Optics: measuring and testing – By light interference – For dimensional measurement
Reexamination Certificate
1999-10-20
2001-02-06
Kim, Robert (Department: 2877)
Optics: measuring and testing
By light interference
For dimensional measurement
C356S515000
Reexamination Certificate
active
06184994
ABSTRACT:
BACKGROUND
High-accuracy interferometric surface metrology is constantly gaining importance, not only in the classical area of optical fabrication, but also for new applications, such as magnetic disc flatness or semiconductor wafer flatness. Requirements for measurement resolution in the sub-nanometer range have become quite common. Of high importance is the slowly varying shape error, as well as the medium to high spatial frequency waviness of the surface under test. Achieving not only repeatability or reproducibility, but also absolute measurement accuracy for surface height measurements, with high spatial resolution, is difficult, since other applicable measurement techniques for calibration do not exist which are considerably more accurate than the interferometric test.
In the two-beam interferometers commonly used for testing, that is Fizeau-interferometer, Twyman-Green interferometer, or Mach-Zehnder interferometer, an illuminating beam is split into two beams. One beam, called the test beam, is directed to the surface under test, where it is reflected. The other beam, called the reference beam, is reflected at a reference surface. After recombination, the two reflected beams travel to a detector, usually a camera, where they interfere. The primary information contained in the resulting interferogram is then the phase difference between these two beams. Therefore, the shape of the test surface is not obtained independently, but only in combination with the reference surface. While the repeatability of the measurements can be extremely high, the measurement result of the test surface is only as accurate as the reference surface. If the reference surface deviations can be determined in a calibration step, they can be eliminated from the measurement. Then, the overall accuracy of the test surface map is limited by the accuracy of this calibration map.
The determination of a test surface independent of the reference surface is called an absolute measurement. Once one surface is absolutely known, it can act as a reference standard in subsequent interferometric tests, allowing for absolute testing. Thus, it is very desirable to have a technique available which provides an absolute surface deviation map without requiring any information about the shape of the other surfaces involved in the interferometric test.
The Fizeau interferometer configuration inherently is best suited for high accuracy testing, since the test beam and the reference beam are split by the last surface of the interferometer optics. The reference beam is reflected at this reference surface; and it is directed to the interferogram detector. The test beam is transmitted through the reference surface to the surface under test, from where it is reflected back to the interferometer and the interferogram detector. Consequently, all internal optical components of the interferometer are traversed by the test beam, as well as by the reference beam. These optical components are all in the common path of the two beams. Phase distributions resulting from the optics in the common path are the same for both beams. Consequently, these optics phase distributions drop out of the phase difference between the two beams. The only two surfaces which then are not in a common path are the reference surface and the test surface, and the interferogram phase is proportional only to the sum of both of these surface deviations.
The cancellation of the phase distributions due to the internal interferometer optics is strictly true only when the test beam and the reference beam travel on identical paths through the interferometer optics. This can only be the case when the test surface and the reference surface are identical, and are placed close to each other. Otherwise, a residual phase error, the so-called retrace error, due to the interferometer optics, is superposed on the measurement. Furthermore, in order to avoid difraction effects on the two beams interfering on the detector, the test surface has to be well imaged onto the interferogram detector. Thus, a highly accurate interferometric test requires that the surface deviations of the test surface are small, that the test and reference surfaces are aligned parallel to one another, and that the optical design of the interferometer optics minimizes re-trace errors.
Several techniques for absolute flatness testing have been described in the past; and they are listed below in the following articles:
List of Articles
1. G.Schulz, J.Schwider, “PRECISE MEASUREMENT OF PLANENESS”
Applied Optics
6, 1077 (1967)
2. G.Schulz, J.Schwider, “INTERFEROMETRIC TESTING OF SMOOTH SURFACES”
Progress in Optics
13, Ed.E Wolf, No.Holland 1976
3. B. S. Fritz, “ABSOLUTE CALIBRATION OF AN OPTICAL FLAT”
Optical Engineering
23, 379 (1984)
4. J.Grzanna, G.Schulz, “ABSOLUTE TESTING OF FLATNESS STANDARDS AT SQUARE-GRID POINTS”,
Optics Communications,
77, 107 (1990)
5. M.Kuchel, “METHOD AND APPARATUS FOR ABSOLUTE INTERFEROMETRIC TESTING OF PLANE SURFACES,
U.S. Pat. No.
5,106,194, 1992
6. G.Schulz, ABSOLUTE FLATNESS TESTING BY THE ROTATION METHOD USING TWO ANGLES OF ROTATION”,
Applied Optics
32, 1055 (1993)
7. G. Schulz, J. Grzanna, ABSOLUTE FLATNESS TESTING BY THE ROTATION METHOD WITH OPTIMAL MEASURING-ERROR COMPENSATION”,
Applied Optics
31, 3767 (1992)
8. C.Ai, J. C.Wyant, ABSOLUTE TESTING OF FLATS BY USING EVEN AND ODD FUNCTIONS,
Applied Optics
32, 4698 (1993)
9. C. J. Evans, R. N. Kestner, “TEST OPTICS ERROR REMOVAL”,
Applied Optics
35,1015 (1996)
10. C.Ai, J. Wyant, L. Z. Shao, R. E. Parks, “METHOD AND APPARATUS FOR ABSOLUTE MEASUREMENT OF ENTIRE SURFACES OF FLATS”, U.S. Pat. No. 5,502,566, 1996
11. K. Freischlad and C. L. Koliopoulos, “FOURIER DESCRIPTION OF DIGITAL PHASE-MEASURING INTERFEROMETRY”,
Journal Optical Soc. Am.A,
Vol. 7, 542-551 (1990)
12. W. H. Press, B. P.Flannery, S. A. Teukolsky and W. T. Vetterling, “NUMERICAL RECIPES IN C”,
Cambridge University Press
. Cambridge 1988.
Other than the Kuchel article, all of the techniques referenced in the above articles are based on what is known as the classic 3-flat test. For the 3-flat test, three flats are intercompared interferometrically in different combinations, using a Fizeau interferometer, with a short cavity between the reference surface and the test surface. The measurements of the three flats, labeled A, B and C, are carried out in the following manner:
Measurement M
1
:reference surface=A, test surface=C
Measurement M
2
:reference surface=B, test surface=C
Measurement M
3
:reference surface=B, test surface=A
A numerical combination of the three measured surface maps, M
1
, M
2
, and M
3
, allows the determination of the absolute one-dimensional surface profile along one diameter of each surface. Outside of that line, no absolute surface data are obtained. These previously described techniques for absolute testing represent one or more of the following shortcomings (A to C):
(A) An assumption or approximation, about the surface shape of at least one flat has to be made. Thus, the test is absolute only if the surface actually follows that assumption. For example, the above article No. 3, by B. S. Fritz, assumes that the surface shape is adequately represented by an expansion in Zernike-polynomials; and the three articles listed above as references 8, 9 and 10, assume that certain angular frequencies are not present.
(B) The spatial resolution of the two-dimensional map is either coarse, or the error in the absolute maps, due to measurement errors in the measured maps M
1
, . . . M
m
is large. In this case, as noted in the articles of references 1, 2 and 4 above, discussion about a large error propagation factor from the measurement to the absolute map is made.
(C) A large amount of numerical computation is required as noted in reference No. 6 by G. Schulz.
The method described in reference No. 5, to M. Kuchel is based on measurements in a folded beam path, where the surfaces to be tested constitute the two fold mirrors and the return mirror. Measurements at different deflecti
ADE Phase Shift Technology
Kim Robert
Ptak LaValle D.
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