 |
Description  |
|
|
FIELD OF INVENTION
This invention relates to an optical path length difference detecting
interferometer method and system, and more particularly to one which uses
intensity levels sensed at three different discrete optical path length
differences to determine the optical path length difference between the
surfaces being compared.
BACKGROUND OF INVENTION
Conventional contouring machines which determine the difference in height
of points on one surface relative to a second surface typically use an
interferometric device. Generally one of the surfaces is being tested
against the other reference surface and the height difference is
ascertained through determination of the optical path length difference
between the surfaces in an interferometer. This determination is made by
considering that the intensity at any point is generally represented by
the expression:
I.sub.o =.vertline.a.sub.1 .vertline..sup.2 +.vertline.a.sub.2
.vertline..sup.2 +2a.sub.1 a.sub.2 cos (2.pi./.lambda.) .DELTA.(1)
where
(2.pi./.lambda..DELTA. is the phase angle .phi.
.lambda. is the wavelength of the radiation
.DELTA. is the difference in height of the surfaces at corresponding
points.
This can be written:
I.sub.o =K.sub.o +K.sub.1 cos k.DELTA. (2)
where:
K.sub.o =.vertline.a.sub.1 .vertline..sup.2 +.vertline.a.sub.2
.vertline..sup.2
K.sub.1 =2a.sub.1 a.sub.2
k=2.pi./.lambda.
Applying this expression the optical path length may be varied
continuously, resulting in the form
I.sub.o (t)=K.sub.o +K.sub.1 cos k(.DELTA.+t) (3)
where t is the changing path length. This term may be expanded:
I.sub.o (t)=K.sub.o +K.sub.1 cos k.DELTA. cos kt-K.sub.1 sin k.DELTA. sin
kt (4)
which is then subject to Fourier analysis. Performance of such analysis
requires a very powerful analog computing network or special or general
purpose digital computer because of the inherently complex nature of
Fourier analysis. In one system over two hundred different intensities
I.sub.o are sensed and must be analyzed; and this must be done for each
position or spot on the surfaces to be compared. For example, an array of
detectors one hundred square requires ten thousand such calculations. Thus
an extremely complex task, Fourier analysis, becomes a truly
brobdingnagian task used in such applications.
The Fourier analysis produces the first harmonic coefficients:
A.sub.1 =K.sub.1 cos k.DELTA. (5)
B.sub.1 =K.sub.1 sin k.DELTA. (6)
which are then used to obtain a trigonometric function of the phase angle
.phi.=k.DELTA., such as:
B.sub.1 /A.sub.1 =-tan k.DELTA. (7)
From this the phase angle is determined and then the difference in height
of the surfaces is calculated:
.phi.=(2.pi./.lambda.).DELTA. (8)
.DELTA.=.lambda..phi./2.pi. (9)
This approach thus requires large, very powerful computing equipment which
is expensive and in spite of its size and speed requires much time to
complete the computations. These machines must be specially constructed or
specially programmed to perform the analysis. The measurement is also time
consuming in the case where over two hundred samples of the intensity are
made for each position, which takes a minute or more. The extended time
required for measurement leads to additional problems: vibrations taking
place in the area of the machine interfere with the interferometer
operations.
SUMMARY OF INVENTION
It is an object of this invention to provide an improved optical path
length difference detecting system and method which greatly reduces
necessary measurement and computational operations and time.
It is a further object of this invention to provide such a system and
method which uses intensity levels sensed at three discrete optical path
length differences to determine the path length difference.
It is a further object of this invention to provide such a system and
method which uses only a few simple arithmetic operations to obtain the
path length difference.
It is a further object of this invention to provide a small, compact and
extremely simple optical path length difference detecting method and
system which can be implemented with inexpensive, standard components.
It is a further object of this invention to provide such a system which can
compute measurement operations in a tenth of a second or less and which is
virtually unaffected by normal building vibrations.
The invention results from the realization that the optical path length
difference between two surfaces can be determined from the intensity
levels detected at only three different discrete optical path lengths at
quarter wavelength intervals.
The invention features a method and a system for interferometrically
determining the optical path length difference between two surfaces. The
method includes varying the interferometric optical path length difference
between a first and a second surface in three steps at one-quarter
wavelength intervals. The interferogram radiation intensity is sensed at
at least one position of the interferogram at each of the steps, and those
intensities are then stored. For each of the positions, the intensity of
the first and third steps is added to produce the d.c. spatial frequency
amplitude. The same intensities are subtracted to obtain the cosinusoidal
spatial frequency amplitude and the sinusoidal spatial frequency amplitude
is obtained by subtracting from the d.c. spatial frequency amplitude the
intensity of the second step. The sinusoidal and cosinusoidal amplitudes
are then combined to produce a trigonometric function of the phase angle
of the radiation reflected from each position of the first and second
surfaces. The trigonometric function of the phase angle is used to
generate an output representative of the optical path length difference at
each position.
The system includes an interferometer including a radiation source of
predetermined wavelength for producing an interferogram from radiation
reflected from a first surface and radiation reflected from a second
surface. There are means for varying the optical path length difference
between the first and second surfaces in three steps at one-quarter
wavelength intervals. There is at least one detector for sensing the
intensity of the incident interferogram radiation and in most applications
there will be an array of such detectors. There is means for scanning each
of the detectors at each step to obtain a signal representative of the
level of intensity at each detector. The intensity level so sensed is then
stored to retain the interferogram image presented at each of the steps.
There are means responsive to the storing means for determining the d.c.
spatial frequency amplitude from the sum of the intensity levels derived
from the first and third steps and the cosinusoidal spatial frequency
amplitude from the difference between those intensities. The sinusoidal
spatial frequency amplitude is determined by the difference between the
d.c. spatial frequency amplitude and the intensity level derived from the
second step.
There are means for combining the sinusoidal and cosinusoidal spatial
frequency amplitudes to generate an amplitude representative of the
trigonometric function of the phase angle of the radiation reflected from
the first and second surfaces. The optical path length difference between
the surfaces at each position monitored by a detector is generated from
the trigonometric function of the phase angle.
The sign of the optical path length difference may be determined by
comparing the d.c. amplitude to twice the intensity level at the second
step and indicating that the sign is positive when the d.c. amplitude is
greater, and negative when it is smaller, than the intensity level at the
second step.
DISCLOSURE OF PREFERRED EMBODIMENT
Other objects, features and advantages will occur from the following
description of a preferred embodiment and the accompanying drawings, in
which:
FIG. 1 is a simplified block diagram of an optical path length difference
detecting interferometer system according to this invention;
FIG. 2 is a more detailed schematic diagram of the interferometer, detector
circuit and portions of the optical path length difference control of FIG.
1;
FIG. 3 is a more detailed block diagram of the scanning circuit and optical
path length difference control of FIG. 1;
FIG. 4 is a more detailed block diagram of the storage circuit of FIG. 1;
FIG. 5 is a more detailed block diagram of the arithmetic circuit of FIG.
1;
FIG. 6 is a block diagram of an alternative arithmetic circuit;
FIG. 7 is a more detailed block diagram of a multi-function implementation
of the trigonometric function generator of FIG. 1;
FIG. 8 is a more detailed block diagram of an implementation of the optical
path length difference calculator circuit of FIG. 1; and
FIG. 9 is a flow chart showing the simplified method of this invention.
The invention may be accomplished using an interferometer including a
radiation source of predetermined wavelength for producing an
interferogram from radiation reflected from first and second surfaces.
Some means is necessary for varying the optical path length difference
between the first and second surfaces by varying either one or both of the
surfaces relative to each other. The optical path length difference is
varied in three discrete steps at one-quarter wavelength intervals: the
first or zero step; the second step at a one-quarter wavelength
(90.degree.) interval from the first step; and a third step at an
additional one-quarter wavelength interval and a half wavelength
(180.degree.) from the first.
There is at least one detector for sensing the intensity of the incident
interferogram radiation. More typically, there is an array of such
detectors so that the process is carried out at each of the detectors
immediately. For satisfactory results, the detector width is approximately
one-fifth of the spacing of the fringes of the interferogram for good
resolution. Each detector is scanned at each step to obtain from the
detector a signal representative of the level of intensity of the
interferogram at each detector. These intensity levels are stored
separately for each detector for each step in order to retain the
interferogram image presented at each of the steps. The means for storing
may include a sample and hold circuit for receiving the scanned inputs and
submitting them to an A to D converter, which then delivers them to a
digital memory for subsequent processing. For each detector, the first and
third intensities are combined additively to produce the d.c. spatial
frequency amplitude, and differentially to produce the cosinusoidal
spatial frequency amplitude. The sinusoidal spatial difference in
amplitude is then found from the difference between the d.c. amplitude and
the second intensity. These three amplitudes may include a constant which
can be eliminated at the generation of these amplitudes or subsequently
when the trigonometric function is being generated. The sign of the
optical path length difference can be immediately determined by
subtracting from the d.c. amplitude twice the intensity level at the
second step. If the d.c. amplitude is greater, the sign is positive; if
smaller, the sign is negative. This does not necessarily require a second
circuit, as the sinusoidal spatial frequency amplitude is the result of
that arithmetic combination and may be used as an ancillary source to
determine the sign.
Once the cosinusoidal and sinusoidal spatial frequency amplitudes have been
determined, they are used to generate any one of a number of trigonometric
functions of the phase angle of the radiation from the first and second
surfaces, e.g. sine, cosine, tan, cotan, sine.sup.2, and cosine.sup.2.
Subsequent to the development of a trigonometric function of the phase
angle, the phase angle is specifically determined and from it the optical
path length difference between the surface at each position may be simply
calculated.
That this approach is sound can be seen from substituting the values 0,
.lambda./4 and .lambda./2 in equation (4), supra. When t=0, equation (4)
is simplified to:
I.sub.1 (t)=K.sub.0 +K.sub.1 cos k.DELTA..sub.0 (10)
when t=.lambda./4, to:
I.sub.2 (t)=K.sub.0 -K.sub.1 sin k.DELTA..sub.0 (11)
when t=.lambda./2, to:
I.sub.3 (t)=K.sub.0 -K.sub.1 cos k.DELTA..sub.0 (12)
The sum of (10) and (12)
I.sub.1 +I.sub.3 =2K.sub.0 (13)
while the difference
I.sub.1 -I.sub.3 =2K.sub.1 cos k.DELTA..sub.0 (14)
and the difference of (13) and (11)
I.sub.1 +I.sub.3 -I.sub.2 =2K.sub.1 sin k.DELTA..sub.0
The term 2K.sub.0 represents the d.c. spatial frequency amplitude; 2K.sub.1
cos k.DELTA..sub.0 the cosinusoidal spatial frequency amplitude; and
2K.sub.1 sin k.DELTA..sub.0 the sinusoidal spatial frequency amplitude.
Once the cosinusoidal and sinusoidal amplitudes are obtained the
generation of a trigonometric function of the phase angle .phi.
(k.DELTA..sub.0) is easily made with any of a number of prior art
techniques used in conjunction with the Fourier analysis approach and the
value of .DELTA..sub.0 is calculated.
In one embodiment the system 10, FIG. 1, includes an interferometer 12
whose output interferogram is sensed by detector circuit 14. The optical
path length difference between the two surfaces being compared in
interferometer 12 is controlled by the optical path length difference
control 16, which provides the variation in the optical path length
difference in three steps at one-quarter wavelength intervals. At each of
those steps, detector 14 is read out by scanning circuit 18, whose output
is delivered to storage circuit 20. Each of the intensity levels derived
from each of the three steps I.sub.1, I.sub.2, I.sub.3 is delivered from
storage circuit 20 to arithmetic circuit 22, which simply calculates for
each detector the d.c. spatial frequency amplitude 24, the cosinusoidal
spatial frequency amplitude 26 and the sinusoidal spatial frequency
amplitude 28. The d.c. spatial frequency amplitude 24 is combined with the
second intensity I.sub.2 in the sign determining circuit 30, which
determines whether the sign of the path length difference between the
surfaces being compared is positive or negative, depending upon whether
the d.c. amplitude is greater or less than twice the intensity level of
the second step.
The cosinusoidal and sinusoidal amplitudes are combined in a trigonometric
function generator 32 to provide a trigonometric function of the phase
angle, which is then delivered to optical path difference calculator 34,
which determines the phase angle and from it the actual optical path
length difference .DELTA..sub.0 between the surfaces at each point
monitored by a detector.
Interferometer 12 includes a laser 40, FIG. 2 which provides radiation of
predetermined wavelength through beam-expanding telescope 41 including
lens 42 and 44 to beam splitter 46, from which the radiation is directed
to two surfaces to be compared; for example, reference surface 48 and test
surface 50, which is to be evaluated against reference surface 48. The
interference pattern formed by the recombination of the radiation
reflected from surfaces 48 and 50 is projected by lens 52 onto detector
14, which is typically an array of detectors including a matrix of
individual detectors 32 on a side, 50 on a side, or even 100 on a side.
Typically surfaces 48 and 50 may be four inches square, while array 14 is
but one inch square. Reference surface 48 is moved in quarter wavelength
intervals by a Piezoelectric crystal 54 in optical path length difference
control 16. Crystal drive 56 operates crystal 54 to provide the zero,
quarter wavelength, and half wavelength interval steps by moving surface
48 one-eighth of a wavelength at the second step to obtain the overall
quarter wavelength interval and by moving it a quarter wavelength and the
third step to obtain the overall half wavelength interval. The halving of
the motion of surface 48 is required because of the doubling factor
introduced by the reflection of the radiation from its surface. Crystal 54
and crystal drive 56 may be implemented by a device such as a Burleigh PZT
aligner/translator, model PZ-91, with which the first step would require
no volts, the second or quarter wavelength step would require 31.64 volts,
and the third or half-wavelength step would require 63.28 volts. Scanning
circuit 18, FIG. 3, includes an X scan 60 driven by clock control 62, and
a Y scan 64 driven by X scan 60. An end of scan circuit 66 monitors the
scanning operation and counter 68 is used to initiate a step request to
optical path length difference control 16. In operation, pulses from clock
control 62 cause X scan 60 to read out a row of detectors in the array of
detector circuit 14. At the end of a row scan, the signal from the X scan
output causes Y scan 64 to step to the next row. After the Y scan has
stepped to the last row, the signal is provided to end scan 66 which upon
the subsequent arrival of the last scan signal from X scan 60 produces an
end of scan signal which turns off clock control 62 and steps counter 68
from the first step to the second. The X scan circuit 60 and Y scan
circuit 64 may be set to scan 1, 32, 50, 100, or any other number of
detectors that may be contained in detector circuit 14. Voltage generator
70 in optical path length difference control 16 generates zero voltage at
the first step, the one-eighth wavelength drive voltage at the second, and
the one-quarter wavelength drive voltage at the third. Detector circuit 14
and portions of scanning circuit 18 may be implemented with a single
device known as a solid state self-scanning image photo detector array,
such as Fairchild CCD211; RCA 320X512 CED; Reticon RA-32X32A; and IPI 2D1.
Storage circuit 20 may include sample and hold circuit 72, FIG. 4, which
supplies the intensity level sensed by detector circuit 14 to A to D
converter 74, which converts the signals to digital form for storage in
digital memory 76. Each of the three interferogram images sensed at each
step by each of the detectors in detector circuit 14 is separately stored
in memory 76.
Arithmetic circuit 22 may include simply an adder circuit 80, FIG. 5, and
two subtractor circuits 82, 84. For each detector, the intensities from
the first and third steps I.sub.1 and I.sub.3 are added by adder circuit
80 to produce the d.c. amplitude 2K.sub.0. The same intensities I.sub.1
and I.sub.3 may be subtracted in circuit 82 to provide the cosinusoidal
amplitude 2K.sub.1 cos k.DELTA..sub.0. The subtractor circuit 84 may
subtract from the d.c. amplitude the intensity I.sub.2 from the second
step to produce the sinusoidal amplitude 2K.sub.1 sin k.DELTA..sub.0. The
cosinusoidal and sinusoidal amplitudes thus obtained may be forwarded
directly to the trigonometric function generator 32. Sign determining
circuit 30 may include a multiplication circuit 90 which multiplies by 2
the intensity level I.sub.2 derived from the second step, and a subtractor
circuit 92, which subtracts from the d.c. amplitude (I.sub.1 +I.sub.3)
from adder circuit 80 the output of multiplier circuit 90, I.sub.2. If the
d.c. amplitude is greater than twice I.sub.2 , the output of subtractor
circuit 92 is sensed by polarity sensor 94 to indicate a positive sign.
If, conversely, the value of 2(I.sub.2) is greater than the d.c.
amplitude, then polarity sensor 94 indicates that the sign is negative.
Alternatively, instead of providing a doubling circuit 90 in the I.sub.2
input, a halving circuit could be supplied in the d.c. amplitude input
from adder circuit 80.
Alternatively, arithmetic circuit 22', FIG. 6, may include adder circuit
100, divider circuit 102 or multiplier circuit 104, and two subtractor
circuits 106 and 108. From this circuit the outputs K.sub.1 cos k.DELTA.
from subtractor circuit 106 and K.sub.1 sin k.DELTA. from subtractor
circuit 108 are obtained directly without the additional factor of 2,
primarily from the use of divider circuit 102 which halves the input, or
alternatively the multiplying circuit 104 which doubles the complementary
input. As a result of this factor of 2 being removed from the arithmetic
circuit, the output of subtractor circuit 108, that is K.sub.1 sin
k.DELTA..sub.0 signal, may be fed directly to polarity sensor 94 to
determine sign without multiplying circuit 90 and subtractor circuit 92.
Trigonometric function generator 32, FIG. 7, may include simply a divider
circuit 110 for obtaining the trigonometric function, tangent, by simply
dividing the sinusoidal amplitude K.sub.1 sin k.DELTA..sub.0 by the
cosinusoidal amplitude K.sub.1 cos k.DELTA..sub.0.
Alternatively, trigonometric function generator 32 may include squaring
circuit 112, squaring circuit 114, adder circuit 116, and either divider
circuit 118 to obtain the trigonometric function cosine squared by
dividing the square of the cosine by the sum of the squares of the sine
and the cosine, or divider circuit 120 for obtaining the trigonometric
function sine squared by dividing the square of the sine by the sum of the
squares of the sine and the cosine.
Further, alternatively, trigonometric function generator 32 may include
squaring circuits 112 and 114, adder circuit 116, square root circuit 122,
and either divider circuit 124 for obtaining the trigonometric function
cosine by dividing the cosine by the square root of the sum of the cosine
squared and sine squared, or divider circuit 126 for obtaining the
trigonometric function sine by dividing the sine by the square root of the
sum of the cosine squared and sine squared.
The factor of two introduced by the arithmetic circuit 22 of FIG. 5 is
removed by generator 32.
Any one of these outputs: tangent, cosine squared, sine squared, cosine, or
sine, may be used in optical path length difference calculator circuit 34.
The squared functions of cosine and sine are preferred since their values
run only between zero and +1, making for a limited table memory
requirement.
Optical path length difference calculator circuit 34 includes a
trigonometric function table memory and cycle circuit 130, and comparator
circuit 132 which compares the incoming trigonometric function such as
cosine squared, for example, with the values of that function stored in
table 130. When a match is found, comparator circuit 132 enables gate 134
to pass the corresponding phase angle .phi. equal to k.DELTA..sub.0 to
multiplier circuit 136, where it is multiplied by the value of 1/k, or
.lambda./2.pi., to obtain the optical path length difference .DELTA..sub.0
between the two surfaces at the position monitored by the particular
detector.
The method of this invention may be more easily understood from the flow
diagram, FIG. 9, wherein at the first or zero step the first scan is made
and the level of intensity I.sub.1 is stored for each detector 140.
Following this, the optical path length is shifted by one quarter
wavelength 144, and the second scan and store of I.sub.2 is accomplished,
146. The optical path length difference is then shifted by a quarter
wavelength to obtain a total shift of a half wavelength, 148, and the
third scan and store of intensity I.sub.3 is accomplished, 150. Then the
d.c. amplitude is calculated frm I.sub.1 +I.sub.3, 152. The cosine
amplitude is calculated from I.sub.1 -I.sub.3, 154, and the sine amplitude
is calculated from I.sub.1 +I.sub.3 -I.sub.2, 156. Once this has been
done, the cosine and sine amplitudes are combined to generate any
particular trigonometric function of the phase angle between the
interfering wave fronts, 158. This phase angle is then determined, 160,
and used to calculate the optical length difference .DELTA..sub.0 between
the surfaces at a particular detector 162. The method is carried out for
each of the detectors in the detector circuit. The sign of .DELTA..sub.0
may be determined by comparing the d.c. amplitude term I.sub.1 +I.sub.3
with twice the intensity I.sub.2, 164; and if the d.c. amplitude term is
greater indicating a positive sign and if it is smaller indicating a
negative sign.
The operations performed by arithmetic circuit 22 in conjunction with
storage circuit 20, as well as those performed by the sign-determining
circuit 30, trigonometric function generator 32, and optical path length
difference calculator 34, may be carried out using a micro-processor such
as a an Intel-8080 or by a properly programmed digital mini-computer. The
table look-up function of optical path length calculator circuit 34 may be
implemented by an EPROM. Subsequent to obtaining .DELTA..sub.0 and the
sign, these outputs may be further processed, as is known in the prior
art, to detect and eliminate any tilt and tip factors between the two
surfaces being compared and to ascertain the n order determination to
resolve any uncertainties of .DELTA..sub.0 between zero and P/2.
Other embodiments will occur to those skilled in the art and are within the
following claims:
* * * * *
|
|
 |
|
 |
Description |
|
