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Claims  |
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What is claimed is:
1. A method of producing information representing the distribution of the
phase difference between first and second interfering beams, the first and
second interfering beams producing an interference pattern, the method
comprising the steps of:
(a) changing the phase difference between the first and second beams at a
constant rate;
(b) guiding the interference pattern into an array of photodetectors;
(c) integrating photocurrents produced by the individual photodetectors,
respectively, to produce integrated buckets that correspond to intensities
of various points across the interference pattern;
(d) measuring first, second, third and fourth integrated buckets produced
by each photodetector at times that correspond to first, second, third,
and fourth approximately 90 degree changes in the phase difference between
the first and second beams while continuously maintaining the rate of
change of the phase difference between the first and second beams at a
constant value;
(e) computing a first phase value corresponding to each photodetector from
the first, second, and third integrated buckets produced by that
photodetector;
(f) computing a second phase value, corresponding to each photodetector,
from the second, third, and fourth integrated buckets produced by that
photodetector; and
(g) adding the first and second phase values corresponding to each of the
photodetectors to cancel sinusoidal error produced by small errors in the
approximately 90 degree changes in the phase difference between the first
and second beams.
2. The method of claim 1 wherein the second beam is a reference beam and
step (a) includes changing the phase of the reference beam at the constant
rate.
3. The method of claim 2 wherein the reference beam is produced by varying
the phase of a first portion of a beam produced by a light source, and the
second beam is produced by reflecting a second portion of the light source
beam from a test surface to produce a test beam.
4. The method of claim 3 including using a two-beam interferometer to
produce the reference beam and the test beam, and varying the phase of the
reference beam by moving a reference mirror reflecting a portion of the
light source beam at a constant velocity, and moving the reference mirror
by applying a constant slope voltage ramp signal to a piezoelectrical
transducer supporting the reference mirror, before performing step (d).
5. The method of claim 4 including allowing the piezoelectric transducer
and reference mirror to attain a constant velocity before producing any of
the integrated buckets to eliminate nonlinearities in the phase shift
between the first and second phases.
6. The method of claim 1 wherein step (c) includes conducting photocurrents
of the photodetectors into a plurality of integrated bucket capacitors,
respectively, to produce the integrated buckets.
7. The method of claim 6 wherein the measuring of step (d) includes
strobing various transfer devices coupling the respective integrated
bucket capacitors to corresponding cells of a shift register device to
discharge the integrated buckets from the integrated bucket capacitors
into corresponding cells of the shift register device and to begin
producing of subsequent integrated buckets.
8. The method of claim 7 including sequentially shifting the integrated
buckets out of the shift register to produce an analog signal having
various analog levels that represent the magnitudes of the various
integrated buckets, respectively, amplifying the analog levels, and
converting them to digital numbers, and reading the digital numbers
representing the various integrated bucket magnitudes by means of a
computer.
9. The method of claim 8 including performing steps (e), (f), and (g) by
means of the computer.
10. The method of claim 1 wherein step (e) includes computing the first
phase in accordance with the equation
.phi..sub. (x)=arctangent (C-B)/(A-B),
and step (f) includes computing the second phase in accordance with the
equation
.phi..sub.2 (x)=arctangent (D-C)/(B-C),
wherein A is the magnitude of the first integrated bucket, B is the
magnitude of the second integrated bucket, C is the magnitude of the third
integrated bucket, and D is the magnitude of the fourth integrated bucket,
and wherein step (g) includes producing an average phase in accordance
with the equation
.phi.=(.phi..sub.1 (x)+.phi..sub.2 (x))/2.
11. The method of claim 10 wherein the first beam is a test beam reflected
from a test surface, the method including computing the height of
variations in the test surface in accordance with the equation
h(x)=(.lambda./(4.pi.).phi.(x).
12. The method of claim 10 further including determining if modulation of
intensity of the reference beam caused in response to variations in the
phase difference between the first and second beams exceeds a
predetermined noise threshold before computing the first and second
phases.
13. The method of claim 12 including assigning a predetermined mask value
to an average phase variable for a particular photodetector if the
modulation of the intensity corresponding to that photodetector does not
exceed the predetermined noise threshold.
14. The method of claim 12 including determining whether the modulation of
the intensity exceeds the predetermined noise threshold by performing the
steps of comparing the absolute values of C-B, A-B, D-C, and B-C to the
predetermined noise threshold and determining that the modulation of
intensity is greater than the noise threshold if at least one of those
quantities is greater than the predetermined noise threshold.
15. The method of claim 1 including determining a first group of
intensities corresponding to integrated buckets produced by a
predetermined group of photocells at a first phase difference between the
first and second beams, shifting the phase difference between the first
and second beams by 180 degrees, determining a second group of intensities
detected by the same group of photocells, respectively, from the
integrated buckets produced thereby, adding corresponding first and second
intensities to cancel variations due to interference between the first and
second beams and to obtain an average intensity value, and adjusting the
filament voltage of a light source from which the first and second beams
are derived so that the average intensity value equals a predetermined
intensity level.
16. The method of claim 1 wherein the small errors are in the range of zero
degrees to approximately five degrees.
17. A method of providing information representing the distribution of
phase difference between first and second interfering beams, the first and
second interfering beams producing an interference pattern, the method
comprising the steps of:
(a) changing the phase difference between the first and second beams at a
constant rate;
(b) guiding the interference pattern into a photodetector;
(c) integrating the interference pattern by of the photodetector to produce
integrated buckets that correspond intensities of various points across
the interference pattern;
(d) measuring first, second, third, and fourth integrated buckets produced
by the photodetector at times that correspond to first, second, third, and
fourth approximately 90 degree changes in the phase difference between the
first and second beams while continuously maintaining the rate of change
of the phase difference between the first and second beams at a constant
value;
(e) computing a first phase value from the first, second, and third
integrated buckets;
(f) computing a second phase value from the second, third, and fourth
integrated buckets; and
(g) adding the first and second phase values to cancel sinusoidal error
produced by small errors in the 90 degree changes in the phase difference
between the first and second beams.
18. An interferometric apparatus comprising:
(a) means for producing first and second beams and causing the first and
second beams to interfere, producing an interference pattern;
(b) means for changing a phase difference between the first and second
beams at a constant rate;
(c) means for guiding the interference pattern into an array of
photodetectors, the array of photodetectors including means for
integrating photocurrents produced by the individual photodetectors,
respectively, to produce integrated buckets that correspond to intensities
of various points across the interference pattern;
(d) means for measuring first, second, third and fourth integrated buckets
produced by each photodetector at times that correspond to first, second,
third, and fourth approximately 90 degree changes in the phase difference
between the first and second beams while the rate of change in the phase
difference between the first and second beams remain constant;
(e) means for computing a first phase value corresponding to each
photodetector from the first, second, and third integrated buckets
produced by that photodetector;
(f) means for computing a second phase value, corresponding to each
photodetector, from the second, third, and fourth integrated buckets
produced by that photodetector; and
(g) means for adding the first and second phase values corresponding to
each of the photodetectors to cancel sinusoidal error produced by small
errors in the approximately 90 degree changes in the phase difference
between the first and second beams.
19. The interferometric apparatus of claim 18 wherein the small errors are
in the range from zero degrees to approximately five degrees.
20. The interferometric apparatus of claim 18 wherein the array of
photodetectors is included in a self-scanning optical sensor array device
having a plurality of clock input conductors and an analog output
conductor on which voltages representative of integrated buckets scanned
in response to the clock inputs are sequentially output, respectively.
21. The interferometric apparatus of claim 20 wherein the measuring means
includes clock and data acquisition circuitry for producing a plurality of
clock signals applied to the clock input conductors of the self-scanning
optical sensor array device, a computer, an interface circuit coupled
between the computer and the clock and data acquisition circuitry, a
piezoelectric transducer driver circuit, and wherein the phase difference
changing means includes a piezoelectric transducer responsive to the
piezoelectric transducer driver circuit and a reference mirror supported
by the piezoelectric transducer and reflecting one of the first and second
beams and movable to vary the phase of that beam.
22. The interferometric apparatus of claim 21 wherein the clock and data
acquisition ciruitry includes an amplifier for amplifying the voltages
representative of the integrated buckets produced by the self-scanning
optical sensor array device and an analog-to-digital converter for
converting the amplified voltages into digital representations of the
respective integrated buckets, the interface circuit including means for
interfacing between the computer and the output of the analog-to-digital
converter to enable the computer to read the digital representations of
the integrated buckets in synchronization with the scanning of the
self-scanning optical sensor array device.
23. The interferometric apparatus of claim 22 wherein the piezoelectric
transducer driver circuit includes an address circuit that is incremented
by one of the clock signals in synchronization with the clocking of the
self-scanning optical sensor array device, a random access memory couple
to the computer for storing information representative of a voltage ramp
signal, a digital-to-analog converter for converting data output the
random access memory in response to the address circuit for producing the
voltage ramp signal, and an output amplifier for producing an amplified
voltage ramp signal and applying it to the piezoelectric transducer.
24. The interferometric apparatus of claim 21 including means for allowing
the piezoelectric transducer and the reference mirror supported thereby to
attain a constant velocity before the measuring means begins measuring the
first, second, and fourth integrated buckets. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
The invention relates to minimizing inaccuracies in two-beam interferometer
measurements that are due to vibration, temperature variations, air
turbulence, nonlinearities in the phase of the reference beam, and errors
in the starting points of a phase shifting mirror of the interferometer.
Use of phase shifting interferometry to make optical profilers or
profilometers to measure the roughness of a test surface is known, for
example, as described in "An Optical Profilometer for Surface
Characterization of Magnetic Media", presented by Wyant et al. at the 38th
Annual Meeting of the ASLE (American Society of Lubrication Engineers) in
Houston, Tex., Apr. 24-28, 1983 and incorporated herein by reference, and
also as described in "Optical Profilers for Surface Roughness", by Wyant,
published in the Proceedings of the International Society for Optical
Engineers, Vol. 525, Jan. 21-22, 1985, a copy of which is attached hereto
as Appendix A. One phase shifting technique provides more effective and
accurate height measurements than can be obtained by viewing interference
fringes and measuring how far they depart from being straight and equally
spaced, is the "phase stepping" technique, described in the foregoing
references. Another phase shifting technique, first described by Wyant in
"Use of an AC Hetrodyne Lateral Shear Inteferometer with Real-Time
Wavefront Correction Systems", Applied Optics, Volume 14, No. 11, November
1975, page 2622, and incorporated herein by reference, is known as the
integrating-bucket technique, wherein the reference mirror of the
interferometer is moved at a constant velocity, rather than a stepped
velocity. The integrating-bucket technique is often preferred, since less
vibration is introduced into the system than when the movement of the
interferometer mirror is stepped.
Those skilled in the art will recognize that any vibration of
interferometry apparatus results in measurement inaccuracies. For example,
in an optical profiler in which measurement techniques that approach the
limits of the present state of the art, variations in air turbulence, and
expansion and contraction of the apparatus as a result of changes in
temperature, nonlinearities and calculation in the piezoelectric
transducer and environmental effects on the piezoelectric transducer also
are sources of significant error in the phase calculations and hence in
the height measurements that must be made. As another example, in a laser
diode tester using interferometry techniques to measure an interference
pattern by means of a photodetector array and utilizing integrated bucket
techniques to obtain the needed phase computations, the foregoing
variations also are sources of significant error.
One approach for reducing such inaccuracies has been to use the single
pass, four-bucket integrating technique, wherein all four "buckets" are
utilized in a single calculation to obtain the phase for each detected
point across the inteference pattern, as described by Wyant in the above
November, 1975 article. This technique suffers from certain shortcomings,
the main one being that it does not result in effective cancellation of
sinusoidal error caused by phase differences other than 90.degree. between
the integrated buckets, so severe errors are introduced phase computations
by slight (i.e., half degree) errors in the 90.degree. phase shifts that
constitute the integrating boundaries of the integrated buckets. Another
prior approach has been to make a second pass and "collect" four more
integrated buckets and use them to compute a second phase value, with the
reference beam phase 90.degree. different than for the first phase value,
and then average the first and second phase values. This technique, which
is described in "Digital Wave-Front Measuring Interferometer: Some
Systematic Error Sources" by Schwider, Applied Optics, November 1983,
Volume 22, No. 21, page 3421, does not avoid errors caused by vibration
and the other above-mentioned sources of error.
As those skilled in the art realize, there are numerous subtleties in the
physics of interferometry. Slight alterations in the structure of the
apparatus used and/or in the method of operating the apparatus may result
in unexplained errors and/or anomalous results.
Thus, despite a strong market demand for faster, more accurate optical
profilers, and despite extensive continuing research in the art, there
still remains an unmet need for a reasonably priced optical profilometer
(and other interferometry-based apparatus) that avoid the above-indicated
sources of error more effectively than the prior art.
SUMMARY OF THE INVENTION
Accordingly, it is an object of the invention to provide an improved
integrated bucket technique for determining phase variations in
interference patterns in a two beam interferometer, in such a manner as to
avoid introducing vibration into the system, to avoid inaccuracies in the
measured phase of the interference pattern caused by vibration in the
system, to avoid inaccuracies in the phase measurements due to rapid
variations in temperature of the ambient air, and to avoid variations due
to thermally caused changes in the dimensions of the apparatus.
It is another object of the invention to avoid inaccuracies due to errors
in the phase shifts that constitute the integrating boundaries of an
integrated bucket.
It is another object of the invention to provide an improved non-contact
optical profiler using integrated bucket phase and test surface height
interferometry techniques.
It is another object of the invention to avoid errors due to nonlinearities
in the constant velocity phase shift in an integrated bucket
interferometer.
It is another object of the invention to avoid return errors of the
reference mirror in a two-beam interferometry system.
It is another object of the invention to avoid inaccuracies due to
calibration errors and other errors in a piezoelectric transducer in a
two-beam interferometer.
It is another object of the invention to provide an improved technique for
"masking" inaccurate data points in an integrated bucket interferometer.
Briefly described, and in accordance with one embodiment thereof, the
invention provides an improved single-pass, four-bucket, dual three-bucket
computation integrated bucket technique for two-beam interferometers
wherein the effects of fixed-pattern noise and gain variation across a
photodetector array are cancelled, and effects of system vibration, rapid,
thermally induced dimensional changes in the apparatus, fluctuations in
air density and temperature, and reference mirror return errors are
reduced. In one embodiment of the invention, a non-contact optical
profiler or profilometer is provided wherein a Mirau interferometer is
illuminated through a conventional microscope illumination system. The
reference mirror of the interferometer is moved by a piezoelectric
transducer in response to a ramp voltage signal applied thereto. An
interference light pattern produced by interference between light
reflected from a test surface and the interferometer reference mirror is
directed onto a 256.times.256 array of photodiodes, the photocurrents of
which are integrated by integrated bucket capacitors, analog voltage
levels of which are discharged into cells of a bucket-brigade type of
shift register in accordance with clock signals produced by a clock
generator circuit. Ramping of the piezoelectric transducer driver circuit
is synchronized with readout of the photodiode array, so that, after an
initial time has been allowed for a reference mirror to attain constant
velocity, the integrated buckets produced by the entire photodiode array
are discharged into the shift register cells and then read out as the
constant velocity reference mirror moves enough to change the phase of the
inteference beam by approximately 90.degree., to provide a first
integrated bucket. Three more integrated buckets are provided as the
reference mirror maintains the constant velocity to complete a single
pass, after which the reference mirror returns to its starting points.
Each integrated bucket is obtained by reading out a voltage representative
of the integrated currents for the entire array every time the reference
mirror has moved enough to change the phase of the reference beam by
approximately 90.degree.. The first, and second, and third integrated
buckets are utilized to compute a first value of the phase of the
interference pattern, and the second, third, and fourth integrated bucket
values are used to compute a second phase value. The first and second
phase values are averaged, thereby cancelling sinusoidal error caused by
inpreciseness in the desired 90.degree. phase changes during which the
four integrated buckets for each photodetector are produced. Data points
corresponding to each photocell of the array are tested to determine
whether a sufficiently high degree of modulation of the intensity of the
interference pattern is produced in response to the variations in the
phase of the reference beam that the corresponding data point can be
considered meaningful. If not, a value is assigned to the average phase
indicating that it is an invalid data point. Automatic control of the
intensity of the lamp illuminating the Mirau interferometer is achieved by
averaging two intensity measurements that are taken with the phase
differences between the two interfering beams 180.degree. apart. The two
intensity measurements are averaged, cancelling the effect of the
interference. The filament voltage of the lamp is adjusted to cause the
average intensity to equal a predetermined value.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of a non-contact optical profiler of the
present invention.
FIG 1A is a detailed block diagram of the clock and data acquisition
circuitry of FIG. 1.
FIG. 1B is a detailed block diagram of a piezoelectric transducer driver
circuit of FIG. 1.
FIGS. 2A and 2B are diagrams illustrating constant velocity movement of the
reference mirror in the optical profiler of FIG. 1 for two different kinds
of photodetection arrays, respectively.
FIG. 3 is a flow chart of a routine executed by the computer of FIG. 1 to
automatically control intensity of the lamp of FIG. 1.
FIG. 4 is a block diagram of a program executed by the computer of FIG. 1
to mask out bad data points obtained in scanning the photodiode array of
FIG. 1.
FIG. 5 is a schematic diagram of a laser diode tester embodiment of the
present invention.
DESCRIPTION OF THE INVENTION
Referring first to FIG. 1, reference numeral 10 designates an optical
profiler of the present invention, including a tungsten light source 11.
Tungsten light source 11 produces a beam 13 that is focused by a lens 12
to produce a collimated beam 14 that is further focused by a lens 15 to
produce beam 16. Beam 16 passes through an aperture in a field stop 17 to
another lens 18. The resulting beam 21 passes through an aperture stop 19
and a spectral filter 20 to produce a beam 22 that impinges upon a beam
splitter 23. Lenses 12 and 15 and field stop 17 are components of a
commercially available illuminator sold by Nikon as FE Illuminator Part
No. 79500.
Beam 22 is reflected downward in FIG. 1 by beam splitter 23, producing beam
31, which passes into a microscope objective 33 and a lens 34 therein,
also available from Nikon as Part No. 79101 or 79100. The beam 31 is
thereby focused to produce beam 36, which enters a Mirau interferometer, a
reference mirror 41 and transparent mirror support plate 35 of which are
supported by a piezoelectric transducer (PZT) designated by reference
numeral 32.
The Mirau inteferometer also includes a beam splitter 39. Beam 36 passes
through mirror support 35, is refracted slightly, and emerges as beam 38.
Part of beam 38 impinges on beam splitter 39 and is reflected upward as
beam 37. Beam 37 is reflected as a reference beam 37A from reference
surface 41 back to beam splitter 39.
Part of the light 38 passes through beam splitter 39, as indicated by
reference numeral 40. Beam 40 then is reflected from the irregular upper
surface of the test surface 42, as indicated by reference numeral 40A.
An interference pattern is created at beam splitter 39 as a result of
interference between beams 37A and 40A, producing an interference pattern
on beam 43, passing upward through lens 34, the intensity of which is, of
course, a function of the difference in phase between beams 37A and 40A.
The spacing between the reference surface 41 and the beam splitter surface
39 is varied in accordance with the graph shown in FIG. 2, in response to
an electrical ramp signal on conductor 47 that is proportional to the
vertical movement of the reference surface 41 produced by piezoelectric
transducer 32.
The interference beam 43 passes upward through beam splitter 23, as
indicated by reference numeral 24, is focused by lens 25 onto a 256 by 256
photodiode array, which can be an RA256-x-256 photodiode array
manufactured by E. G. & G. Reticon of Sunnyvale, Calif. Eyepiece 30 allows
an operator to visualize the point of the test surface 42 at which optical
profiling is being performed.
The microscope assembly including eyepiece 30, lens 25, beam splitter 23,
objective 33 and lens 34 therein is a Model 79007 or 79500 produced by
Nikon. The piezoelectrical transducer (PZT) 32 can be a Model PZ-91,
obtained from the Burleigh Company.
The photodiode array 26 is scanned by signals produced on lines 27A by
clock and data acquisition circuit 28. The E. G. & G. Reticon RA256-x-256
includes internal multiplexing circuitry that decodes the seven lines 27A
to produce the necessary diode-by-diode scanning of the 65,536 photodiodes
in array 26 to produce 65,536 sequential analog levels representing the
integrated light intensity of each on conductor 27, which is also
connected to clock and data acquisition circuit 28. The photocurrent
produced by each photodiode is continuously integrated by causing that
photocurrent to flow into a corresponding integrated bucket capacitor that
is coupled to a corresponding cell an analog bucket-brigade type of shift
register. The photodiodes in corresponding shift register cells are
arranged in rows that can be separately strobed each time the phase of the
reference beam 37A changes by 90.degree.. Such strobing turns on transfer
gates that discharge the integrated bucket capacitors into the
corresponding shift register cells to produce analog voltages that are
stored, row-by-row, in the shift register and represent the magnitudes of
the "integrated buckets". The "integrated buckets" are quantities that are
used in computation of the phase variations across the interference beam
43 and the height variations of the test surface 42, as subsequently
explained in detail. As the integrated bucket capacitors are recharged,
the analog voltages representing the prior integrated buckets, which
analog voltages are now stored in the shift register, are synchronously
clocked out to produce a "video" type of analog signal on conductor 27
while the next set of integrated buckets is being generated and
"collected" by the integrated bucket capacitors within the E. G & G.
Reticon photodiode array 26. Clock and data acquisition circuitry 28
produces 10 output bits 44 that are digital representations of the 65,536
integrated buckets collected from photodiode array 26. These 10 bit
digital numbers are formatted by interface circuit 43 so that they can be
properly read by computer 29, which in the preferred embodiment of the
invention is a Hewlett-Packard Model 320 desk top computer.
Computer bus 45, which includes an address bus 45A and a data bus 45B (FIG.
1B), is connected to interface circuit 43, computer 29, and PZT control
circuit 46. During each complete data acquisition cycle, during which all
65,536 integrated buckets are collected, PZT control circuit 46 generates
a ramp control signal on conductor 47 that causes the piezoelectric
transducer 32 to move the inteferometer reference mirror surface 41, at
constant velocity (see FIG. 2A), enough to shift the phase of reference
beam 37A by approximately 90.degree.. The four points at which the first
row of integrated buckets are discharged into the corresponding shift
register cells to "collect" the four sets of integrated buckets needed to
make the phase computations according to the present invention, during a
single constant velocity pass of the PZT and the reference mirror 41, are
designated by points A, B, C, and D in FIG. 2A. Point X in FIG. 2A
designates the time at which the integrating of the intensity begins.
Integrated buckets collected between points O and X in FIG. 2A are
disregarded, since this period of time is, in accordance with one aspect
of the present invention, allowed so that the reference mirror 41 and the
piezoelectric transducer 32 can achieve a truly linear, constant velocity.
Point A in FIG. 2A represents the time at which the first row of
integrated buckets collected between point X and point A are strobed,
row-by-row from the internal rows of the integrated bucket capacitors of
the E. G. & G Reticon self-scanning RA 256.times.256 solid state sensor
array, into the corresponding cells of the shift register. Point B
represents the time at which the first row of integrated buckets collected
during the 90.degree. phase shift between points A and point B are
strobed,row-by-row, from the internal rows of integrated bucket capacitors
into the shift register cells. Similarly, the first row of the third and
fourth sets of integrated buckets are strobed into the shift register at
the times indicated by points C and D in FIG. 2A. Point Y represents the
time at which the last row of the fourth set is strobed and read out of
the shift register. (It should be appreciated that the foregoing
description of the internal operation of the E. G. & G. Reticon
256.times.256 photodiode array is not entirely precise, but is adequate
for understanding the present invention. Appendix B attached hereto
provides a more accurate detailed description thereof.)
The distances between points X, A, B, C, D, and Y in FIG. 2A all represent
the amount of time required for a 90.degree. phase change, or phase
difference, to occur between the interfering beams 37A and 40A (FIG. 1).
FIG. 2B represents the displacement of the reference surface 41 for a
different type of photodiode array, in which the groups of photocells and
corresponding integrated bucket capacitors are grouped and strobed
differently than in the E. G. & G. Reticon photodiode array described
above. The graph of FIG. 2A corresponds to a two-dimensional type of array
in which the integrated bucket capacitors are arranged as 256 rows of 256
integrating capacitors each, each row being separately strobed into a
single 256 bit shift register. The graph of FIG. 2B corresponds to an
arrangement in which all of the integrated bucket capacitors can be
essentially simultaneously strobed into a single long bucket-brigade type
of shift register.
In accordance with the present invention, the time intervals between time O
and point X in FIGS. 2A and 2B are provided to allow inertia of the
piezoelectric transducer 32 and the Mirau interferometer to be overcome so
that reference surface moves at a truly constant velocity. This technique
prevents errors in the subsequent phase calculations due to nonlinearities
in the velocity of the reference surface 41.
In FIGS. 2A and 2B, reference numeral 66 designates the return of the
piezoelectric transducer 32 and the reference surface 41 to their initial
positions prior to the beginning of a new constant velocity cycle.
The clock and data acquisition circuit 28 of FIG. 1 can be easily
implemented by one skilled in the art, as this type of circuitry is
common. The presently preferred implementation is indicated in FIG. 1A,
wherein an ordinary crystal oscillator 48 increments an address counter of
a programmable read-only memory 49. Read-only memory 40 produces a
plurality of clock signals 50 that are applied to inputs of a plurality of
ordinary driver circuits 51. The resulting outputs 27A are applied to the
inputs of photodiode array 26 in accordance with the specifications
thereof in order to effectuate scanning or strobing of the 256 rows of 256
integrated buckets each from the integrated bucket capacitors into the
shift register cells.
The resulting analog signal produced by photodiode array 26 and conductors
127 is amplified by an ordinary amplifier 53, the output of which is
connected to the input of a 10 bit analog to digital converter 52, which
can be an ADC 816 type of analog-to-digital converter which is available
from the Datel-Intersil Company. The resulting 10 bit digital output
produced on conductors 44 then represents the magnitude of the analog
integrated bucket level presently on conductor 27. PROM clock generator
circuit 49 also produces a "convert" signal 50A that synchronizes the
analog-to-digital conversion of each amplified integrated bucket voltage
level with the shifting of that level out of the shift register inside
photodiode array 26. A copy of the preliminary specification sheet of the
E. G. & G. Reticon 256.times.256 photodiode array 26 is attached hereto as
Appendix B.
The presently preferred implementation of PZT driver circuit 46 is shown in
FIG. 1B, wherein a clock circuit 54 that is synchronized with the crystal
oscillator 48 of FIG. 1B increments an address counter circuit 55. An
initial value of the address being incremented is preset by the circuitry
in address counter circuit 55. The resulting address produced on bus 57 is
applied to the address inputs of an 8192 word by 16 bit static random
access memory (RAM) 58. A data pattern corresponding to the presently
desired constant velocity of the reference mirror 41 for implementation of
the integrated bucket technique of the present invention is initially
written into RAM 58 by computer 29 via computer data bus 45B. As a result,
the accessed data is produced on a 12 bit data bus 60. The digital numbers
sequentially produced on RAM data bus 60 represent the uniformly
increasing values of the PZT control signal 47 needed to produce the
constant velocity represented by the slope of the graph in FIG. 2A or 2B.
These digital numbers are converted to an analog signal by a 12 bit
digital-to-analog converter 61, which can be any suitable commercially
available device such as a Model DAC 85, which is available from various
suppliers. The output of DAC 61 is applied to the input of a high voltage
amplifier 62, the output of which produces the ramp voltage necessary on
conductor 47 to produce the piezoelectric transducer and reference mirror
displacement shown in FIG. 2A or 2B.
Now that the structure of the optical profiler of FIG. 1 has been set
forth, and the functional operational of its components have been
described, the mathematical techniques for computing the phase .phi.(x),
which is the phase difference between the reference beam 37A and the test
surface beam 40A, will be described. The height distribution h(x) is
determined by the equation:
h(x)=(.lambda./4 .pi.).phi.(x). (1)
The basic equation for the intensity of the two beam interference produced
by the Mirau interferometer at beam splitter 39 is 9iven by the equation:
I=I.sub.1 +I.sub.2 cos[.phi.(x)+.phi.(t)], (2)
where .phi.(x) represents the phase difference between the reference beam
37A and the reference beam 40A at beam splitter 39 as a function of
distance across the interference field and .phi.(t) represents the phase
of the reference beam as a function of time.
If the intensity I is integrated while .phi.(t) varies from zero to
90.degree., from 90.degree. to 180.degree., from 180.degree. to
270.degree., and from 270.degree. to 360.degree., the resulting signals
are represented by A(x), B(x), C(x), and D(x), in accordance with the
following equations:
A(x)=I.sub.1 '+I.sub.2 '[cos .phi.(x)-sin .phi.(x)] (3)
B(x)=I.sub.1 '+I.sub.2 '[-cos .phi.(x)-sin .phi.(x)] (4)
C(x)=I.sub.1 '+I.sub.2 '[-cos .phi.(x)+sin .phi.(x)] (5)
D(s)=I.sub.1 '+I.sub.2 '[cos .phi.(x)+sin .phi.(x)]. (6)
The quantities A, B, and C represented by equations (3)-(6) are the four
integrated buckets that are obtained during each constant velocity pass
for each photodiode, as mentioned above, and as obtained by causing the
photodiode current, to flow into the above-mentioned integrated bucket
capacitors.
In accordance with the present invention, a first value of .phi.(x),
designated .phi..sub.1 (x), is computed in accordance with the following
equation:
.phi..sub.1 (x)=tan.sup.-1 [C(x)-B(x)]/[A(x)-B(x)] (7)
and a second value of .phi.(x) is given by the equation:
.phi..sub.2 (x)=tan.sup.-1 [D(x)-C(x)]/[B(x)-C(x)] (8)
If the phase shift between consecutive readouts of integrated buckets for
the shift register of the detector array 26 differs from 90.degree., a
nearly sinusoidal error is introduced into the measured phase. The spatial
frequency of the sinusoidal error is equal to twice the spatial frequency
of the fringes. For small variations, for example, less than about
5.degree., in the phase shift between consecutive readouts, the peak to
peak amplitude of the sinusoidal error is approximately proportional to
the deviation.
In accordance with the present invention, the sinusoidal error is nearly
eliminated by calculating the phase .phi..sub.1 (x) using the first three
integrated buckets A(x), B(x), and C(x), as indicated in equation (7), and
using the second group of three buckets B(x), C(x), and D(x) to obtain the
second phase measurement .phi..sub.2 (x).
The average phase .phi.(x) then is obtained from the equation:
.phi.(x)=[.phi..sub.1 (x)+.phi..sub.2 (x)]/2. (9)
Each of the phase measurements .phi..sub.1 (x) and .phi..sub.2 (x) has
therein the above-mentioned sinusoidal error if there is any error in the
phase of the reference beam 37A, but the phase errors associated with
.phi..sub.1 (x) and .phi..sub.2 (x) are 180.degree. out of phase (since
the sinusoidal error has twice the spatial frequency of the interference
fringes and hence of .phi.(x). Consequently, the sinusoidal error almost
completely cancels when .phi..sub.1 (x) and .phi..sub.2 (x) are added, as
in equation (9).
The advantage of this technique over prior single pass four bucket
integrated bucket techniques for computing .phi.(x), as disclosed in the
above-mentioned November, 1975 Applied Optics article by Wyant, is that
the present techique effectively cancels out the sinusoidal error, while
the prior single pass four bucket technique does not. The advantage of the
present technique over the two pass, four bucket technique disclosed in
the above-mentioned November, 1983 Applied Optics article is that in that
reference, the two sets of measurements are separate in time, making the
system very susceptible to errors caused by vibration of the apparatus,
thermal expansion or contraction of the apparatus, variations in air
density, variations in air temperature, etc.
The program executed by computer 29 in solving equations (4)-(9) is given
in Appendix C attached hereto.
The optical profiler of FIG. 1, operated in accordance with the above
method and equations (7)-(9), provides the capability of accurate, zero
contact surface-heighth measurements and generating surface profiles over
a small region of a sample. The data collected and the phase and/or
surface heighth values computed provides a basis for statistical analysis,
surface-height distributions, autocovariance functions, and
spectral-density functions. Slopes and curvatures of asperities also can
be computed.
The beam splitter 39 of the Mirau interferometer forms a second optical
path that ends at the reference mirror surface 41. If the optical path
length between the beam splitter 39 and the test surface 42 is equal to
the optical path length between the beam splitter and the reference
surface 41, a white light source produces a distribution of interference
fringes across the beam having an intensity distribution that is
represented by the various currents produced by the cells of the
photodiode array 26.
The single pass integrating techniques avoid the error of the double pass
four bucket technique of the above-mentioned 1983 Applied Optics article
by avoiding errors that result from failure to return the piezoelectric
transducer 32 and reference mirror 41 back (i.e., via path 66 in FIG. 2A
or 2B) back to precisely the same starting point from which the reference
surface 41 began its present constant velocity path.
As mentioned above, the intensity of the tungsten source 11 is controlled
in response to the readout obtained from photodiode array 26, by virtue of
the coupling 63 from the interface circuit 43 to an intensity control
circuit 64. Intensity control circuit 64 contains a counter circuit that
can be incremented or decremented by signals on conductor 63 to increase
or decrease the voltage on conductor 65, which voltage is applied to the
filament of tungsten lamp 11 and thereby controls its intensity.
A problem with prior intensity control devices for interferometers,
particularly those used in non-contact profilers, is that the intensity of
the light in the intereference fringes (see equation (2) above) depends
both the intensity of the light source and the phase difference between
the two interfering beams 37 and 40 (FIG. 1). In accordance with the
present invention, a first integrated intensity measurement is taken for
each of about 50 photodiode cells, each resulting in an intensity I.sub.A
given by the equation:
I.sub.A =I.sub.1 +I.sub.2 cos .phi.. (10)
This step is indicated by block 68 in FIG. 3, which is a flow chart of the
program executed by computer 29 in order to effectuate automatic control
of the tungsten source intensity. Next, computer 29 produces signals that
are applied to the PZT driver circuit 46 so as to cause reference surface
41 to shift the phase of the reference beam 37A by 180.degree., as
indicated in block 69 of FIG. 3. Next, the intensities of the same 50
photodiodes are measured and the data is read by computer 29, the
integrated intensity for each cell being given by the equation:
I.sub.B =I.sub.1 -I.sub.2 cos .phi.. (11)
Averagin | | |
