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Description  |
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BACKGROUND OF THE INVENTION
The invention relates measuring device capable of profiling a surface with
large height variations.
Conventional phase shifting interferometers require that the surface of an
object being profiled be quite smooth, so that continuous interference
fringes are produced by it. A large step change (i.e., a quarter of a
wavelength of the light used to make the measurement or more) in the
height of the surface often destroys the continuity of interference
fringes, and consequently conventional phase shifting algorithms executed
by a computer in response to fringe intensity data produced by a
solid-state imaging array, such as a CCD array, are unable to accurately
compute the profile of the surface.
At the present time, measurement of accurate profiles of surface areas is
limited to RMS average roughness of approximately one thousand Angstroms
using single wavelength interferometric techniques. Using multiple
wavelength techniques (such as those described in commonly assigned U.S.
Pat. No. 4,832,489, issued May 23, 1989, to Wyant et al.), surfaces with
approximately one micron average roughness may be measured. With single
wavelength techniques, the present state of the art limits measurement to
surface step features of no greater height than approximately 0.16
microns. With multiple wavelength techniques, step height measurements are
limited to steps less than approximately 15 microns in height.
U.S. Pat. No. 4,818,110 (Davidson) discloses a Linnik Microscope in
combination with a video camera, a wafer transport stage, and data
processing electronics, based on the use of an interference microscope to
measure height and width of surface features on an integrated circuit.
However, this reference does not disclose pixel-by-pixel mapping of the
surface of a sample, does not generate a profile, and is incapable of
generating an accurate pixel-by-pixel area profile of a surface that is
too "rough" to be measured by conventional interferometry.
The article "Profilometry with a Coherent Scanning Microscope", by Byron S.
Lee and Timothy C. Strand, Applied Optics, Volume 29, No. 26, Sept. 10,
1990, discloses a "coherence scanning microscope" in which an object is
scanned in the z direction. White light interference fringes that result
from the scanning are demodulated to find the peak amplitude of an
envelope of the fringes to determine the value of z at the peak
interference fringe. The Lee and Strand paper discloses no specific way of
demodulating the fringes, and indicates that ambiguities introduced by
phase change on reflection due to dissimilar materials renders the
technique inoperable. No interpolation techniques or curve fitting
techniques that might improve accuracy are disclosed. Optical path
difference increments apparently are limited by the step size of stepper
motors used, as is the speed of incrementing. The disclosed profile data
is two-dimensional, rather than three-dimensional. The Lee and Strand
reference clearly does not teach a technique to accomplish fast, highly
accuracy surface profiling of surfaces having wide ranges of smoothness or
roughness, or of dealing with phase ambiguity errors that result from
phase change on reflection due, for example, to dissimilar surface
materials.
Although phase-shifting techniques can produce measurements of surface
roughness of the order of one thousandth of a wavelength, most present
methods detect phase modulo 2.pi., and consequently give rise to errors
sometimes referred to as "2.pi. ambiguities" but hereinafter referred to
as "phase ambiguities" or "phase ambiguity errors". Various kinds of
"phase unwrapping" algorithms are used to track the phase over a large
range of surface heights and resolve the phase ambiguity errors. Problems
arise when there is a height variation between two adjacent pixels that
cannot be unambiguously "unwrapped". The result is an integration error
that usually manifests itself as a streak across the field of view.
It is well known that different materials on a surface to be profiled
produce a phase shift known as "phase shift on reflection", which
introduces phase ambiguity errors when conventional phase shifting
techniques are utilized to determine the surface profile. More
specifically, it is known that if the material of a surface being
interferometrically profiled has optical properties such that the incident
ray is delayed in phase by an appreciable amount, there will be a shift,
i.e., by the "phase shift on reflection", in the phase of the fringe
pattern received at the detector. Phase shifts which can cause phase
ambiguity errors also may occur when there is a thin transparent film on
the surface being optically profiled, because the film adds delay to the
light propagation time therethrough.
There is an unmet need for an accurate, high speed, non-contact profiler
capable of profiling a wide variety of rough surfaces.
SUMMARY OF THE INVENTION
Accordingly, it is an object of the invention to rapidly produce an
accurate area profile of a rough surface having height variations that
exceed the focus range of conventional interferometric profilers.
It is another object of the invention to provide a method and apparatus for
accurate area profiling of a rough surface composed of differing materials
which produce phase changes on reflection.
It is another object of the invention to provide a method and apparatus for
interferometrically profiling rough surface areas without the need to use
a phase unwrapping algorithm.
It is another object of the invention to provide a method and apparatus for
interferometrically profiling rough surface areas very rapidly, without
requiring excessive amounts of computer memory and algorithm execution
time.
It is another object of the invention to provide an improved apparatus and
technique for real time demodulation of interference fringe signals in an
interferometric area profiling system.
It is another object of the invention to provide method and technique for
measuring surfaces with RMS average roughness of more than approximately
one micron.
Briefly described, and in accordance with one embodiment thereof, the
invention provides a method of profiling a rough surface of an object by
producing an optical path difference so that initially a highest point of
the rough surface is optically aligned with and outside of the focus range
of a solid-state imaging array. Then an interferogram of the rough surface
is produced by means of an interferometer. The solid-state imaging array
is operated to scan the rough surface along x and y axes to produce
intensity data for each pixel of the solid-state imaging array for a
plurality of frames each shifted in time from the previous one to vary the
optical path difference by a preselected phase difference. The contrast or
modulation for each pixel is determined from the intensity data. That
contrast or modulation is compared with a stored prior value of contrast
or modulation of that pixel. The prior value is replaced with the most
recently computed contrast or modulation if the most recently computed one
is greater than the one previously stored. The corresponding relative
height or optical path difference is also stored for that pixel. The
optical path difference is either incrementally or linearly varied through
a selected distance, and the foregoing procedure is repeated until maximum
values of contrast are obtained and stored for each pixel. In one
embodiment, the modulation is computed from intensity data obtained during
conventional phase-shifting interferometric measurements. In another
embodiment, the phase is also computed for each pixel from the intensity
data and is used along with the modulation to improve vertical resolution.
In another embodiment, intensity data is "amplitude demodulated" using
classical communications theory to extract an "envelope" of the intensity
data and determine the peak thereof. The envelope signal or modulation
signal is "separated" from the "carrier" signal of the intensity waveform
produced as the solid-state imaging array passes through focus. The
separation is accomplished by a digital low pass filtering operation. The
resulting separated modulation signal is input to a digital correlator
which detects the peak and correlates it to the surface height of the
present pixel.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram of the rough surface profiler of the present invention.
FIG. 2 is a diagram showing an output signal that can be produced by
detector cells in FIG. 1 as the optical path difference is varied through
the best focus point of the objective.
FIG. 3 is a simplified block diagram of another embodiment of the
invention.
FIG. 4 is a detailed block diagram of another embodiment of the invention.
FIG. 5 is a flow chart useful in describing the operation of the embodiment
of FIG. 4.
FIG. 6 is a diagram useful in explaining a phase interpolation technique to
improve resolution of surface height measurements.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to FIG. 1, rough surface profiler 1 includes a Mirau
interferometer 2 having a reference mirror 2A on a glass plate 2B, and a
beamsplitter 2C. A microscope objective 4 is supported above a test
surface 3 by a piezoelectric transducer (PZT) 5. PZT 5 is supported by a
frame of Mirau interferometer 2. Mirau interferometer 2 is supported by
the frame of microscope section 1A The vertical or z position of
microscope section 1A is controlled by a motor 60, which is connected by a
mechanical link 60A to microscope section 1A Test surface 3 is supported
on a stage 66. The optical path difference (OPD) is precisely controlled
by PZT 5 in response to PZT driver signal 59 produced by computer 30.
Motor 60 is controlled by signal 63 produced by motor controller circuitry
58.
A white light source, which can be a typical quartz halogen lamp, directs
white light through a typical commercially available illumination assembly
7, which directs the white light beam onto an ordinary beamsplitter 9.
Beamsplitter 9 reflects the white light beam 10 into the upper end of
microscope objective 4.
The beams reflected from the reference mirror 2A and the sample surface 3
then pass back up through microscope objective 4, upward through
beamsplitter 9, through a collimating lens 31, and through a
multilayer-coated beamsplitter 12 which deflects approximately 30 percent
of the interference beam 20 into eyepiece assembly 13. Most of the
interference beam 20 continues upward through imaging lens 11 to
solid-state imaging array 18. Camera electronics 19 processes the signals
of the individual CCD (Charge Coupled Device) cells or other solid-state
imaging array cells of solid-state imaging array 18 and outputs them via
bus 27 to computer 30. Computer 30 communicates via bus 28A with
microcontroller 28.
Microcontroller 28 can be an Intel 8098. Block 68 includes a z joystick
controller by means of which an operator can manually control motor 60 to
control the vertical position of microscope section IA relative to sample
surface 3, and is connected by suitable conductors 68A to inputs of
microcontroller 28. Microcontroller 28 communicates by bi-directional bus
28A with computer 30, which can be a desk-top computer in combination with
a commercially available WYKO PMI (Phase Measuring Interface).
Microcontroller 28 generates outputs 57 which control motor controller
circuitry 58. Microcontroller 28 and motor controller circuitry 58
actually are included in the above WYKO PMI unit.
A filter 17 may be positioned under solid-state imaging array 18 and camera
scanning electronics 19. The signals produced by detector array represent
the profile of sample surface 3, and are scanned by camera scanning
electronics in block 19 which produce amplified signals on bus 27 that are
digitized and input to computer 30 for suitable processing in accordance
with the needs of the user.
The reference path and sample path in Mirau interferometer 2 are
essentially identical except that the reference path is focused on mirror
surface 2A and the sample path is focused on the test surface 3. Numeral
26 designates the vertical z axis of interference microscope 1.
The waveform shown in FIG. 2 is typical of those produced by the individual
CCD cells in detector 18 in response to light of the interferogram
impinging on detector array 18 as the optical path difference is changed.
It is seen that this response is very peaked, and identification of the
ideal microscope objective focus point is quite distinct. Dotted line 25
designates an "envelope" of waveform 23, which in accordance with one
embodiment of the invention, is extracted from the "carrier signal" using
classical communications techniques to obtain the "modulation" signal that
is highest when the microscope objective is optimally focused on the rough
sample surface at the pixel under consideration.
The image formed by a properly focused interference microscope typically
consists of a pattern of light and dark alternating interference fringes.
The number of fringes and the orientation of the fringes across the image
plane are dependent on the relative tilt between the sample surface and
the reference surface. Interference microscopes are assembled such that
the brightest fringe occurs at "best focus", i.e., within the depth of
focus of the microscope objective.
FIG. 3 shows a simplified diagram of a different embodiment of the
invention in which the stage 66, rather than the microscope objective, is
vertically moveable in the z direction. Stage 66 is precisely moveable,
either linearly or in minute (e.g., 0.1 micron or less) increments in
response to increment signals 59 from computer 30.
The specimen to be profiled has a "rough" surface 3, as in FIG. 1, that
exceed height variations which can be profiled by the closest prior art
interferometer-type surface profilers. Solid-state imaging array 18, which
has an objective 4, is supported in a fixed position above stage 66.
Camera electronics 19 are connected by bi-directional bus 27 to
solid-state imaging array 18 to control scanning of rough test surface 3
by the solid-state imaging array in camera 18 and to receive intensity
data from each pixel of the solid-state imaging array. Camera electronics
19 communicate with computer 30, mainly to supply measured pixel intensity
data to it. Computer 30 executes software that converts the data into a
surface profile and may perform further analysis thereon, and displays the
surface area profile and/or analysis results on a screen, or outputs the
data to control a plotter that plots the surface profile. In FIG. 3, the
elements of the interferometer that produce the fringe pattern (which
results from interferon source light reflected from rough surface 3 and a
reference surface) viewed by solid-state imaging array 18 are omitted, for
simplicity. The interferometer hardware is similar to that shown in FIG.
1.
In accordance with the present invention, either stage 66 is lowered (FIG.
1) or microscope objective section 1A is raised (FIG. 3) so that the image
of rough surface 3 is beyond the range of solid-state imaging array 18.
Then, computer 30 causes the OPD between solid-state imaging array 18 and
the rough surface 3 to be either reduced in minute (e.g., 0.1 micron)
increments or reduced linearly and sampled at the same increments by
controlling the position of stage 66. For each such increment, solid-state
imaging array 18 scans rough surface of sample 3. The intensity data of
the interference fringe pattern is sent to computer 30 after the intensity
data has been converted to digital form by camera electronics 19.
Computer 30 then, for each pixel (i.e., x-y location) scanned by the
solid-state imaging array 18, computes the modulation (or other suitable
parameter) of that pixel, and compares it with the highest modulation
stored so far for that pixel. If the new contrast or modulation is higher
than the prior highest stored modulation, computer 11 updates the stored
highest modulation by replacing it with the new one, and also stores the
corresponding value of OPD or relative surface height presently being
scanned.
After this has been accomplished for every pixel of solid-state imaging
array 30 for the present value of z, the OPD is, in effect, incremented
and the entire process is repeated. This happens many times, until the OPD
or relative surface height variable z has changed enough to pass the best
focus point of objective 4 through the maximum possible height range of
all of the rough surface features of rough surface 3 in the field of view.
When the process is completed, computer 30 then has stored both the maximum
contrast for each pixel and the value of z (i.e., the height) at which it
occurred. This, of course constitutes the profile of the surface 3.
The advantage of the forgoing technique is that it does not require any
continuity of fringes on steep, high step features of specimen surface 3.
The general interference equation for the intensity measured in a 2-beam
interferometer is as follows:
I.dbd.I.sub.0 [1+Mcos(.phi.+.alpha.)], (1)
where I.sub.o is the DC bias term, .phi. is the initial phase angle,
.alpha. is the incremental phase change, and M is the modulation.
Phase-shifting techniques usually make use of a narrow-band light source
and assume that M is constant throughout the measurement. Multiple frames
of data are taken while the OPD is varied by a known amount between each
frame. The resulting group of above equations (1) then can be solved using
least-squares techniques or the like to determine the phase of each pixel
at which the intensity is measured. The relative height at each pixel then
is given by the formula
##EQU1##
The present invention makes use of the modulation information and the
interference data corresponding to each pixel at which the intensity of
the sample is measured, and correlates that information to the relative
surface height of the sample at that pixel. If a broad bandwidth source,
i.e., white light, is used instead of a filtered narrow bandwidth light
source, the intensities of the fringes produced fall off sharply as the
optical path difference is varied, as indicated in FIG. 2.
If the assumption is made that the maximum value of modulation M occurs
when the OPD is near zero, then the position of the peak of the modulation
function may be used to map the relative surface height throughout the
field of view. The modulation function has the advantage of being
non-periodic, and therefore will not have the above mentioned phase
ambiguity errors.
It should be noted that measuring the modulation of fringes produced by a
white light source is somewhat problematic. If standard phase-shifting
methods are used to solve the basic interference equation for modulation
M, the phase shift between frames must be very accurately calibrated. This
becomes difficult due to spectral variations in the reflectivity of the
sample and variations in the peak wavelength of the light source. The
basic interference equation (1) assumes that the modulation is constant
with respect to z, which of course is not true for a white light source.
The result is a very noisy modulation signal. Even so, respectable results
were obtained on "very" rough surfaces using the methods described herein,
because the modulation noise was small compared to the roughness of the
surface.
In one experimental embodiment of the invention, phase information was used
along with modulation information to improve the resolution. In another
(presently preferred) embodiment of the invention, "amplitude
demodulation" of the fringes was performed using techniques similar to
those used in AM radio receivers.
An initial attempt at profiling a rough surface used a stepper head and
motor-driven micropositioner as shown in FIG. 3 to produce relative
translation of the test surface 3 along the z axis. Standard
interferometric phase-shifting techniques were used to obtain intensity
data used to compute the modulation. This first attempt proved the general
workability of the concept of focusing the microscope on each point of the
rough surface to obtain a surface map of values of z at which maximum
modulation was computed for each pixel, but worked well only for very
rough surfaces. A second attempt used computed phase information, in
addition to the computed modulation information, from the measured
intensity data to improve measurement resolution. A third attempt, which
seemed to produce the best results, used amplitude demodulation techniques
somewhat similar to those commonly used in communications systems to
decode the modulation function. These three experimental embodiments of
the invention will now be described in detail.
The above-mentioned initial attempt to implement the invention used
hardware similar to that of FIG. 3, which is a simplified diagram that,
for simplicity of illustration, omits the interferometer elements shown in
FIG. 1. A vertical translating stage (a KLINGER P/N UZ80 PP) was used to
vary the OPD by moving the rough sample surface 3 through "focus" (i.e.,
the best focus point of microscope objective 4), as controlled by a
Hewlett-Packard 330 microcomputer, through a programmable indexer (a
KLINGER P/N CC-1.2). The assignee's commercially available TOPO 3D version
4.9 software, revised slightly to provide suitable control of stage 66 and
to make calculations described hereinafter, was used. The assignee's
standard TOPO five-frame phase-shifting algorithm was used to collect five
intensities I.sub.1 -I.sub.5 at each pixel for each OPD value. The
intensities were used to calculate the modulation M at each pixel in
accordance with the equation
##EQU2##
I.sub.1 -I.sub.5 are five consecutive frames of intensity data for every
pixel, taken with relative phase shifts of .pi./2 between the frames,
I.sub.o being the average light level, which is constant and need not even
be used if the purpose of the computations is to find the value of z at
which the maximum modulation occurs.
Stage 66 (FIG. 3) was stepped at a 0.1 micron rate for a sufficient total
scan length that the entire range of surface height of rough sample
surface 3 could pass through focus. More specifically, at each step the
piezoelectric transducer (PZT) 5 (e.g., see FIG. 1) was shifted, and five
frames of intensity data were taken. The value of M was calculated in
accordance with equation (3) for each pixel, and then was compared to a
previously stored value. For each pixel, if the new value of M was larger
than the previously stored one for that pixel, the new value of M was
stored, along with the current z value. Thus, after a complete scan, a
complete profile of rough surface 3 consisting of the relative surface
height of each pixel at which the maximum modulation or fringe contrast
occurred was stored.
The resolution obtained for the above described initial experiment was
reasonably good, but not satisfactory. The experiment was repeated, but
with the "best focus" of each pixel being selected as the point at which
the intensity for that pixel was maximum. However, the results were no
better. The same experiments were performed for both filtered light and
white light, using a standard GAR P/N S-22 for the purpose of evaluating
performance of the device. The amount of time taken to execute the frame
shifting algorithm was considered to be too long. Varying degrees of
"noise" or error were present on smoother samples, although good results
were obtained for the roughest samples, which had peaks of about 30
microns.
In a second attempt to improve the resolution, phase information was used
in addition to the modulation M computed in accordance with equation (3),
in the hope of obtaining better resolution than the 0.1 to 0.6 micron
resolution obtained for the above described embodiment of the invention.
The vertical distance between measurements was selected to equal
approximately one eighth of the mean wavelength of the broadband light
source. The equations used for 3-frame phase shifting with a linear
ramping of the OPD with distance or time precisely producing 90 degree
phase shifts between frames, are as follows:
##EQU3##
The step size was calibrated for a phase shift of .pi./2. The algebraic
signs (i.e., +or -) of the numerator and denominator of equation (5) are
used along with the modulation M of equation (4) calculated at each step,
and the new modulation M is stored only if both signs are negative and M
is greater than the previous stored value. For this value of z, the phase
is also calculated from the measured intensity values and also stored with
the current step number. This technique ensures that the peak modulation M
is always stored in the same quadrant along with the peak of the fringe
and that the phase calculated there will be independent of the phase
calculated at adjacent pixels.
The profile of the test surface 3 then is produced at the end of the
measurement by taking each stored "step number" (the step number is a
variable that is incremented for each phase shift) and multiplying that by
the distance per step, and adding or subtracting an incremental distance
from that using the corresponding phase data, as indicated by equation
(6). This is done for each pixel scanned. The result is a complete three
dimensional map which is obtained without the need for phase discontinuity
removal techniques, and thus is inherently free from integration errors.
The resulting resolution of this technique produced much higher resolution,
almost as good as the assignee's TOPO 3D system, for smooth, flat
surfaces. Measurement of rougher samples produced good results similar to
those obtained for the first-described technique. Moderately rough
surfaces, however, sometimes produce measurements with random spikes that
occur at offsets of approximately 2.pi. from surrounding features. It is
believed that these phase ambiguity errors resulted from not being able to
reliably detect the peak fringe position, causing the calculated z value
to jump to the next fringe, a distance of 2.pi. away. Some of these phase
shifts are believed to be due to phase shift on reflection. Thin
transparent or semi-transparent films (of thickness less than a coherence
length of the light source) also produce similar phase shifts. Although
the foregoing technique produced very good results on "very" rough
surfaces (e.g., several microns RMS roughness), on "moderately" rough
surfaces (e.g., 100 to 300 nanometers RMS roughness), it was clear that
additional processing would be required to detect the peak fringe and that
it would be necessary to continually recalibrate the phase shift produced
by PZT 5, as the accuracy of such shifting was found to be critical.
Referring to FIG. 6, the above-mentioned improvement in resolution is
accomplished by "offsetting" the phase .phi. between intensity measurement
points such as 88, 89 and 90 on the highest intensity fringe 23C of
intensity waveform 23. The highest intensity fringe 23C is previously
isolated by using the peak of envelope 25 of intensity waveform 23C shown
in FIG. 2. Points 88, 89, and 90 indicate already measured intensity
points at phases spaced .pi./2 apart. The above-described resolution
problem is caused by the fact that none of intensity measurement points
88, 89, or 90 is located at the value of z at which the peak 23A is
located. In order to get an accurate value of the right hand "phase offset
term" in equation (6), the present invention involves computing values of
M "on the fly" according to equation (4) using intensities measured from
points 88, 89, and 90 and storing that value if both 1) it is the highest
value of M computed so far, and 2) the terms (I.sub.1 -I.sub.2) and
(I.sub.3 -I.sub.2) are both negative or one is negative and the other
zero. When that condition is met, the phase offset term .phi. is computed
according to equation (5), and is used to "adjust" or "refine" the more
approximate value given by the left term of equation (6). This later term
represents the peak of the modulation envelope 25 (FIG. 2). It should be
noted that the actual phase of the peak modulation relative to the height
calculated using equation (6) is 3.pi./2, but since this relative offset
is added to every pixel, the net result is the same. (Those skilled in the
art know that the basic interference equation is equation (1), which has
three unknown variables. Therefore, at least three measurements of
intensity must be measured at different phases to solve for the three
unknown variables. Measurement of additional values of intensity at
additional phases can, as a practical matter, further improve accuracy of
phase computation if the well known least squares technique is used to
solve for the unknown variables.)
The above-mentioned third embodiment of the invention involved modifying
the system of FIG. 1 so as to produce the system essentially as shown in
FIG. 4. In FIG. 4, microcomputer system 30 includes a "frame processor"
36, which can be a digital signal processor (DSP) board plugged into a
back plane bus 37 of an IBM AT computer system. Vertical motion control
circuitry and PZT control circuitry in block 38 also is connected to the
internal bus 37 and to digital signal processor 36. An 80.times.86 CPU 39
that is connected to internal bus 37 is the main processor of
microcomputer system 30. An optional color video monitor 35 can be
connected to digital signal processor and video interface circuit 36, for
the purpose of effectuating real time video display.
Numeral 41 designates a conventional color monitor of microcomputer system
30, to which keyboard 42, printer 43, and work station bus 40 also are
connected. The PZT control circuitry in block 38 produces a linear ramp
signal 45 that drives a PZT amplifier 50, which can be a conventional
amplifier such as the one used in the assignee's commercially available
TOPO 3D system. PZT amplifier 50 produces a high voltage PZT drive signal
on conductor 53 to control a PZT (not shown) that is used to increment the
fine vertical translator 71, which is shown in FIG. 4 as being "nested" in
a coarse vertical translator 70. (OPD variation can, of course, also be
produced by incrementing the stage 66 in the z direction.) Coarse vertical
translator 70 is driven in response to a circuit shown in block 55, which
can be an "autofocus" printed circuit board contained in the assignee's
commercially available TOPO A/F system. The coarse position control signal
on conductor 61 controls coarse vertical translator 70.
The relative position of test surface 3 and optical system 18 is measured
by a conventional linear variable differential transducer (LVDT) 73 or the
like, which produces signals on conductor 74 and inputs them to LVDT
signal conditioning or buffer circuitry 51. LVDT signal conditioning
circuit 51 produces an output signal which is applied as an input to PZT
amplifier 50, and also supplies an encoded voltage on conductor 52 to the
PZT control circuitry in block 38. The encoded voltage on conductor 52
represents the precise position of the solid-state imaging array 18
relative to the present pixel of rough surface 3. Dotted line 76
designates an optical coupling between solid-state imaging array 18 and
rough surface 3.
LVDT signal conditioning circuit 51 produces very precise feedback in the
form of encoder voltage 52 indicating the present position of the
objective of solid-state imaging array 18. PZT control circuitry in block
38 adjusts the ramp signal on conductor 45 so that solid-state imaging
array 18 moves very linearly. The -PZT control circuitry in block 38, PZT
amplifier 50, PZT included in fine vertical translator 71 of FIG. 4, LVDT
73, and LVDT signal conditioner 51 function as a servo circuit that
maintains the translation or variation of the OPD precisely linear. for
accomplishing this is well known to those skilled in the communications
art.
It was hoped that the same demodulation techniques that apply to classical
AM detection theory would apply to obtaining the modulation envelope 25
and "detecting" its peak to profile rough surface 3.
A basic operation that must be accomplished to make the above-mentioned
amplitude demodulation technique work in the present invention is the
separation of the modulation signal from the carrier signal in the
frequency domain by use of a low pass filter. For example, in an AM radio,
the low pass filtering is typically accomplished by using a simple RC
network. However, the filtering of the fringe intensity data becomes more
complicated, due to the fact that the intensity data through focus for
each pixel is not available as a continuous analog signal, as in the case
of an AM radio, but instead is sampled and digitized once each video
frame.
Therefore, a digital technique must be used to perform the low pass
filtering function. One possibility to accomplish the low pass filtering
would be to perform a Fourier transform on the data collected for each
pixel for an entire measurement and then perform "computational filtering"
in the Fourier domain. This approach would require storing a large number
of frames of video
Waveform 23 in FIG. 2 is of the same general shape for each of the
intensity signals produced at the outputs of each of the pixels of
solid-state imaging array 18 as the OPD is incrementally or linearly
ramped so that the microscope objective 4 scans through the entire range
of rough surface features of test surface 3. This waveform can be
considered to be analogous to an ordinary AM radio signal. Waveform 23 of
FIG. 2 is defined by the above interference equation of equation (1)
I=I.sub.0 +I.sub.0 Mcos(.phi.+.alpha.). (1)
It is useful to compare this equation to the equation for an amplitude
modulated rf signal, used in radio communications:
s(t)=[1+m(t)]Ucos(2.pi.ft+.alpha.), (7)
where s(t) is the product of a modulating signal s(t)=1+m(t) and a
sinusoidal carrier signal Ucos(2.pi.ft+.alpha.), where U is a constant.
The two equations (1) and (7) are very similar, with the optical
interference signal of equation (1) offset by the DC term I.sub.o. Those
skilled in the electronic communications art know that amplitude
modulation is generally defined as a linear operation where a frequency
translation of a modulating signal is performed by multiplication of the
signal by a sinewave carrier. Amplitude demodulation is a reverse
operation, i.e., the reconstruction of the modulating signal from the
modulated signal. The technology data, thereby imposing massive memory
requirements on the system. Another possibility for performing the low
pass filtering would be to use a digital filter algorithm to calculate a
new filter output at each step (i.e., at each OPD) of the profiling
process. The amount of memory required then would be reduced to one frame
of video data for each "order" of the filter. The higher the order of the
filter, the steeper its cutoff characteristics are, indicating better
separation of the modulation envelope and the carrier signal. The details
of the design are common knowledge, and are selected from pages 218 to 223
of "Digital Signal Processing" by J. V. Oppenhiem and R. W. Schafer,
Prentice-Hall, N.J., 1975.)
The flow chart of FIG. 5 shows the operation of "extracting" or detecting
the "envelope" 25 of waveform 23 in FIG. 2. The peak of the envelope 25
then corresponds to the point of best focus, and therefore correlates to
the relative height of the present pixel of rough surface 3.
The intensity data obtained from the phase shifting operation is shown in
FIG. 5 as an input to block 80, in which the sampled intensity data I(n)
is stripped of the DC component I.sub.0, by use of either a digital high
pass filter or by subtracting an average DC value from the intensity
signal produced by each pixel (by digital low pass filtering or averaging
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