - P 2 P 2 ' cos B 4 C 4 4 ) 2 2 2 '2 B 4 ; C 4 , F 4 ( S ) = ( P
1 P 1 ' + P 2 P 2 ' ) [ ( A 1 2 + A 2 2 ) ( 1 2 1 '2 ) - ( A 3 2 +
A 4 2 ) ( 2 2 2 '2 ) ] + ( P 1 P 1 ' + P 2 P 2 ' ) [ ( B 1 2 + B 2
2 ) ( 1 2 1 '2 ) - ( B 3 2 + B 4 2 ) ( 2 2 2 '2 ) ] + ( P 1 P 1 ' +
P 2 P 2 ' ) [ ( C 1 2 + C 2 2 ) ( 1 2 1 '2 ) - ( C 3 2 + C 4 2 ) (
2 2 2 '2 ) ] + 2 ( P 1 P 1 ' - P 2 P 2 ' ) [ ( 1 1 1 '2 ) + ( 2 2 2
'2 ) ( A 3 A 1 ) ( C 3 C 1 ) A 1 ; C 1 cos A 1 C 1 + 2 ( P 1 P 1 '
+ P 2 P 2 ' ) ( A 2 A 1 ) ( C 2 C 1 ) [ ( 1 1 1 '2 ) + ( 2 2 2 '2 )
( A 4 A 2 ) ( C 4 C 2 ) ] A 1 ; C 1 sin A 1 C 1 + 2 ( P 1 P 1 ' cos
A 1 B 1 1 + P 2 P 2 ' cos A 1 B 1 3 ) 1 1 1 '2 A 1 ; B 1 - 2 ( P 1
P 1 ' cos A 3 B 3 2 + P 2 P 2 ' cos A 3 B 3 4 ) 2 2 2 '2 A 3 ; B 3
+ 2 ( P 1 P 1 ' cos A 2 B 2 1 + P 2 P 2 ' cos A 2 B 2 3 ) 1 1 1 '2
A 2 ; B 2 - 2 ( P 1 P 1 ' cos A 4 B 4 2 + P 2 P 2 ' cos A 4 B 4 4 )
2 2 2 '2 A 4 ; B 4 + 2 ( P 1 P 1 ' cos B 1 C 1 1 + P 2 P 2 ' cos B
1 C 1 3 ) 1 1 1 '2 B 1 ; C 1 - 2 ( P 1 P 1 ' cos B 3 C 3 2 + P 2 P
2 ' cos B 3 C 3 4 ) 2 2 2 '2 B 3 ; C 3 + 2 ( P 1 P 1 ' cos B 2 C 2
1 + P 2 P 2 ' cos B 2 C 2 3 ) 1 1 1 '2 B 2 ; C 2 - 2 ( P 1 P 1 '
cos B 4 C 4 2 + P 2 P 2 ' cos B 4 C 4 4 ) 2 2 2 '2 B 4 ; C 4 . ( 20
)
[0119] The parameters 13 [ ( A 2 A 1 ) ( C 2 C 1 ) ] , ( 21 ) ( A 4
A 2 ) ( C 4 C 2 ) , ( 22 ) [ ( A 3 A 1 ) ( C 3 C 1 ) ] ( 23 )
[0120] need to be determined in order to complete the determination
of a conjugated quadratures for certain end use applications. The
parameters given by Equations (21), (22), and (23) can for example
be measured by procedures analogous to the procedure described for
the bi-homodyne detection method with respect to measuring the
quantity specified by Equation (5).
[0121] The remaining description of the quad-homodyne detection
method is the same as corresponding portion of the description
given for the bi-homodyne detection method.
[0122] It is also evident that since the conjugated quadratures of
fields are obtained jointly when using the quad-homodyne detection,
there is a significant reduction in the potential for an error in
tracking phase as a result of a phase redundancy unlike the
situation possible in single-homodyne detection of conjugated
quadratures of fields.
[0123] There are a number of advantages of the quad-homodyne
detection described herein as a consequence of the conjugated
quadratures of fields being jointly acquired quantities.
[0124] One advantage of the quad-homodyne detection method in
relation to the bi-homodyne detection method is a factor of two
increase in throughput.
[0125] Another advantage is a reduced sensitivity the effects of an
overlay error of a spot in or on the substrate that is being imaged
and a conjugate image of a pixel of a conjugate set of pixels of a
multipixel detector during the acquisition of the four electrical
interference signal values of each spot in and/or on a substrate
imaged using interferometric far-field and/or near-field confocal
microscopy. Overlay errors are errors in the set of four conjugate
images of a respective set of conjugate detector pixels relative to
the spot being imaged.
[0126] Another advantage is that when operating in the scanning
mode there is reduced sensitivity to effects of pulse to pulse
variations of a respective conjugate set of pulses of the input
beam 24 to the interferometer system.
[0127] Another advantage is that when operating in the scanning
mode there is an increase in throughput since only one pulse of the
source is required to generate the four electrical interference
values.
[0128] A first embodiment is shown schematically in FIG. 2a. The
first embodiment comprises a first imaging system generally
indicated as numeral 110, pinhole beam-splitter 112, detector 170,
and a second imaging system generally indicated as numeral 210. The
second imaging system 210 is low power microscope having a large
working distance, e.g. Nikon ELWD and SLWD objectives and Olympus
LWD, ULWD, and ELWD objectives. The first imaging system 110
comprises the interferometric confocal microscopy system described
in cited commonly owned U.S. Provisional Application No. 60/442,982
(ZI-45).
[0129] The first imaging system 110 is shown schematically in FIG.
2b. The imaging system 110 is a catadioptric system such as
described in commonly owned U.S. Pat. No. 6,552,852 B1 (ZI-38)
entitled "Catoptric and Catadioptric Imaging System" and U.S.
patent application Ser. No. 10/366,651 filed Feb. 3, 2003 (ZI-43)
and entitled "Catoptric and Catadioptric Imaging System" for which
the patent and patent application are by Henry A. Hill and the
contents of the patent and patent application are incorporated
herein in their entirety by reference.
[0130] Catadioptric imaging system 110 comprises catadioptric
elements 140 and 144, beam splitter 148, and convex lens 150.
Surfaces 142A and 146A are convex spherical surfaces with nominally
the same radii of curvature and the respective centers of curvature
of surfaces 142A and 146A are conjugate points with respect to beam
splitter 148. Surfaces 142B and 146B are concave spherical surfaces
with nominally the same radii of curvature. The centers of
curvature of surfaces 142B and 146B are the same as the centers of
curvature of surfaces 146A and 142A, respectively. The center of
curvature of convex lens 150 is the same as the center of curvature
of surfaces 142B and 146A. The radius of curvature of surface 146B
is selected so as to minimize the loss in efficiency of the imaging
system 110 and to produce a working distance for imaging system 110
acceptable for an end use application. The radius of curvature of
convex lens 150 is selected so that the off-axis aberrations of the
catadioptric imaging system 110 are compensated. The medium of
elements 140 and 144 may be for example fused silica or
commercially available glass such as SF11. The medium of convex
lens 150 may be for example fused silica, YAG, or commercially
available glass such as SF11. An important consideration in the
selection of the medium of elements 140 and 144 and convex lens 150
will the transmission properties for the frequencies of beam
124.
[0131] Convex lens 152 has a center of curvature the same as the
center of curvature of convex lens 150. Convex lenses 150 and 152
are bonded together with pinhole beam-splitter 112 in between.
Pinhole array beam-splitter 112 is shown in FIG. 2c. The pattern of
pinholes in pinhole array beam-splitter is chosen to match the
requirements of an end use application. An example of a pattern is
a two dimensional array of equally spaced pinholes in two
orthogonal directions. The pinholes may comprise circular
apertures, rectangular apertures, or combinations thereof such as
described in commonly owned U.S. patent application Ser. No.
09/917,402 filed Jul. 27, 2001 (ZI-15) and entitled
"Multiple-Source Arrays for Confocal and Near-field Microscopy" by
Henry A. Hill and Kyle Ferrio. The contents of the cited patent
application are incorporated herein in its entirety by reference.
The spacing between pinholes of pinhole array beam-splitter 112 is
shown in FIG. 2c as b with aperture size a.
[0132] Input beam 124 is reflected by mirror 154 to pinhole
beam-splitter 112 where a first portion thereof is transmitted as
reference beam components of output beam 130A and 130B and a second
portion thereof scattered as measurement beam components of beams
126A and 126B. The measurement beam components 126A and 126B are
imaged as components of beams 128A and 128B to an array of image
spots in an image plane close to substrate 160. A portion of the
components of beams 128A and 128B incident on substrate 160 are
reflected and/or scattered as return measurement beam components of
beams 128A and 128B. Return measurement beam components of beams
128A and 128B are imaged by catadioptric imaging system 110 to
spots that are coincident with the pinholes of pinhole
beam-splitter 112 and a portion thereof is transmitted as return
measurement beam components of output beams 130A and 130B.
[0133] The description of the imaging properties of catadioptric
imaging system 110 is the same as the corresponding portion of the
description given for the imaging properties of catadioptric
imaging system 10 in cited U.S. Provisional Application No.
60/442,982 (ZI-45) and U.S. Patent Application filed Jan. 27, 2004
entitled "Interferometric Confocal Microscopy Incorporating Pinhole
Array Beam-Splitter".
[0134] The next step is the imaging of output beams 130A and 130B
by imaging system 210 to an array of spots that coincide with the
pixels of a multi-pixel detector such as a CCD to generate an array
of electrical interference signals 172. The array of electrical
interference signals is transmitted to signal processor and
controller 180 for subsequent processing.
[0135] The description of input beam 124 is the same as
corresponding portions of the description given for input beam 24
of FIG. 1a with beam-conditioner 122 configured as a two frequency
generator and frequency-shifter shown in FIG. 1c. Input beam 124
comprises two components that have different frequencies and have
the same state of plane polarization. The frequency of each
component of input beam 124 are shifted between two different
preselected frequency values by beam-conditioner 122 according to
control signal 174 generated by electronic processor and controller
180. Source 118 of beam 120 to beam-conditioner 122, such as a
laser, can be any of a variety of single frequency lasers.
[0136] The conjugated quadratures of fields of the return
measurement beams are obtained using the bi-homodyne detection as
described in the description of FIGS. 1a-1c wherein sets of four
measurements of the electrical interference signals 172 are made.
For each of the set of four measurements of the electrical
interference signals 172, a known sequence of phase shifts is
introduced between the reference beam component and the return
measurement beam component of output beams 130A and 130B.
[0137] The sequence of phase shifts is generated in the first
embodiment by shifting the frequencies of components of input beam
124 by beam-conditioner 122. There is a difference in optical path
length between the reference beam components and the return beam
components of output beams 130A and 130B and as a consequence, a
change in frequencies of components of input beam 124 will generate
corresponding phase shifts between the reference beam components
and the return beam components of output beams 130A and 130B. For
an optical path difference L between the reference beam components
and the return beam components of output beams 130A and 130B, there
will be for a frequency shift .DELTA.f a corresponding phase shift
.phi. where 14 = 2 L ( f c ) ( 24 )
[0138] and c is the free space speed of light. Note that L is not a
physical path length difference and depends for example on the
average index of refraction of the measurement beam and the return
measurement beam paths. For an example of a phase shift
.phi.=.pi./2 and a value of L=0.25 m, the corresponding frequency
shift .DELTA.f=300 MHz.
[0139] Referring to the quad-homodyne detection method used in
various embodiments, a set of four electrical interference signals
are obtained for each spot on and/or in substrate 60 being
imaged.
[0140] Two different modes are described for the acquisition of the
electrical interference signals 172. The first mode to be described
is a step and stare mode wherein substrate 160 is stepped between
fixed locations corresponding to locations where image information
is desired. The second mode is a scanning mode. In the step and
stare mode for generating a one-dimensional, a two-dimensional or a
three-dimensional profile of substrate 160, substrate 160 mounted
in wafer chuck 184/stage 190 is translated by stage 190. The
position of stage 190 is controlled by transducer 182 according to
servo control signal 178 from electronic processor and controller
180. The position of stage 190 is measured by metrology system 188
and position information acquired by metrology system 188 is
transmitted to electronic processor and controller 180 to generate
an error signal for use in the position control of stage 190.
Metrology system 188 may comprise for example linear displacement
and angular displacement interferometers and cap gauges.
[0141] Electronic processor and controller 180 translates wafer
stage 190 to a desired position and then acquires a set of four
electrical interference signal values corresponding. After the
acquisition of the sequence of four electrical interference
signals, electronic processor and controller 180 then repeats the
procedure for the next desired position of stage 190. The elevation
and angular orientation of substrate 160 is controlled by
transducers 186A and 186B.
[0142] The second mode for the acquisition of the electrical
interference signal values is next described wherein the electrical
interference signal values are obtained with the position of stage
190 scanned in one or more directions. In the scanning mode, source
118 is pulsed at times controlled by signal 192 from signal
processor and controller 180. Source 118 is pulsed at times
corresponding to the registration of the conjugate image of
pinholes of pinhole array beam-splitter 112 with positions on
and/or in substrate 160 for which image information is desired.
[0143] There will be a restriction on the duration or "pulse width"
of a beam pulse sequence .tau..sub.p1 produced by source 120 as a
result of the continuous scanning mode used in the third variant of
the first embodiment. Pulse width .tau..sub.p1 will be a parameter
that in part controls the limiting value for spatial resolution in
the direction of a scan to a lower bound of
.tau..sub.p1v, (25)
[0144] where v is the scan speed. For example, with a value of
.tau..sub.p1=50 nsec and a scan speed of v=0.20 m/sec, the limiting
value of the spatial resolution .tau..sub.p1v in the direction of
scan will be
.tau..sub.p1v=10 nm. (26)
[0145] Pulse width .tau..sub.p1 will also determine the minimum
frequency difference that can be used in the bi-homodyne detection.
In order that there be no contributions to the electrical
interference signals from interference between fields of conjugated
quadratures, the minimum frequency spacing .DELTA.f.sub.min is
expressed as 15 f min 1 p1 . ( 27 )
[0146] For the example of .tau..sub.p1=50 nsec, 1/.tau..sub.p1=20
MHz.
[0147] The frequencies of input beam 124 are controlled by signal
174 from signal processor and controller 180 to correspond to the
frequencies that will yield the desired phase shifts between the
reference and return measurement beam components of output beams
130A and 130B. In the first mode for the acquisition of the
electrical interference signals 172, the set of four electrical
interference signals corresponding to a set of four electrical
interference values are generated by common pixels of detector 170.
In the second mode for the acquisition of electrical interference
signals 172, a set of four electrical interference signal values
are not generated by a common pixel of detector 170. Thus in the
second mode of acquisition, the differences in pixel efficiency and
the differences in sizes of pinholes in pinhole array beam-splitter
112 are compensated in the signal processing by signal processor
and controller 180 as described in the description of the
bi-homodyne detection given with respect to FIGS. 1a-1c. The joint
measurements of conjugated quadratures of fields are generated by
electric processor and controller 180 as previously described in
the description of the bi-homodyne detection method.
[0148] A second embodiment comprises the interferometer system of
FIGS. 1a-1c with interferometer 10 comprising an interferometric
far-field confocal microscope such as described in cited U.S. Pat.
No. 5,760,901. In the second embodiment, beam-conditioner 22 is
configured as the two frequency generator and phase-shifter shown
in FIG. 1b. Embodiments in cited U.S. Pat. No. 5,760,901 are
configured to operate in either the reflection or transmission
mode. The second embodiment has reduced effects of background
because of background reduction features of cited U.S. Pat. No.
5,760,901.
[0149] A third embodiment comprises the interferometer system of
FIGS. 1a-1c with interferometer 10 comprising an interferometric
far-field confocal microscope such as described in cited U.S. Pat.
No. 5,760,901 wherein the phase masks are removed. In the third
embodiment, beam-conditioner 22 is configured as the two frequency
generator and phase-shifter shown in FIG. 1b. Embodiments in cited
U.S. Pat. No. 5,760,901 are configured to operate in either the
reflection or transmission mode. The third embodiment with the
phase masks of embodiments of cited removed U.S. Pat. No. 5,760,901
represent applications of confocal techniques in a basic form.
[0150] A fourth embodiment comprises the interferometer system of
FIGS. 1a-1c with interferometer 10 comprising an interferometric
far-field confocal microscope such as described in cited U.S. Pat.
No. 6,480,285 B1. In the fourth embodiment, beam-conditioner 22 is
configured as the two-frequency generator and phase-shifter shown
in FIG. 1b. Embodiments in cited U.S. Pat. No. 6,480,285 B1 are
configured to operate in either the reflection or transmission
mode. The fourth embodiment has reduced effects of background
because of background reduction features of cited U.S. Pat. No.
6,4980,285 B1.
[0151] A fifth embodiment comprises the interferometer system of
FIGS. 1a-1c with interferometer 10 comprising an interferometric
far-field confocal microscope such as described in cited U.S. Pat.
No. 6,480,285 B1 wherein the phase masks are removed. In the fifth
embodiment, beam-conditioner 22 is configured as the two-frequency
generator and phase-shifter shown in FIG. 1b. Embodiments in cited
U.S. Pat. No. 6,480,285 B1 are configured to operate in either the
reflection or transmission mode. The fifth embodiment with the
phase masks of embodiments of cited removed U.S. Pat. No. 6,480,285
B1 represent applications of confocal techniques in a basic
form.
[0152] A sixth embodiment comprises the interferometer system of
FIGS. 1a-1c with interferometer 10 comprising an interferometric
near-field confocal microscope such as described in U.S. Pat. No.
6,445,453 entitled "Scanning Interferometric Near-Field Confocal
Microscopy" by Henry A. Hill, the contents of which are herein
incorporated in their entirety by reference. In the sixth
embodiment, beam-conditioner 22 is configured as the two-frequency
generator and phase-shifter shown in FIG. 1b. Embodiments in cited
U.S. Pat. No. 6,445,453 are configured to operate in either the
reflection or transmission mode. The fifth embodiment of cited U.S.
Pat. No. 6,445,453 in particular is configured to operate in the
transmission mode with the measurement beam separated from the
reference beam and incident on the substrate being imaged by a
non-confocal imaging system, i.e., the measurement beam at the
substrate is not an image of an array of pinholes but an extended
spot. Accordingly, the corresponding embodiments of the sixth
embodiment represent an application of bi-homodyne detection method
in a non-confocal configuration for the measurement beam.
[0153] Interferometer 10 may comprise an interferometric apparatus
such as described in U.S. Pat. No. 4,685,803 entitled "Method And
Apparatus For The Measurement Of The Refractive Index Of A Gas" or
U.S. Pat. No. 4,733,967 entitled "Apparatus Of The Measurement Of
The Refractive Index Of A Gas" configured for bi-homodyne
detection. Both of the cited patents are by Gary E. Sommargren and
the contents of both cited patents are herein incorporated in their
entirety by way of reference. Embodiments which comprise
interferometric apparatus such as described in the two cited U.S.
patents represents configurations of a non-confocal type.
[0154] Interferometer 10 may comprise a .GAMMA. monitor such as
described in U.S. Pat. No. 6,124,931 entitled "Apparatus And
Methods For Measuring Intrinsic Optical Properties Of A Gas" by
Henry A. Hill, the contents of which are here within incorporated
in their entirety by way of reference. For embodiments which
comprise interferometric apparatus such as described in the cited
U.S. patent, the described .GAMMA. monitor is configured for
bi-homodyne detection and the embodiments represent configurations
that are of a non-confocal type.
[0155] Interferometer 10 may comprise a wavelength monitor such as
described in U.S. Patent Provisional Application No. 60/337,459
entitled "A Method For Compensation For Effects Of Non-Isotropic
Gas Mixtures In Single-Wavelength And Multiple-Wavelength
Dispersion Interferometry" [Z-384, Z-339] by Henry A. Hill, the
contents of which are here within incorporated in their entirety by
way of reference. For embodiments which comprise interferometric
apparatus such as described in the cited U.S. patent, the
wavelength monitor is configured for bi-homodyne detection and the
embodiments represent configurations that are of a non-confocal
type.
[0156] Interferometer 10 may further comprise any type of
interferometer, e.g., a differential plane mirror interferometer, a
double-pass interferometer, a Michelson-type interferometer and/or
a similar device such as is described in an article entitled
"Differential Interferometer Arrangements For Distance And Angle
Measurements: Principles, Advantages And Applications" by C.
Zanoni, VDI Berichte Nr. 749, 93-106 (1989) configured for
bi-homodyne detection. Interferometer 10 may also comprise a
passive zero shear plane mirror interferometer as described in U.S.
patent application Ser. No. 10/207,314 entitled "Passive Zero Shear
Interferometers" or an interferometer with a dynamic beam steering
element such as described in U.S. Patent Application with Ser. No.
09/852,369 entitled "Apparatus And Method For Interferometric
Measurements Of Angular Orientation And Distance To A Plane Mirror
Object" and U.S. Pat. No. 6,271,923 entitled "Interferometry System
Having A Dynamic Beam Steering Assembly For Measuring Angle And
Distance," all of which are by Henry A. Hill. For embodiments which
comprise interferometric apparatus such as described in the cited
U.S. patents and the article by Zanoni, the described
interferometers are configured for bi-homodyne detection and the
embodiments represent configurations that are of a non-confocal
type. The contents of the article by Zanoni and the three cited
patents by Hill are herein incorporated in their entirety by
reference. The interferometer can be designed to monitor, for
example, changes in optical path length, changes in physical path
length, changes in wavelength of a beam, or changes in direction of
propagation of a beam.
[0157] Interferometer 10 may further comprise a dispersion
interferometer such as described in U.S. Pat. No. 6,219,144 B1
entitled "Apparatus and Method for Measuring the Refractive Index
and Optical Path Length Effects of Air Using Multiple-Pass
Interferometry" by Henry A. Hill, Peter de Groot, and Frank C.
Demarest and U.S. Pat. No. 6,407,816 entitled "Interferometer And
Method For Measuring The Refractive Index And Optical Path Length
Effects Of Air" by Peter de Groot, Henry A. Hill, and Frank C.
Demarest. The contents of both of the cited patents are herein
incorporated in their entirety by reference. For embodiments which
comprise interferometric apparatus such as described in the cited
U.S. patents, the described interferometers are configured for
bi-homodyne detection and the embodiments represent configurations
that are of a non-confocal type.
[0158] Other embodiments may use the quad-homodyne detection method
instead of the bi-homodyne detection method as variants of the
embodiments. For the embodiments that are based on the apparatus
shown in FIGS. 1a-1c, the corresponding variants of the embodiments
that use the quad-homodyne detection method use variants of the
apparatus shown in FIGS. 1a-1c. In the variants of the apparatus
such as used in the first embodiment, microscope 220 is modified to
include a dispersive element such as a direct vision prism and/or a
dichroic beam-splitter. When configured with a dichroic
beam-splitter, a second detector is further added to the system.
Descriptions of the variants of the apparatus are the same as
corresponding portions of descriptions given for corresponding
systems in cited U.S. Provisional Application No. 60/442,982
[ZI-45]. Corresponding variants of apparatus are used for
embodiments that comprise interferometers such as linear
displacement interferometers.
* * * * *