Optics: measuring and testing – By light interference – For dimensional measurement
Reexamination Certificate
2001-04-09
2004-11-16
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By light interference
For dimensional measurement
C356S521000
Reexamination Certificate
active
06819435
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to wavefront analysis generally and to various applications of wavefront analysis.
BACKGROUND OF THE INVENTION
The following patents and publications are believed to represent the current state of the art:
U.S. patents:
U.S. Pat. Nos. 5,969,855; 5,969,853; 5,936,253; 5,870,191; 5,814,815; 5,751,475; 5,619,372; 5,600,440; 5,471,303; 5,446,540; 5,235,587; 4,407,569; 4,190,366;
Non-U.S. patents:
JP 9230247 (Abstract); JP 9179029 (Abstract); JP 8094936 (Abstract); JP 7261089 (Abstract); JP 7225341 (Abstract); JP 6186504 (Abstract);
Other publications:
Phillion D. W. “General methods for generating phase-shifting interferometry algorithms”—Applied Optics, Vol. 36, 8098 (1997).
Pluta M. “Stray-light problem in phase contrast microscopy or toward highly sensitive phase contrast devices: a review”—Optical Engineering, Vol. 32, 3199 (1993).
Noda T. and Kawata S. “Separation of phase and absorption images in phase-contrast microscopy”—Journal of the Optical Society of America A, Vol. 9., 924 (1992).
Creath K. “Phase measurement interferometry techniques”—Progress in Optics XXVI, 348 (1988).
Greivenkamp J. E. “Generalized data reduction for heterodyne interferometry”—Optical Engineering, Vol. 23, 350 (1984).
Morgan C. J. “Least-squares estimation in phase-measurement interferometry”—Optics Letters, Vol. 7, 368 (1982).
Golden L. J. “Zernike test. 1: Analytical aspects”—Applied Optics, Vol. 16, 205 (1977).
Bruning J. H. et al. “Digital wavefront measuring interferometer for testing optical surfaces and lenses”—Applied Optics, Vol. 13, 2693 (1974).
SUMMARY OF THE INVENTION
The present invention seeks to provide methodologies and systems for wavefront analysis as well as for surface mapping, phase change analysis, spectral analysis, object inspection, stored data retrieval, three-dimensional; imaging and other suitable applications utilizing wavefront analysis.
There is thus provided in accordance with a preferred embodiment of the present invention a method of wavefront analysis. The method includes obtaining a plurality of differently phase changed transformed wavefronts corresponding to a wavefront being analyzed which has an amplitude and a phase, obtaining a plurality of intensity maps of the plurality of phase changed transformed wavefronts and employing the plurality of intensity maps to obtain an output indicating the amplitude and phase of the wavefront being analyzed.
There is also provided in accordance with a preferred embodiment of the present an apparatus for wavefront analysis including a wavefront transformer operating to provide a plurality of differently phase changed transformed wavefronts corresponding to a wavefront being analyzed which has an amplitude and a phase, an intensity map generator operating to provide a plurality of intensity maps of the plurality of phase changed transformed wavefronts and an intensity map utilizer, employing the plurality of intensity maps for providing an output indicating the amplitude and phase of the wavefront being analyzed.
Further in accordance with a preferred embodiment of the present invention the plurality of intensity maps are employed to provide an analytical output indicating the amplitude and phase.
Still further in accordance with a preferred embodiment of the present invention the plurality of differently phase changed transformed wavefronts are obtained by interference of the wavefront being analyzed along a common optical path.
Additionally in accordance with a preferred embodiment of the present invention the plurality of differently phase changed transformed wavefronts are realized in a manner substantially different from performing a delta-function phase change to the transformed wavefront.
Further in accordance with a preferred embodiment of the present invention the plurality of intensity maps are employed to obtain an output indicating the phase which is substantially free from halo and shading off distortions.
Preferably, the plurality of differently phase changed transformed wavefronts include a plurality of wavefronts resulting from at least one of application of spatial phase changes to a transformed wavefront and transforming of a wavefront following application of spatial phase changes thereto.
Additionally in accordance with a preferred embodiment of the present invention, the step of obtaining a plurality of differently phase changed transformed wavefronts includes applying a transform to the wavefront being analyzed thereby to obtain a transformed wavefront and applying a plurality of different phase changes to the transformed wavefront, thereby to obtain a plurality of differently phase changed transformed wavefronts. Preferably, the plurality of different phase changes includes spatial phase changes and the plurality of different spatial phase changes are effected by applying a time-varying spatial phase change to part of the transformed wavefront.
Further in accordance with a preferred embodiment of the present invention the plurality of different spatial phase changes are effected by applying a spatially uniform, time-varying spatial phase change to part of the transformed wavefront. Preferably, the transform applied to the wavefront being analyzed is a Fourier transform and wherein the step of obtaining a plurality of intensity maps of the plurality of phase changed transformed wavefronts includes applying a Fourier transform to the plurality of differently phase changed transformed wavefronts.
Further in accordance with a preferred embodiment of the present invention the transform applied to the wavefront being analyzed is a Fourier transform and the plurality of different spatial phase changes includes at least three different phase changes. Preferably, the plurality of intensity maps includes at least three intensity maps and the step of employing the plurality of intensity maps to obtain an output indicating the amplitude and phase of the wavefront being analyzed includes: expressing the wavefront being analyzed as a first complex function which has an amplitude and phase identical to the amplitude and phase of the wavefront being analyzed, expressing the plurality of intensity maps as a function of the first complex function and of a spatial function governing the spatially uniform, time-varying spatial phase change, defining a second complex function, having an absolute value and a phase, as a convolution of the first complex function and of a Fourier transform of the spatial function governing the spatially uniform, time-varying spatial phase change. Expressing each of the plurality of intensity maps as a third function of: the amplitude of the wavefront being analyzed, the absolute value of the second complex function, a difference between the phase of the wavefront being analyzed and the phase of the second complex function and a known phase delay produced by one of the at least three different phase changes corresponding to one of the at least three intensity maps, solving the third function to obtain the amplitude of the wavefront being analyzed, the absolute value of the second complex function and the difference between the phase of the wavefront being analyzed and the phase of the second complex function, solving the second complex function to obtain the phase of the second complex function and obtaining the phase of the wavefront being analyzed by adding the phase of the second complex function to the difference between the phase of the wavefront being analyzed and the phase of the second complex function.
Further in accordance with a preferred embodiment of the present invention the absolute value of the second complex function is obtained by approximating the absolute value to a polynomial of a given degree.
Still further in accordance with a preferred embodiment of the present invention the second complex function is obtained by expressing the second complex function as an eigen-value problem where the complex function is an eigen-vector obtained by an iterative process.
Preferably the second complex function is obtained by: approx
Arieli Yoel
Shekel Eyal
Wolfling Shay
Font Frank G.
Ladas & Parry
Lee Andrew H.
Nano Or Technologies Inc.
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