Solution to the shearing problem

Applied Optics

Volumn 38, Issue 23, 1999, Pages 5024-5031

  Elster, Clemens ^a   Weingärtner, Ingolf ^a  

^a PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000133858     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.38.005024     Document Type: Article

References (33)

1. V. Ronchi, “Le frangie di combinazione nello studio delle superficie e dei sistemi ottici,” Riv. Ottica Mecc. Precis. 2, 9-35 (1923).
2. W. J. Bates, “A wavefront shearing interferometer,” Proc. Phys. Soc. London 59, 940-952 (1947).
3. G. Schulz, “Ein Interferenzverfahren zur absoluten Eben-heitsprufung langs beliebiger Zentralschnitte,” Opt. Acta 14, 375-388 (1967).
4. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1989).
5. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437-450 (1964).
6. S. Baumer, “Quantitative Mikro-Messtechnik mit einem Lateral Shearing Interferometer,” Ph.D. dissertation (Optics Institute of Berlin Technical University, Berlin, 1995).
7. H. von Brug, “Zernike polynomials as a basis for wave-front fitting in lateral shearing interferometry,” Appl. Opt. 36, 2788-2790 (1997).
8. K. R. Freischlad and C. L. Koliopoulos, “Modal estimation of a wave front from difference measurements using the discrete Fourier transform,” J. Opt. Soc. Am. A 3, 1852-1861 (1986).
9. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370-375 (1977).
10. R. L. Frost, C. K. Rushforth, and B. S. Baxter, “Fast FFT-based algorithm for phase estimation in speckle imaging,” Appl. Opt. 18, 2056-2061 (1979).
11. D. C. Ghiglia and L. A. Romero, “Direct phase estimation from phase differences using elliptic partial differential equation solvers,” Opt. Lett. 14, 1107-1109 (1989).
12. F. Guse, “Auswertung von Messungen mit Optimierungsverfahren—demonstriert an Interferometrie und Ellipsomet-rie,” Ph.D. dissertation (Optics Institute of Berlin Technical University, Berlin, 1996).
13. G. Harbers, P. J. Kunst, G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162-6172 (1996).
14. R. H. Hudgin, “Wavefront reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375-378 (1977).
15. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393-399 (1979).
16. G. W. R. Leibbrandt, G. Harbers, and P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151-6161 (1996).
17. S. Loheide and I. Weingartner, “New procedure for wavefront reconstruction,” Optik 108, 53-62 (1998).
18. R. J. Noll, “Phase estimates from slope-type wavefront sensors,” J. Opt. Soc. Am. 68, 139-140 (1978).
19. M. P. Rimmer, “Method for evaluating lateral shearing interferometer,” Appl. Opt. 13, 623-629 (1974).
20. M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142-150 (1975).
21. F. Roddier and C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325-1327 (1991).
22. H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi gratings in series,” Appl. Opt. 36, 5321-5324 (1997).
23. M. Servin, D. Malacara, and J. L. Marroquin, “Wave-front recovery from two orthogonal sheared interferograms,” Appl. Opt. 35, 4343-4348 (1996).
24. W. H. Southwell, “Wavefront estimation from wavefront slope measurements,” J. Opt. Soc. Am. 70, 998-1006 (1980).
25. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416-425 (1988).
26. X. Tian, M. Itoh, and T. Yatagai, “Simple algorithm for large-grid phase reconstruction of lateral-shearing interferometry,” Appl. Opt. 34, 7213-7220 (1995).
27. K. Freischlad, “Sensitivity of heterodyne shearing interferometers,” Appl. Opt. 26, 4053-4054 (1987).
28. S. Loheide and I. Weingartner, “Verfahren zur Ermittlung einer optischen, mechanischen, elektrischen oder anderen Messgrösse,” German patent 197 05 609.1 (15 May 1997).
29. W. Weingartner and H. Stenger, “A simple shear-tilt interferometer for the measurement of wavefront aberration,” Optik 70, 124-126 (1985).
30. J. B. Saunders, “Measurement of wavefronts without a reference standard. Part 1. The wavefront shearing interferometer,” J. Res. Natl. Bur. Stand. Sect. B 65B, 239-244 (1961).
31. F. Fricke and I. Weingartner, “Verfahren zur Ermittlung einer Winkelteilung aus der Winkelteilungsdifferenz, bestimmt aus der Differenz zweier Winkelpositionen mit jeweils konstantem Winkelabstand,” German patent 197 20 968.8 (patent pending).
32. Elster, S. Loheide, and I. Weingartner, “Verfahren zur Ermittlung einer optischen, mechanischen, elektrischen oder anderen Messgrosse,” German patent 198 33 269.6 (patent pending).
33. E. Elster and I. Weingartner, “Method for exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A (in press).