Abstract

Fizeau interferometers with an additional diffractive optical element are frequently used for measuring spherical and aspherical surfaces. We present a new (to our knowledge) optical test method, in which the Fizeau principle is now perfectly fulfilled by generating reference and measuring wavefront on the last optical surface, which carries a diffractive optical element. This method has been examined experimentally by testing a reference f0.68 spherical mirror and can be applied identically for testing aspheres. Several advantages of this method are discussed and proved experimentally.

© 2006 Optical Society of America

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  1. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
    [CrossRef]
  2. V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
    [CrossRef]
  3. A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.
  4. J. H. Burge, L. R. Dettmann, and S. C. West, "Null correctors for 6.5-m f/1.25 paraboloidal mirrors," in Fabrication and Testing of Aspheres, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 182-186.
  5. A. G. Poleshchuk, J. H. Burge, and E. G. Churin, "Design and application of CGHs for simultaneous generation in several specified wavefronts," in Diffraction Optical Elements (DOE)-1999, Vol. 22 of EOS Topical Meeting Digest Series (European Optical Society, 1999), pp. 155-156.
  6. M. Beyerlein, N. Lindlein, and J. Schwider, "Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics," Appl. Opt. 41, 2440-2447 (2002).
    [CrossRef] [PubMed]
  7. S. Reichelt and H. J. Tiziani, "Twin-CGHs for absolute calibration in wavefront testing interferometry," Opt. Commun. 220, 23-32 (2003).
    [CrossRef]
  8. S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
    [CrossRef]
  9. Yu-C. Chang and J. H. Burge, "Error analysis for CGH optical testing," in Proc. SPIE 3782, 358-366 (1999).
    [CrossRef]
  10. T. Kim, J. H. Burge, Y. Lee, and S. Kim, "Null test for a highly paraboloidal mirror," Appl. Opt. 43, 3614-3618 (2004).
    [CrossRef] [PubMed]
  11. J. H. Burge and D. S. Anderson, "Full aperture interferometric test of convex secondary mirrors using holographic test plates," in Proc. SPIE 2199, 181-192 (1994).
    [CrossRef]
  12. A. G. Poleshchuk, "Diffractive light attenuators with variable transmission," J. Mod. Opt. 45, 1513-1522 (1998).
    [CrossRef]

2004

2003

S. Reichelt and H. J. Tiziani, "Twin-CGHs for absolute calibration in wavefront testing interferometry," Opt. Commun. 220, 23-32 (2003).
[CrossRef]

2002

1999

1998

A. G. Poleshchuk, "Diffractive light attenuators with variable transmission," J. Mod. Opt. 45, 1513-1522 (1998).
[CrossRef]

1997

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

1996

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

1994

J. H. Burge and D. S. Anderson, "Full aperture interferometric test of convex secondary mirrors using holographic test plates," in Proc. SPIE 2199, 181-192 (1994).
[CrossRef]

Anderson, D. S.

J. H. Burge and D. S. Anderson, "Full aperture interferometric test of convex secondary mirrors using holographic test plates," in Proc. SPIE 2199, 181-192 (1994).
[CrossRef]

Arnold, S. M.

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

Beyerlein, M.

Burge, J.

A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.

Burge, J. H.

T. Kim, J. H. Burge, Y. Lee, and S. Kim, "Null test for a highly paraboloidal mirror," Appl. Opt. 43, 3614-3618 (2004).
[CrossRef] [PubMed]

Yu-C. Chang and J. H. Burge, "Error analysis for CGH optical testing," in Proc. SPIE 3782, 358-366 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

J. H. Burge and D. S. Anderson, "Full aperture interferometric test of convex secondary mirrors using holographic test plates," in Proc. SPIE 2199, 181-192 (1994).
[CrossRef]

J. H. Burge, L. R. Dettmann, and S. C. West, "Null correctors for 6.5-m f/1.25 paraboloidal mirrors," in Fabrication and Testing of Aspheres, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 182-186.

A. G. Poleshchuk, J. H. Burge, and E. G. Churin, "Design and application of CGHs for simultaneous generation in several specified wavefronts," in Diffraction Optical Elements (DOE)-1999, Vol. 22 of EOS Topical Meeting Digest Series (European Optical Society, 1999), pp. 155-156.

Chang, Yu-C.

Yu-C. Chang and J. H. Burge, "Error analysis for CGH optical testing," in Proc. SPIE 3782, 358-366 (1999).
[CrossRef]

Cherkashin, V. V.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.

Churin, E. G.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

A. G. Poleshchuk, J. H. Burge, and E. G. Churin, "Design and application of CGHs for simultaneous generation in several specified wavefronts," in Diffraction Optical Elements (DOE)-1999, Vol. 22 of EOS Topical Meeting Digest Series (European Optical Society, 1999), pp. 155-156.

Dettmann, L. R.

J. H. Burge, L. R. Dettmann, and S. C. West, "Null correctors for 6.5-m f/1.25 paraboloidal mirrors," in Fabrication and Testing of Aspheres, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 182-186.

Kharissov, A. A.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

Kim, S.

Kim, T.

Kiryanov, A. V.

Kiryanov, V. P.

Kokarev, S. A.

Kooronkevich, V. P.

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

Korolkov, V. P.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.

Koronkevich, V. P.

Lee, Y.

Lindlein, N.

Maxey, L. C.

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

Poleshchuk, A. G.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, "Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure," Appl. Opt. 38, 1295-1301 (1999).
[CrossRef]

A. G. Poleshchuk, "Diffractive light attenuators with variable transmission," J. Mod. Opt. 45, 1513-1522 (1998).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.

A. G. Poleshchuk, J. H. Burge, and E. G. Churin, "Design and application of CGHs for simultaneous generation in several specified wavefronts," in Diffraction Optical Elements (DOE)-1999, Vol. 22 of EOS Topical Meeting Digest Series (European Optical Society, 1999), pp. 155-156.

Reichelt, S.

S. Reichelt and H. J. Tiziani, "Twin-CGHs for absolute calibration in wavefront testing interferometry," Opt. Commun. 220, 23-32 (2003).
[CrossRef]

Rogers, J. E.

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

Schwider, J.

Tiziani, H. J.

S. Reichelt and H. J. Tiziani, "Twin-CGHs for absolute calibration in wavefront testing interferometry," Opt. Commun. 220, 23-32 (2003).
[CrossRef]

Verhoglyad, A. G.

West, S. C.

J. H. Burge, L. R. Dettmann, and S. C. West, "Null correctors for 6.5-m f/1.25 paraboloidal mirrors," in Fabrication and Testing of Aspheres, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 182-186.

Yoder, R. C.

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

A. G. Poleshchuk, "Diffractive light attenuators with variable transmission," J. Mod. Opt. 45, 1513-1522 (1998).
[CrossRef]

Opt. Commun.

S. Reichelt and H. J. Tiziani, "Twin-CGHs for absolute calibration in wavefront testing interferometry," Opt. Commun. 220, 23-32 (2003).
[CrossRef]

Proc. SPIE

S. M. Arnold, L. C. Maxey, J. E. Rogers, and R. C. Yoder, "Figure metrology of deep aspherics using a conventional interferometer with CGH null," in Proc. SPIE 2536, 106-116 (1996).
[CrossRef]

Yu-C. Chang and J. H. Burge, "Error analysis for CGH optical testing," in Proc. SPIE 3782, 358-366 (1999).
[CrossRef]

V. V. Cherkashin, E. G. Churin, V. P. Korolkov, V. P. Kooronkevich, A. A. Kharissov, A. G. Poleshchuk, and J. H. Burge, "Processing parameters optimization for thermochemical writing of DOEs on chromium films," in Proc. SPIE 3010, 168-179 (1997).
[CrossRef]

J. H. Burge and D. S. Anderson, "Full aperture interferometric test of convex secondary mirrors using holographic test plates," in Proc. SPIE 2199, 181-192 (1994).
[CrossRef]

Other

A. G. Poleshchuk, V. P. Korolkov, V. V. Cherkashin, and J. Burge, "Methods for certification of CGH fabrication," in Diffractive Optics and Micro-optics, Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 438-440.

J. H. Burge, L. R. Dettmann, and S. C. West, "Null correctors for 6.5-m f/1.25 paraboloidal mirrors," in Fabrication and Testing of Aspheres, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 182-186.

A. G. Poleshchuk, J. H. Burge, and E. G. Churin, "Design and application of CGHs for simultaneous generation in several specified wavefronts," in Diffraction Optical Elements (DOE)-1999, Vol. 22 of EOS Topical Meeting Digest Series (European Optical Society, 1999), pp. 155-156.

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Figures (9)

Fig. 1
Fig. 1

Layout of a null CGH test of an asphere. BS, beam splitter.

Fig. 2
Fig. 2

Configuration of a combined off-axis CGH optical test: (a) null lens component, (b) linear grating component.

Fig. 3
Fig. 3

Layout of a null CGH test of an aspherical surface, using one single CGH working in a collimated interferometer beam without reference flat.

Fig. 4
Fig. 4

Formation of a combined CGH.

Fig. 5
Fig. 5

Relative output intensities of the test beam (curves 1, 2, 3) and reference beam (curve 4) as a function of the duty cycle of the linear grating. The reflectance of the tested surface is (1) ρ test = 40 % , (2) ρ test = 10 % , (3) ρ test = 5 % .

Fig. 6
Fig. 6

Microscope images with transmission illumination: (a) central part of the chromium mask fabricated with the CLWS, (b) final amplitude–phase CGH.

Fig. 7
Fig. 7

3D image of the central part of the fabricated combined CGH.

Fig. 8
Fig. 8

(a) CGH (left), mounted directly into a Zygo Fizeau interferometer, and lens surface (right) under test. (b) Alignment pattern with CGH null.

Fig. 9
Fig. 9

(a) Interferogram and (b) phase map of a reference spherical mirror with f 0.68 , measured with the combined CGH null.

Equations (7)

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ϕ 1 ( x , y ) = O ( x , y ) C S O ( x 0 , y 0 ) C S .
φ = λ S = 2 α ,
ϕ 2 ( x , y ) = O ( x , y ) C O ( x 0 , y 0 ) C = x tan ( α ) .
ϕ ( x , y ) = C ( x , y ) S C ( x 0 , y 0 ) S .
I 1 = I 0 ρ grat D 2 sinc ( m D ) 2 ,
I 2 = I 0 η 1 2 ρ test D 4 ,
Δ W ( x , y ) = m λ ε ( x , y ) S ( x , y ) ,

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