Abstract

Various interferometric methods can be used for testing aspheric surfaces with high accuracy. Using a partially compensating lens in a Twyman-Green arrangement together with a computer-generated hologram instead of a null corrector gives great flexibility. For quantitative analysis a high-resolution automatic fringe analysis is necessary. The interferometric arrangement and the setup for the interferogram data acquisition are described along with different algorithms for calculating the wave front data. Tilt and decentering of the aspheric surface and the synthetic hologram as well as the actual aspherical parameters can be derived from the calculated wave front using Zernike polynomials to communicate with a ray tracing program. For small adjustment and shape errors the linearity will hold, leading to fast correction and numerical compensation of their effects on the surface error. The method is verified by several examples. Experimental results agree with the proposed model.

© 1985 Optical Society of America

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References

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  1. J. C. Wyant, V. P. Bennett, “Using Computer Generated Holograms to Test Aspheric Wavefronts,” Appl. Opt. 11, 2833 (1972).
    [CrossRef] [PubMed]
  2. A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).
  3. M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
    [CrossRef]
  4. J. C. Wyant, P. K. O’Neill, “Computer Generated Hologram; Null Lens Test of Aspheric Wavefronts,” Appl. Opt. 13, 2762 (1974).
    [CrossRef] [PubMed]
  5. R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
    [CrossRef]
  6. A. F. Fercher, “Computer-Generated Holograms for Testing Optical Elements: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
    [CrossRef]
  7. A. Handojo, J. de Jong, “Interferometer for Optical Testing with Computer-Generated Holograms,” Appl. Opt. 16, 546 (1977).
    [CrossRef] [PubMed]
  8. T. Yatagai, H. Saito, “Interferometric Testing with Computer-Generated Holograms: Aberration Balancing Method and Error Analysis,” Appl. Opt. 17, 558 (1978).
    [CrossRef] [PubMed]
  9. J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).
  10. J. Schwider, R. Burow, “Wave Aberrations Caused by Misalignments of Aspherics and Their Elimination,” Opt. Appl. 9, 33 (1979).
  11. H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).
  12. J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
    [CrossRef]
  13. N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).
  14. R. Mercier, S. Lowenthal, “Comparison of In-Line and Carrier Frequency Holograms in Aspheric Testing,” Opt. Commun. 33, 251 (1980).
    [CrossRef]
  15. J. C. Wyant, “Testing Aspherics Using Two-Wavelength Holography,” Appl. Opt. 10, 2113 (1971).
    [CrossRef] [PubMed]
  16. J. D. Rancourt, “Interferometric Fringe Analysis,” in Optical Shop Notebook IX, J. B. Houston, Ed. (Optical Society of America, Washington, D.C., 1975) p. 69.
  17. E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).
  18. W. Augustyn, “Versatility of Microprocessor-Based Interferometric Data Reduction System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 128 (1979).
  19. P. F. Forman, “The Zygo Interferometer System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 41 (1979).
  20. W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
    [CrossRef] [PubMed]
  21. T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
    [CrossRef]
  22. G. E. Bernal, J. Loomis, “Interactive Video Image Digitizer-Application to Interferogram Analysis,” Proc. Soc. Photo-Opt. Instrum. Eng. 126, 143 (1977).
  23. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  24. Y. Ichioka, M. Inuiya, “Direct Phase Detecting System,” Appl. Opt. 11, 1507 (1972).
    [CrossRef] [PubMed]
  25. L. Mertz, “Real-Time Fringe-Pattern Analysis,” Appl. Opt. 22, 1535 (1983).
    [CrossRef] [PubMed]
  26. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  27. B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrah-linterferometern,” Optik 60, 156 (1982).
  28. L. M. Frantz, A. A. Sawchuk, W. von der Ohe, “Optical Phase Measurement in Real Time,” Appl. Opt. 18, 3301 (1979).
    [CrossRef] [PubMed]
  29. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
    [CrossRef] [PubMed]
  30. N. A. Massie, “Real-Time Digital Heterodyne Interferometry: a System,” Appl. Opt. 19, 154 (1980).
    [CrossRef] [PubMed]
  31. D. T. Moore, R. P. Murray, F. B. Neves, “Large Aperture ac Interferometer for Optical Testing,” Appl. Opt. 173959 (1978).
    [CrossRef] [PubMed]

1983 (2)

1982 (3)

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrah-linterferometern,” Optik 60, 156 (1982).

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
[CrossRef]

1981 (2)

W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
[CrossRef] [PubMed]

E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).

1980 (5)

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).

R. Mercier, S. Lowenthal, “Comparison of In-Line and Carrier Frequency Holograms in Aspheric Testing,” Opt. Commun. 33, 251 (1980).
[CrossRef]

N. A. Massie, “Real-Time Digital Heterodyne Interferometry: a System,” Appl. Opt. 19, 154 (1980).
[CrossRef] [PubMed]

1979 (5)

L. M. Frantz, A. A. Sawchuk, W. von der Ohe, “Optical Phase Measurement in Real Time,” Appl. Opt. 18, 3301 (1979).
[CrossRef] [PubMed]

W. Augustyn, “Versatility of Microprocessor-Based Interferometric Data Reduction System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 128 (1979).

P. F. Forman, “The Zygo Interferometer System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 41 (1979).

J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).

J. Schwider, R. Burow, “Wave Aberrations Caused by Misalignments of Aspherics and Their Elimination,” Opt. Appl. 9, 33 (1979).

1978 (2)

1977 (2)

G. E. Bernal, J. Loomis, “Interactive Video Image Digitizer-Application to Interferogram Analysis,” Proc. Soc. Photo-Opt. Instrum. Eng. 126, 143 (1977).

A. Handojo, J. de Jong, “Interferometer for Optical Testing with Computer-Generated Holograms,” Appl. Opt. 16, 546 (1977).
[CrossRef] [PubMed]

1976 (2)

R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
[CrossRef]

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Elements: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

1974 (2)

1973 (1)

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

1972 (3)

1971 (1)

Augustyn, W.

W. Augustyn, “Versatility of Microprocessor-Based Interferometric Data Reduction System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 128 (1979).

Bennett, V. P.

Bernal, G. E.

G. E. Bernal, J. Loomis, “Interactive Video Image Digitizer-Application to Interferogram Analysis,” Proc. Soc. Photo-Opt. Instrum. Eng. 126, 143 (1977).

Blume, H.

R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

J. Schwider, R. Burow, “Wave Aberrations Caused by Misalignments of Aspherics and Their Elimination,” Opt. Appl. 9, 33 (1979).

J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).

de Jong, J.

Dörband, B.

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrah-linterferometern,” Optik 60, 156 (1982).

Elssner, K.-E.

Fercher, A. F.

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Elements: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Forman, P. F.

P. F. Forman, “The Zygo Interferometer System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 41 (1979).

Foulde, M.

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

Frantz, L. M.

Freniere, E. R.

E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).

Funnell, W. R. J.

Gallagher, J. E.

Grzanna, J.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).

Handojo, A.

Herriott, D. R.

Ichioka, Y.

Idesawa, M.

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

Ina, H.

Inuiya, M.

Kobayashi, S.

Kriese, M.

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Larionov, N. P.

N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).

Loomis, J.

G. E. Bernal, J. Loomis, “Interactive Video Image Digitizer-Application to Interferogram Analysis,” Proc. Soc. Photo-Opt. Instrum. Eng. 126, 143 (1977).

Lowenthal, S.

R. Mercier, S. Lowenthal, “Comparison of In-Line and Carrier Frequency Holograms in Aspheric Testing,” Opt. Commun. 33, 251 (1980).
[CrossRef]

Lukin, A. V.

N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).

Massie, N. A.

Mercier, R.

R. Mercier, S. Lowenthal, “Comparison of In-Line and Carrier Frequency Holograms in Aspheric Testing,” Opt. Commun. 33, 251 (1980).
[CrossRef]

Merkel, K.

Mertz, L.

Moore, D. T.

Murray, R. P.

Nakadate, S.

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

Neves, F. B.

O’Neill, P. K.

Race, R.

E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).

Rafikov, R. A.

N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).

Rancourt, J. D.

J. D. Rancourt, “Interferometric Fringe Analysis,” in Optical Shop Notebook IX, J. B. Houston, Ed. (Optical Society of America, Washington, D.C., 1975) p. 69.

Rosenbruch, K.-J.

R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
[CrossRef]

Rosenfeld, D. P.

Saito, H.

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

T. Yatagai, H. Saito, “Interferometric Testing with Computer-Generated Holograms: Aberration Balancing Method and Error Analysis,” Appl. Opt. 17, 558 (1978).
[CrossRef] [PubMed]

Sawchuk, A. A.

Schwider, J.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

J. Schwider, R. Burow, “Wave Aberrations Caused by Misalignments of Aspherics and Their Elimination,” Opt. Appl. 9, 33 (1979).

J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).

Sirohi, R. S.

R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
[CrossRef]

Spolaczyk, R.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

Takeda, M.

Tiziani, H. J.

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

Toler, O. E.

E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).

Torge, R.

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

von der Ohe, W.

White, A. D.

Wilson, R. N.

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

Wyant, J. C.

Yatagai, T.

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

T. Yatagai, H. Saito, “Interferometric Testing with Computer-Generated Holograms: Aberration Balancing Method and Error Analysis,” Appl. Opt. 17, 558 (1978).
[CrossRef] [PubMed]

Appl. Opt. (13)

Y. Ichioka, M. Inuiya, “Direct Phase Detecting System,” Appl. Opt. 11, 1507 (1972).
[CrossRef] [PubMed]

J. C. Wyant, V. P. Bennett, “Using Computer Generated Holograms to Test Aspheric Wavefronts,” Appl. Opt. 11, 2833 (1972).
[CrossRef] [PubMed]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
[CrossRef] [PubMed]

T. Yatagai, H. Saito, “Interferometric Testing with Computer-Generated Holograms: Aberration Balancing Method and Error Analysis,” Appl. Opt. 17, 558 (1978).
[CrossRef] [PubMed]

D. T. Moore, R. P. Murray, F. B. Neves, “Large Aperture ac Interferometer for Optical Testing,” Appl. Opt. 173959 (1978).
[CrossRef] [PubMed]

L. M. Frantz, A. A. Sawchuk, W. von der Ohe, “Optical Phase Measurement in Real Time,” Appl. Opt. 18, 3301 (1979).
[CrossRef] [PubMed]

N. A. Massie, “Real-Time Digital Heterodyne Interferometry: a System,” Appl. Opt. 19, 154 (1980).
[CrossRef] [PubMed]

W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
[CrossRef] [PubMed]

L. Mertz, “Real-Time Fringe-Pattern Analysis,” Appl. Opt. 22, 1535 (1983).
[CrossRef] [PubMed]

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

J. C. Wyant, “Testing Aspherics Using Two-Wavelength Holography,” Appl. Opt. 10, 2113 (1971).
[CrossRef] [PubMed]

J. C. Wyant, P. K. O’Neill, “Computer Generated Hologram; Null Lens Test of Aspheric Wavefronts,” Appl. Opt. 13, 2762 (1974).
[CrossRef] [PubMed]

A. Handojo, J. de Jong, “Interferometer for Optical Testing with Computer-Generated Holograms,” Appl. Opt. 16, 546 (1977).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Acta (3)

R. S. Sirohi, H. Blume, K.-J. Rosenbruch, “Optical Testing Using Synthetic Holograms,” Opt. Acta 23, 229 (1976).
[CrossRef]

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Elements: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

J. Schwider, J. Grzanna, R. Spolaczyk, R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta 27, 683 (1980).
[CrossRef]

Opt. Appl. (2)

J. Schwider, R. Burow, J. Grzanna, “CGH-Testing of Rotational-Symmetric Aspheric in Compensated Interferometers,” Opt. Appl. 9, 39 (1979).

J. Schwider, R. Burow, “Wave Aberrations Caused by Misalignments of Aspherics and Their Elimination,” Opt. Appl. 9, 33 (1979).

Opt. Commun. (2)

M. Foulde, A. F. Fercher, R. Torge, R. N. Wilson, “Optical Testing by Means of Synthetic Holograms and Partial Lens Compensation,” Opt. Commun. 7, 363 (1973).
[CrossRef]

R. Mercier, S. Lowenthal, “Comparison of In-Line and Carrier Frequency Holograms in Aspheric Testing,” Opt. Commun. 33, 251 (1980).
[CrossRef]

Opt. Eng. (2)

E. R. Freniere, O. E. Toler, R. Race, “Interferogram Evaluation Program for the HP-9825A Calculator,” Opt. Eng. 20, 253 (1981).

T. Yatagai, S. Nakadate, M. Idesawa, H. Saito, “Automatic Fringe Analysis Using Digital Image Processing Techniques,” Opt. Eng. 21, 432 (1982).
[CrossRef]

Optik (2)

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrah-linterferometern,” Optik 60, 156 (1982).

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

G. E. Bernal, J. Loomis, “Interactive Video Image Digitizer-Application to Interferogram Analysis,” Proc. Soc. Photo-Opt. Instrum. Eng. 126, 143 (1977).

W. Augustyn, “Versatility of Microprocessor-Based Interferometric Data Reduction System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 128 (1979).

P. F. Forman, “The Zygo Interferometer System,” Proc. Soc. Photo-Opt. Instrum. Eng. 192, 41 (1979).

Sov. J. Opt. Technol. (1)

N. P. Larionov, A. V. Lukin, R. A. Rafikov, “Testing of Aspherical Surfaces by Means of Axial Synthesized Holograms,” Sov. J. Opt. Technol. 47, 667 (1980).

Other (1)

J. D. Rancourt, “Interferometric Fringe Analysis,” in Optical Shop Notebook IX, J. B. Houston, Ed. (Optical Society of America, Washington, D.C., 1975) p. 69.

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Figures (7)

Fig. 1
Fig. 1

Twyman-Green interferometer with a CGH to test aspheric surfaces.

Fig. 2
Fig. 2

Fourier spectrum of fringe pattern with high carrier frequency.

Fig. 3
Fig. 3

(a) Interferogram of 0.01-mm decentered aspheric; (b) interferogram of 0.10-mm decentered aspheric; (c) vertical cross section through wave fronts for 0.01-, 0.03-, 0.05-, and 0.10-mm decentered aspherics; (d) compensated curves from (c).

Fig. 4
Fig. 4

(a) Interferogram of three units tilted aspheric; (b) interferogram of thirty units tilted aspheric; (c) vertical cross section through wave fronts for three, nine, fifteen, and thirty units tilted aspheric; (d) compensated curves from (c).

Fig. 5
Fig. 5

(a) Interferogram of 0.1-mm decentered hologram; (b) interferogram of 1.0-mm decentered hologram; (c) vertical cross section through wave fronts for 0.1-, 0.3-, 0.5-, and 1.0-mm decentered holograms; (d) compensated curves from (c).

Fig. 6
Fig. 6

(a) Interferogram of 0.03-mm decentered and six units tilted aspheric with 0.1-mm decentered hologram; (b) interferogram of 0.06-mm decentere and fifteen units tilted aspheric with centered hologram; (c) vertical cross section through wave fronts from (a) and (b); (d) compensated curves from (c).

Fig. 7
Fig. 7

(a) Interferogram of aspheric Ge surface; (b) 2-D analysis of wave front; (c) cross section through wave front from (b); (d) deviations from best-fitting asphere.

Tables (2)

Tables Icon

Table I Zenike Polynomials with Azimuth Frequency m = ±1

Tables Icon

Table II Rotational Symmetric Zernike Polynomials up to the 10th Degree

Equations (15)

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I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + k x sin θ ] ,
I ( x , y ) = a ( x , y ) + c ( x , y ) exp ( i k x sin θ ) + c * ( x , y ) exp ( i k x sin θ ) ,
I ˜ ( f , y ) = A ( f , y ) + C ( f f 0 , y ) + C * ( f + f 0 , y ) ,
F 1 { C ( f , y ) } = c ( x , y ) = 1 2 b ( x , y ) exp [ i ϕ ( x , y ) ] .
ϕ ( x , y ) = arctan Im { c ( x , y ) } Re { c ( x , y ) }
ln c ( x , y ) = ln b ( x , y ) 2 + i ϕ ( x , y )
I 1 ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) Δ ] , I 2 ( x , y ) = a ( x , y ) + b ( x , y ) cos ϕ ( x , y ) , I 3 ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + Δ ] .
ϕ ( x , y ) = arctan [ I 3 I 1 I 1 + I 3 2 I 2 · tan Δ 2 ] .
W ( r , θ ) w ( r , θ ) = j = 0 N A j U j ( r , θ ) ,
U j ( r , θ ) = U n m ( r , θ ) = R n m ( r ) { sin cos } m θ
n 0 , n m n ( n m is an even number ) .
j = n ( n + 2 ) m 2 + 1
R n m ( r ) = s = 0 n m 2 ( 1 ) s ( n s ) ! s ! ( n + m 2 s ) ! ( n m 2 s ) ! r ( n 2 s ) .
( A 2 A 3 A 8 A 9 A 18 A 19 A 32 A 33 ) = ( A 2 β R x A 2 β R y A 2 H x A 2 H y · · · · · · · · · · · · A 33 β R x A 33 β R y A 33 H x A 33 H y ) · ( β R x β R y A x A y β A x β A y H x H y ) ,
( A 5 A 13 ) = ( A 5 r A 5 e A 13 r A 13 e ) · ( Δ r Δ e ) ,

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