Optical system for surface topography measurement

An interferometric system for characterizing the surface of a test object, such as an aspheric surface. A white light interferogram is produced wherein the principal fringe indicates zero optical path difference between a test surface and a reference surface. Wavefronts from either of the test or reference surfaces are translated by incremental amounts. A multi-point detector array is used to make multi-point contrast readings. Points of contrast maxima for each detector point are computed by a statistical determination. A centroid function is preferred. By recording the points of maximum contrast and the incremental wavefront translation, two dimensional plots showing zero optical path differences for the two surfaces are obtained, thereby comparing the test and reference surfaces.

TECHNICAL FIELD 
The invention relates to an interferometric system for measuring the 
point-for-point distance deviation of an unknown surface from a known 
reference surface. The invention features a surface or a wavefront 
measuring interferometer system with a large measurement dynamic range. In 
particular, it deals with the method and apparatus for measuring optical 
path difference of a wavefront reflected from an unknown surface figure 
from that of a wavefront reflected from a known reference surface. 
BACKGROUND ART 
The use of interferometric systems for surface and wavefront measurement is 
well known in optics. In most of the automated interferomatic surface 
measurement systems, the geometry and the shape of the fringes produced 
are analyzed to obtain the required measurement data. Such measurement 
systems are particularly useful for measuring and testing aspheric lens 
surfaces. In recent years there has been considerable interest in making 
use of complex and higher order aspheric surfaces in optical system 
design. 
Aspheric lenses are well known in optics. For many years, simple aspheric, 
such as parabolic surfaces, have been used in telescopes. More recently, 
computer controlled lens grinding machines have been able to produce 
complicated aspheric lens surfaces. Some of these complicated aspheric 
surfaces are for spatial compression of multi-element convex-concave lens 
systems. For example, in microscopes and cameras it has been the practice 
in the prior art to achieve desired corrections and magnifications by 
means of groups of lenses having specified concave or convex lens 
curvatures, refractive powers and spacings. Now, however, it is possible 
to produce a single aspheric lens which will replace a group of lenses. 
When testing such surfaces using conventional interferometers, the density 
of the fringe pattern becomes too high and their shapes too complex to 
handle. A lack of good and simple means of testing such complex surfaces 
has been somewhat responsive for the delay in their widespread use. Even 
though the desired shape of a lens may be specified, it is difficult to 
determine when a precision surface has been attained. A precision surface 
is one having a point-for-point accuracy of the order of a fraction of a 
wavelength. The object of the present invention is to devise a method and 
apparatus for the testing of complex and higher order aspherical optical 
surfaces which are impossible to test based on existing testing methods. 
In U.S. Pat. No. 4,022,532, issued May 10, 1977, Montagnino teaches use of 
a dual beam laser interferometer for comparing phases of multiple 
reflective spots on a test object. A reference beam, whose path length is 
modulated, is combined with the light reflected from the spots. Separate 
detector elements measure the interference pattern from at least two spots 
simultaneously. A shift in position of one spot relative to a reference 
spot is determined by measuring the phase shift between spots. Using this 
approach, the surface configuration of an optical surface may be 
monitored. 
In U.S. Pat. No. 3,694,088, issued Sept. 26, 1972 Gallagher et al. teach 
use of a dual beam laser interferometer for the study of intensity changes 
in a fringe pattern by means of a TV camera. The pattern intensity is 
changed twice by rotation of a quarter-wave plate, producing two known 
phase shifts. By storing pattern intensity values before and after the 
rotations, the intensity values can be correlated with the phase shift to 
solve simultaneous equations which yield phase and amplitude plots for the 
wavefront from the object under study. 
In my prior patent application, Ser. No. 912,212, now U.S. Pat. No. 
4,225,240 granted Sept. 30, 1980, an interferometric method is disclosed 
for measuring the optical path difference between a test surface and a 
reference surface. The method consists of varying the interferometric 
optical path length difference between a reference and a test surface in 
three steps at one-quarter wavelength intervals. Next, the intensity of 
the interferogram radiation is sensed at least at one position of the 
interferogram for each of the steps. The intensity sensed at each position 
and at each step is stored. For each of the positions the intensity of the 
first and third steps is added to produce a d.c. spatial frequency 
amplitude, and the intensity of the second step is subtracted from the 
d.c. amplitude to produce the sinusoidal spatial frequency amplitude. The 
sinusoidal and cosinusoidal amplitudes are combined to produce a 
trigonometric function of the phase angle of the radiation reflected from 
each position of the reference and test surfaces. This function is 
representative of the optical path length difference at each position. A 
multi-aperture CCD detector is used to detect intensity changes of the 
fringes. An advantage of my prior invention is that the sign of optical 
path differences may be determined, depending on whether the d.c. 
amplitude is larger or smaller than twice the intensity at the second 
step. 
In the book "Optical Shop Testing" by Malacara (Wiley, publisher), p. 17, a 
procedure is described for determining the deviation of an aspheric 
surface from a spherical surface or an irregular surface from a reference 
flat surface. One surface is placed atop the other so that an optical path 
difference between the two will produce fringes when illuminated by a 
monochromatic source. 
In an article entitled "Quasi-Real-Time High Precision Interferometric 
Measurements of Deforming Surfaces" in SPIE, Vol. 153 (1978) p. 126, 
Massie describes a system wherein two beams with orthogonal polarizations 
are shifted in frequency by different amounts using acousto-optic devices. 
The reference surface receives one polarization and frequency and the test 
surface the other. With appropriate optics the phase of one beam is 
compared to the other so that optical path differences can be mapped. 
In an article entitled "Automatic Data Reduction of both Simple and Complex 
Interference Patterns" in SPIE, Vol. 171 (1979) W. Augustyn discloses a 
computer fringe pattern analysis method whereby points on a reference 
interferogram representing zero path difference are placed in memory. 
Next, a test interferogram is generated and the stored points are 
subtracted from the actual. The difference between the two patterns is a 
new interferogram for user study. 
White light interferometry has also been used for monitoring surfaces and 
surface profiles, but its application has been limited to interferometric 
objective lenses. The use of white light enables one to identify the 
zero-order fringe as the white light fringe and hence permits 
quantitative, but manual reduction of interferograms. This is extremely 
important when surface discontinuities are involved. Several microscope 
objectives that are capable of producing white light fringes on micro 
specimens are commercially available and they are typically used for 
measuring the film thicknesses and monitoring surfaces with 
discontinuities several wavelengths deep. Unlike other interferogram 
analyzers cited earlier no attempt has been made to automate the detection 
and interpretation of white light fringe patterns. 
An object of the invention is to provide a simple and direct method for 
precision characterization of unknown surfaces which does not require 
visual fringe interpretation and which is suited to the measurement of 
discontinuous and steeply contoured aspheric surfaces. 
DISCLOSURE OF INVENTION 
The above object has been achieved in a test surface measuring system which 
features a white light dual beam interferometer. One beam has wavefronts 
reflected from the unknown test surface of a test object, while the other 
beam has reference wavefronts from a reference surface. Zero order fringes 
produced by interference of the two beams represent zero path differences, 
thereby indicating point coincidences between the reference surface and 
the test surface. A zero order fringe exhibits maximum contrast which is 
identified by modulating the phase of the reference wavedfront by a 
predetermined amount. An array of points on the test surface may be 
measured by scanning the interference pattern, point by point, and 
recording contrast variations by means of a multi-aperture CCD detector, 
with a CCD aperture or diode corresponding to each test point. If a 
maximum contrast level is observed by an aperture, that point is recorded 
as having zero path difference with respect to the reference surface. 
After all of the points of the test surface have been scanned, the 
reference surface is moved by a predetermined very small amount and the 
process is repeated. After all points have been scanned, the test surface 
is again moved, and so on, with the objective of locating points of 
maximum contrast. 
To find points of maximum contrast, a calculation is made involving all 
intensity levels detected at each detector aperture for all increments of 
motion. This calculation, similar to a centroid determination, identifies 
one aperture or point of maximum statistical importance for each detector 
aperture which is defined as the point of maximum contrast. The maximum 
contrast level is recorded, together with the slice number indicating 
where the maximum contrast level occurred. Detector apertures where 
maximum contrast occurs correspond to points of zero path difference 
relative to the reference surface, offset by an amount that the test 
surface was moved. Since the extent of test surface movement is known from 
the slice number, the pointwise distance deviation of the test surface 
from the reference surface is known for each test point corresponding to a 
detector aperture. 
Advantages of the invention are as follows: (1) the measurement method 
relies on maximum contrast to establish zero path difference and thus 
constitutes a direct measurement of a surface, as opposed to indirect 
fringe interpretation methods; (2) the method may be used for non-regular 
reflective surfaces, such as semiconductor integrated circuits, as well as 
for aspheric optical surfaces, including steep aspheric surfaces.

BEST MODE FOR CARRYING OUT THE INVENTION 
With reference to FIG. 1, a scanning dual beam interferometer of the 
Twyman-Green type is shown. Such interferometers have previously used 
laser or monochromatic sources. The long coherence length of these sources 
produced fringe patterns over an entire surface which were useful in 
interferometric measurements of surface contours. In contrast with prior 
practices, it has been discovered that for purposes of the present 
invention, the fringe patterns over the entire surface are not useful 
because the number and spacing of fringes makes fringe detection 
difficult. 
It has been known that when a broad-band source is used in an 
interferometer, as compared to a monochromatic source, the fringes are 
formed only when the optical path difference between the interfering 
wavefronts, D, is small. When the source bandwith is comparable to the 
mean wavelength, the fringe contrast reduces to a minimum, i.e., when the 
path difference is equal to the mean wavelength. This information is 
valuable since it permits one to detect optical path differences by 
measuring the fringe contrast. An ability to detect a fractional change in 
fringe contrast, say ten percent, will result in surface definition of 0.1 
of the mean wavelength. The measurement of the contrast of white light 
fringes provides a means of identifying regions of a test wavefront that 
differ from the reference wavefront by no more than the specified amount, 
say 0.1 wavelength, as a definition of equal phase contours. 
With reference to FIG. 1, such a white light point source is located at 
region 11, in front of reflector 13 facing the beam splitter 15. The 
source may be a common incandescent high intensity lamp which projects a 
diverging beam 17 which is collimated by a collimator 19 prior to entering 
beam splitter 15. One portion of the beam is directed to the reference 
surface 21 of a reference object 23 through a focusing lens 22. The 
reference surface 21 has a precisely known topography, such as being 
spherical to within 0.05 wavelength. The surface need not be spherical and 
may have another precision shape, such as being flat. Under such 
conditions the focusing lens 22 is not used. Light is reflected from the 
reference surface 21 and passes through beam splitter 15 and through a 
focusing telescope 35 to a detector, such as diode array 25 which will be 
discussed below. 
Another portion of beam 17 pssses through beam splitter 15 and through a 
focusing lens 32, identical to focusing lens 22, to the unknown test 
surface 31 of an object 33 such as an aspheric lens. Light which is 
reflected from the unknown surface 31 is also directed by beam splitter 15 
to the diode array 25. Both the reference wavefront from the reference 
surface 21 and the test wavefront from the test surface 31 pass through 
the focusing telescope 35. Telescope 35 produces a flat field image of the 
test and reference surfaces onto the diode array 25. The size of the image 
corresponds to the size of the detector. 
The reference surface 21 and the test surface 31 must be slightly 
reflective to white light, at least 1%, so that an interference pattern 
can be formed. If one of the surfaces is completely absorptive of white 
light, it must be made slightly reflective, perhaps by means of a 
reflective coating, so that measurements can be made in accord with the 
present invention. 
A piezoelectric transducer 29 is positioned behind the reference lens 23. 
The purpose of the transducer 29 is to translate the reference lens by 
incremental distances on the order of 1 micron. The transducer may 
translate lens 23 first in one direction, say 50 microns and then in the 
opposite direction by 50 microns for a total of 100 microns. To accomplish 
this, first a positive d.c. voltage is applied to the transducer in 
incremental amounts and then a negative d.c. voltage is applied to the 
transducer in equal but opposite incremental amounts. Piezoelectric 
transducers respond in well-known ways to such d.c. voltages and 
commercially available transducers for moving mirrors are frequently used 
for the purpose of adjusting laser mirrors. The initial position of the 
reference mirror 21 is in a position of estimated zero path difference 
with respect to test surface 31. The reason for this is that the 
deviations of the test surface from the reference surface will fall on 
either side of the initial position. Alternatively, the initial position 
could be above or below the position of zero path difference and the 
reference surface moved in only one direction until all corresponding 
points of zero path difference have been found. As previously mentioned, 
points of zero path difference are identified by contrast maxima in 
apertures or diodes of the CCD detector array. Such contrast maxima are 
actually interference fringes, but are not observed as fringes. Rather, 
the contrast maxima corresponding to points of zero path difference 
relative to the reference surface, offset by an amount that the test 
surface has been moved. It is therefore important to record test surface 
incremental movement so that the pointwise deviation of the test surface 
from the reference surface is known for each test point. The detector 
array reads all test points for each incremental amount of test surface 
translation. Each reading of the detector array may be thought of as an 
observation of a horizontal slice of the test surface. The number of 
slices will equal the number of incremental translations of the test 
surface. The amount of translation is typically a fraction of the mean 
wavelength of light, 1 micron in the example above, but greater or smaller 
translations may be used, depending upon the desired resolution of the 
test surface and the amount of computing capability available for 
determining contrast maxima and recording such information. The extent of 
test surface incremental motion also depends upon the range over which the 
phase of the reference wavefront can be scanned by the detector array with 
a desired amount of accuracy. 
The information which is recorded consists of multi-point data in a 
two-dimensional slice or slices having a resolution which corresponds to 
the spacing and the aperture of the diodes in the diode array 25. Output 
data characterizing an unknown test surface consists of position 
information regarding contrast maxima within the diode array plus the step 
level. The shape of the test wavefront with respect to the reference 
wavefront is mapped by considering the points of the diode array at which 
maximum contrast has been recorded on each slice. Maximum contrast points 
on all such slices completely characterize the unknown surface. A 
precision of the order of 0.025 micron is easily obtained using the zero 
order fringe scanning method described herein. In the description of the 
method of the present invention, both the a.c. or oscillatory motion 
provided to the reference surface 21, as well as the d.c. or step 
translation of the reference surface 21 necessary to provide the 
incremented zero path differences for the test surface 31 have been 
generated by a single piezoelectric transducer 29. Alternatively, a 
separate transducer could be provided behind object 33 to provide either 
the a.c. component or the d.c. component, while the first transducer 29 
produced the remaining component. 
The range of deviation of the test surface from that of a reference surface 
that can be measured using this measurement concept depends on the range 
over which the phase of the reference wavefront can be scanned with the 
desired accuracy. Hence it is ideally suited for measuring non-regular 
reflective surfaces and steep aspheric surfaces. 
The apparatus of FIG. 1 is especially useful for relatively small test 
surfaces, ranging from less than 1 millimeter to several centimeters in 
width. In general the reference surface is matched, as closely as possible 
with an unknown test surface. For example, a convex aspherical test 
surface is matched with a convex spherical reference surface. A concave 
aspherical test surface is matched with a concave spherical reference 
surface. A continuous or discontinuous near-planar test surface is matched 
with a planar reference surface. 
Data acquisition for the method of the present invention may be understood 
in more detail with reference to FIG. 2. Typically, the CCD array 25 would 
be a rectangular or square grid of diodes or apertures 37, each aperture 
being mutually spaced and equidistant from all neighboring apertures. In 
FIG. 2, a typical array is shown having 100 apertures or diodes to a side 
or a total of 10,000 diodes. A typical size for such an array would be 
approximately 2 centimeters on a side. Such diode arrays are known as 
solid state self-scanning image photodetector arrays, such as Fairchild 
CCD 211; RCA 320 X512 CCD; Reticon RA-32X32A; and IPI 2D1. The array is 
usually scanned by sensing the intensity signal level of each detector 
element, one at a time, in sequence. Each diode is connected to a 
capacitor, such that diode conduction in response to light impinging on 
the diode causes a corresponding voltage drop charging a connected 
capacitor. The capacitor retains its charge long enough to be sensed. The 
voltage on the capacitor is proportional to the light intensity sensed by 
the diode. 
As previously mentioned, the path difference between the test surface and 
the reference surface is translated by a slight amount, say 0.1 
wavelength. The amount of path length difference yields the ultimate 
mapping accuracy. Mapping at accuracies greater than 0.1 wavelength is 
possible because the path length difference may be adjusted by miniscule 
amounts, using the piezoelectric transducer 29. Variations as small as one 
or two atomic layers are theoretically possible. For a test surface having 
a depth of 50 wavelengths to be scanned, 500 levels, each 0.1 wavelength 
apart, are necessary. Of course greater or smaller levels can be taken, 
using larger or smaller separations. The smaller the separation, the 
greater the resolution and the measurement time. 
One of the problems which occurs in carrying out the present invention is 
in determining contrast maxima. With very small incremental translations 
of the reference surface, the contrast changes appear sinusoidal, with 
peaks of approximately equal amplitude. Contrast maxima are determined in 
the following way. FIG. 2 indicates that the detector array 25 has an 
information output, a signal converted to digital form representing the 
amplitude of the light level for each diode. This group of signals is 
transmitted along line 26 to difference registers. It should be understood 
that FIG. 2 is highly schematic, but that the method of determining 
contrast maxima will be understood with reference to the simplification of 
the figure. Three registers 41, 45 and 47 are provided, each register 
consisting of a memory array having a storage location corresponding to 
each of the diodes in the detector 25. Storage array 41 stores the initial 
value of each detector, designated x.sub.o. Register 47 stores a running 
total of the value .vertline.x-x.sub.o .vertline. which is defined as the 
function f(s). The value of this function is stored in locations within 
register 47, one location corresponding to each of the diodes in the 
detector 25. The number of storage locations corresponds to the number of 
storage locations in register 41. 
The third register 45 stores the value of the function f(s) multiplied by 
the slice number, a new function defined as Sf(s). Once again, the value 
of this function is computed for each diode of detector 25 with the number 
of storage locations in the register 45 corresponding to the number of 
storage locations in registers 41 and 47. 
To determine a contrast maxima, a calculation is used which gives a 
meaningful statistical weighting to the various values of 
.vertline.x-x.sub.o .vertline.. The contrast maximum for each point is 
defined in terms of a centroid calculation using the formula 
##EQU1## 
Using this formula a value x may be calculated for each diode in the 
detector. The value which is found is identified with the slice number 
where such a value, or the nearest value to it, is located. Upon 
performing such a calculation, two values are ultimately recorded, one 
being the value of the contrast maximum for each diode detector which is 
stored in register 51 and the slice number where the maximum occurs, 
stored in register 53. Other statistical functions might be used to define 
contrast maxima, but the centroid function has been found to be preferred 
because it gives appropriate weighting to nearby contrast maxima. 
At points of contrast maxima, zero path-length differences occur with 
respect to the reference surface. Thus, information in the contrast 
register 51 and the step register 53 provides two dimensional slices 
indicative of where zero optical differences exist relative to the 
reference surface. By knowing the shape of the reference surface, a direct 
comparison may be made between the reference surface and the deviation of 
the test surface therefrom. Registers 41, 44, 47, 51 and 53, as well as 
controller 50 may be part of a single computer system or separate units. 
The data processing system and method described herein has the advantage 
that only a limited amount of data is stored. Assuming 500 levels to be 
scanned with 50 scans per diode and a total of 10,000 diodes, as in 
detector 25, approximately 250 million data points will be examined. But, 
using the data processing method described herein, only 40,000 points are 
ultimately recorded using that information, two for each diode with one 
point being the contrast maximum value, the other being the level at which 
the contrast maximum value occurred. 
The measurement technique described above using two-beam interferometers, 
such as a Twyman-Green interferometer, can also be carried out with common 
path interferometers. In two-beam interferometers the reference and test 
beams travel widely separated paths and hence are differently affected by 
vibration and air turbulence. This problem is severe particularly when 
large aperture optical systems are involved. In common path 
interferometers, the reference and test beams traverse the same general 
path and hence are not greatly affected by problems of turbulence and 
vibration. 
An example is the scatter plate interferometer shown in FIG. 3 and as 
further described in the book "Optical Shop Testing" by Malacara, page 
818. The lens 51 forms an image of a small white light source S at region 
S' on the mirror being tested. The scattering of the image beam by the 
scatter plate 57 forms several point source images over the rest of the 
test mirror 60. 
The test mirror 60 forms an image of the scatter plate 57 onto an identical 
scatter plate 67, which is placed so that there is point-for-point 
coincidence between scatter plates 57 and 67. A part of the light incident 
on the scatter plate 57 passes through it without scattering and arrives 
at region S'. Since this beam touches the mirror 60 only at a small region 
around S', it is not affected by the errors of the mirror surface. This 
beam acts as the reference beam. Some of the incident light is, however, 
scattered by scatter plate 57 and fills all of the aperture of mirror 60. 
This beam picks up the errors of the mirror and is the test beam. 
Consider a ray incident at a point A on the scatter plate 57. The directly 
transmitted ray, the solid line in FIG. 3, follows the path through half 
mirror 55 designated by the letters AS'A'. After reflection downwardly 
from mirror 55, the ray encounters at image point A' a scattering center 
that is identical to the one at A. This ray is scattered at A' and gives 
rise to a cone of rays 69. The rays scattered at A, dotted lines, fill the 
mirror 60, arrive at the image point A', and pass through scatter plate 67 
without scattering. Thus we have two mutually coherent beams emerging from 
scatter plate 67; one beam is directly transmitted by scatter plate 57 and 
scattered by scatter plate 67, and the second is scattered by scatter 
plate 57 and transmitted by scatter plate 67. An observer looking at the 
mirror surface 60 through scatter plate 67 will see an interferogram 
between these two beams. If the mirror is free of any error in the region 
of S', the interferogram will provide explicit information about the 
mirror aberrations, as in any separate-beam inferferometer. 
This configuration can be slightly modified as shown in FIG. 4 to make use 
of the measurement method described in this invention. The reference beam, 
instead of being reflected by the center of the test mirror, is reflected 
by a piezo driven reference plane mirror 71. By translating the reference 
plane mirror 71 with a piezoelectric crystal 73, a zero path difference 
condition can be established for different zones of the test surface. 
Translational motion is used as previously described. The motion of the 
reference mirror, as in the two-beam interferometer, described with 
reference to FIG. 1, once again provides a means of quantitatively 
defining the test surface. Note that in FIG. 4 the reference surface 
figure is a vertex sphere of the test surface. This adaptation of the 
measurement technique is very important since it permits its use in cases 
involving large and steep astronomical mirror surfaces. 
One type of non-regular reflective surface constitutes semiconductor 
integrated circuits, prior to packaging. Sometimes these circuits are 
existing on wafers, prior to scribing and breaking into individual units. 
Other times, the individual circuits are mounted on a carrier or holder. 
In either case, a beam from the beam splitter may be reflected from the 
surface and caused to form an interference pattern with the wavefront from 
the reference surface. The reference surface could be an optical flat and 
the deviations which are measured would be those of mesas formed by 
coatings having different step heights. Such step heights occur because of 
masking certain portions of the circuit and then dissolving or etching 
unmasked portions. There are also other reasons for these step heights. In 
semiconductor manufacturing, it is important to measure the step heights 
for quality control, research and failure analysis purposes. 
In this application the references to wavelengths and fractions thereof 
refer to the mean wavelength of the white light source.