Claims
- 1. A method comprising:
generating a sequence of phase-shifted interferometry images of an object surface relative to a reference surface; and calculating an unequally weighted average of the phase-shifted interferometry images to produce a final image.
- 2. The method of claim 1, wherein the unequally weighted average reduces interferometric fringes in the final image relative to those in a second final image produced by an equally weighted average of the phase-shifted interferometry images for an equally spaced phase shift sequence that spans 2π.
- 3. The method of claim 1, wherein the final image is a lateral metrology image.
- 4. The method of claim 1, wherein generating the sequence of phase-shifted interferometry images comprises:
interfering a pair of wavefronts derived from a common source, wherein one of the wavefronts reflects from the object surface and the other wavefront reflects from the reference surface, and introducing a sequence of phase-shifts between the interfering wavefronts.
- 5. The method of claim 4, wherein each of the phase-shifted interferometry images corresponds to an intensity image formed by the interfering wavefronts for a corresponding one of the phase shifts.
- 6. The method of claim 4, wherein introducing the sequence of phase shifts comprises varying an optical path length difference between the interfering wavefronts.
- 7. The method of claim 6, wherein the optical path length difference is varied over a range smaller than the coherence length of the common source.
- 8. The method of claim 6, wherein the optical path length difference is varied over a range comparable to, or larger than, the coherence length of the source.
- 9. The method of claim 4, wherein introducing the sequence of phase shifts comprises varying a wavelength of the common source for a non-zero optical path length difference between the interfering wavefronts.
- 10. The method of claim 1, wherein the phase shift between each pair of adjacent images in the sequence of phase-shifted interferometry images is equal to a constant.
- 11. The method of claim 10, wherein the constant is equal to π/4 with respect to a wavelength in light used to produce the interferometry images.
- 12. The method of claim 1, wherein the sequence of phase-shifted interferometry images can be expressed mathematically as:
- 13. The method of claim 12, wherein the final image, Ai, can be expressed as:
- 14. The method of claim 13, wherein φj=(j−j0)α, where j=0, . . . , P−1, P is the number of images in the sequence, α is a constant phase shift interval, and j0 is a constant selected to cause φ(P−1)−j=−φj.
- 15. The method of claim 14, wherein Wj satisfies:
- 16. The method of claim 15, wherein wj further satisfies
- 17. The method of claim 14, wherein P=6 and wj=[1,1,2,2,1,1].
- 18. The method of claim 14, wherein P=7 and wj=[1,2,3,4,3,2,1].
- 19. The method of claim 14, wherein P=8 and wj=[1,1,3,3,3,3,1,1].
- 20. The method of claim 1, further comprising:
calculating a surface profile of the object surface relative to the reference surface based on the series of phase-shifted images.
- 21. The method of claim 12, further comprising calculating a surface profile of the object surface relative to the reference surface by applying a phase-shifting algorithm to the sequence of phase-shifted images to extract the phases θi.
- 22. A method comprising calculating an unequally weighted average of a sequence of phase-shifted interferometry images to produce a final image.
- 23. An apparatus comprising a computer readable medium which causes a processor to calculate an unequally weighted average of a sequence of phase-shifted interferometry images to produce a final image.
- 24. An apparatus comprising:
an interferometer which during operation generates a sequence of phase-shifted interferometry images of an object surface relative to a reference surface; and an electronic controller coupled to the interferometer, wherein during operation the electronic controller calculates an unequally weighted average of the phase-shifted interferometry images to produce a final image.
- 25. The apparatus of claim 24, wherein during operation the electronic controller further calculates a surface profile of the object surface relative to the reference surface based on the sequence of phase-shifted interferometry images.
- 26. The apparatus of claim 24, wherein the unequally weighted average reduces interferometric fringes in the final image relative to those in a second final image produced by an equally weighted average of the phase-shifted interferometry images for an equally spaced phase shift sequence that spans 2π.
- 27. The apparatus of claim 24, wherein the interferometer comprises one of a Linnik interferometer, a Michelson interferometer, and a Fizeau interferometer.
- 28. The apparatus of claim 24, wherein the interferometer comprises a scanning interferometer comprising a broadband source having a coherence length, wherein during operation the scanning interferometer interferes an object wavefront reflected from the object surface with a reference wavefront reflected from the reference surface and varies an optical path length difference between the wavefronts over a range larger than the coherence length of the source.
- 29. The apparatus of claim 24, wherein the interferometer comprises all unequal path length interferometer comprising a tunable source, wherein during operation the unequal path length interferometer introduces phase shifts between an object wavefront reflected firm the object surface and a reference wavefront reflected from the reference surface by varying the wavelength of the source.
- 30. An method for obtaining a fringe-free intensity image from a sequence of phase-shifted interference patterns, the method comprising:
providing the sequence of phase-shifted interference patterns; and calculating a weighted average of the phase-shifted interference patterns to produce the fringe-free intensity image.
- 31. The method of claim 30, wherein the sequence of phase-shifted interference patterns comprises more than four patterns.
- 32. The method of claim 30, wherein the weights for the weighted average are selected to reduce the sensitivity of the weighted average to a deviation in the phase increment between the phase-shifted interference patterns.
- 33. The method of claim 32, wherein the weights define a window function, and the derivative of the Fourier transform of the window function with respect to the deviation in the phase increment is zero when the deviation is zero.
- 34. The method of claim 30, further comprising calculating a surface topology map from the sequence of phase-shifted interference patterns.
- 35. The method of claim 30, further comprising:
using an interferometry system to provide the sequence of phase-shifted interference patterns.
- 36. The method of claim 35, wherein the interferometry system is a white-light scanning interferometry system.
- 37. The method of claim 35, wherein the interferometry system is a wavelength-tuning interferometry system.
- 38. An interferometry system comprising:
an interferometer for providing a sequence of phase-shifted interference patterns; and an electronic controller coupled to the interferometer, wherein during operation the interferometer calculates a weighted average of the phase-shifted interference patterns to produce a fringe-free intensity image.
- 39. The system of claim 38, wherein during operation the electronic controller further calculates a surface topography map from the sequence of phase-shifted interference patterns.
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority under 35 U.S.C §119(e) to U.S. Provisional Patent Application Serial No. 60/373,791 by Peter J. de Groot and filed Apr. 19, 2002, the contents of which are incorporated herein by reference.
Provisional Applications (1)
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Number |
Date |
Country |
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60373791 |
Apr 2002 |
US |