Abstract

We have already reported a method for the quasi-absolute test of rotationally symmetric aspheres by means of combined diffractive optical elements (combo-DOEs). The combo-DOEs carry the information for the ideal shape of an aspheric surface under test as well as a spherical wave for the measurement at the cat's eye position. An experimental demonstration of the procedure is given. Measurements with two different designs of combo-DOEs have been conducted, and their relative advantages and disadvantages are discussed.

© 2006 Optical Society of America

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References

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  1. M. Bosse and T. Blümel, "Interferometric asphere testing without CGH," in Proceedings of the Deutsche Gesellschaft für Angewandte Optik 2004, http://www.dgao-proceedings.de/download/105/105_p47.pdf.
  2. M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).
  3. A. J. MacGovern and J. C. Wyant, "Computer generated holograms for testing optical elements," Appl. Opt. 10, 619-624 (1971).
    [CrossRef] [PubMed]
  4. G. Schulz and J. Schwider, "Interferometric testing of smooth surfaces," in Progress in Optics , E. Wolf, ed. (Elsevier North-Holland, 1976), Vol. 13, p. 93.
    [CrossRef]
  5. M. BeyerleinN. Lindlein, and J. Schwider, "Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics," Appl. Opt. 41, 2440-2447 (2002).
    [CrossRef] [PubMed]
  6. J. Schwider, "Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen," German patent 19822453.2 (20 June 1998).
  7. J. Schwider, "Interferometric tests for aspherics," in Fabrication and Testing of Aspheres, J. S. Taylor, M. Piscotty and A. Lindquist, eds., Vol. 24 of Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.
  8. N. Lindlein, "Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics," Appl. Opt. 40, 2698-2708 (2001).
    [CrossRef]
  9. J. B. Houston, Jr., C. J. Buccini, and P. K. O'Neill, "A laser unequal path interferometer for the optical shop," Appl. Opt. 6, 1237-1242 (1967).
    [CrossRef] [PubMed]
  10. S. M. Arnold, "How to test an asphere with a computer generated hologram," in Holographic Optics: Optically and Computer Generated, I Cindrich and S. H. Lee, eds., Proc. SPIE 1052, 191-197 (1989).
  11. M. P. Rimmer, "Analysis of perturbed lens systems," Appl. Opt. 9, 533-537 (1970).
    [CrossRef] [PubMed]
  12. E. W. Young, "Optimal removal of all mislocation effects in interferometric tests, in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE 661, 116-124 (1986).
  13. http://www.optik.uni-erlangen.de/odem/research/work/index.php?what=ray.
  14. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
    [CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (1)

M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).

1998 (1)

J. Schwider, "Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen," German patent 19822453.2 (20 June 1998).

1989 (1)

S. M. Arnold, "How to test an asphere with a computer generated hologram," in Holographic Optics: Optically and Computer Generated, I Cindrich and S. H. Lee, eds., Proc. SPIE 1052, 191-197 (1989).

1986 (1)

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests, in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE 661, 116-124 (1986).

1983 (1)

1976 (1)

G. Schulz and J. Schwider, "Interferometric testing of smooth surfaces," in Progress in Optics , E. Wolf, ed. (Elsevier North-Holland, 1976), Vol. 13, p. 93.
[CrossRef]

1971 (1)

1970 (1)

1967 (1)

Arnold, S. M.

S. M. Arnold, "How to test an asphere with a computer generated hologram," in Holographic Optics: Optically and Computer Generated, I Cindrich and S. H. Lee, eds., Proc. SPIE 1052, 191-197 (1989).

Beyerlein, M.

Blümel, T.

M. Bosse and T. Blümel, "Interferometric asphere testing without CGH," in Proceedings of the Deutsche Gesellschaft für Angewandte Optik 2004, http://www.dgao-proceedings.de/download/105/105_p47.pdf.

Bosse, M.

M. Bosse and T. Blümel, "Interferometric asphere testing without CGH," in Proceedings of the Deutsche Gesellschaft für Angewandte Optik 2004, http://www.dgao-proceedings.de/download/105/105_p47.pdf.

Buccini, C. J.

Burow, R.

Elssner, K.-E.

Grzanna, J.

Houston, J. B.

Lindlein, N.

MacGovern, A. J.

Merkel, K.

O'Neill, P. K.

Rimmer, M. P.

Schulz, G.

G. Schulz and J. Schwider, "Interferometric testing of smooth surfaces," in Progress in Optics , E. Wolf, ed. (Elsevier North-Holland, 1976), Vol. 13, p. 93.
[CrossRef]

Schulz, M.

M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).

Schwider, J.

M. BeyerleinN. Lindlein, and J. Schwider, "Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics," Appl. Opt. 41, 2440-2447 (2002).
[CrossRef] [PubMed]

J. Schwider, "Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen," German patent 19822453.2 (20 June 1998).

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
[CrossRef] [PubMed]

G. Schulz and J. Schwider, "Interferometric testing of smooth surfaces," in Progress in Optics , E. Wolf, ed. (Elsevier North-Holland, 1976), Vol. 13, p. 93.
[CrossRef]

J. Schwider, "Interferometric tests for aspherics," in Fabrication and Testing of Aspheres, J. S. Taylor, M. Piscotty and A. Lindquist, eds., Vol. 24 of Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.

Spolaczyk, R.

Thomsen-Schmidt, P.

M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).

Weingärtner, I.

M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).

Wyant, J. C.

Young, E. W.

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests, in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE 661, 116-124 (1986).

Appl. Opt. (6)

Progress in Optics (1)

G. Schulz and J. Schwider, "Interferometric testing of smooth surfaces," in Progress in Optics , E. Wolf, ed. (Elsevier North-Holland, 1976), Vol. 13, p. 93.
[CrossRef]

Other (7)

M. Bosse and T. Blümel, "Interferometric asphere testing without CGH," in Proceedings of the Deutsche Gesellschaft für Angewandte Optik 2004, http://www.dgao-proceedings.de/download/105/105_p47.pdf.

M. Schulz, P. Thomsen-Schmidt, and I. Weingärtner, "Reliable curvature sensor for measuring the topography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrews, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger, eds., Proc. SPIE 4098, 84-93 (2000).

S. M. Arnold, "How to test an asphere with a computer generated hologram," in Holographic Optics: Optically and Computer Generated, I Cindrich and S. H. Lee, eds., Proc. SPIE 1052, 191-197 (1989).

J. Schwider, "Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen," German patent 19822453.2 (20 June 1998).

J. Schwider, "Interferometric tests for aspherics," in Fabrication and Testing of Aspheres, J. S. Taylor, M. Piscotty and A. Lindquist, eds., Vol. 24 of Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests, in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE 661, 116-124 (1986).

http://www.optik.uni-erlangen.de/odem/research/work/index.php?what=ray.

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Figures (13)

Fig. 1
Fig. 1

Spherical condenser and DOE. The DOE transforms the incoming spherical wave into the needed aspheric wave. There are only low spatial frequencies in the DOE. The zeroth order of the DOE can be used for the measurement of the cat's eye position. Thus the focus of the spherical wave is on axis.

Fig. 2
Fig. 2

Single DOE as condenser. Generation of an aspheric and a spherical wave out of a plane wave by the combo-DOE. The disturbing reflex can be filtered out by tilting the DOE substrate. The spherical wave has an offset to the aspheric wave to avoid disturbances of both waves (off-axis focus).

Fig. 3
Fig. 3

Setup of the Twyman–Green interferometer.

Fig. 4
Fig. 4

Structure of a combo-DOE with sliced aperture. Spherical and aspheric waves are coded in stripes alternately (here horizontally).

Fig. 5
Fig. 5

Structure of a combo-DOE with superposed hologram functions.

Fig. 6
Fig. 6

Disturbing diffraction orders in the case of a sliced combo-DOE. The stop in the focal plane of the telescope is wide open.

Fig. 7
Fig. 7

With a superposed combo-DOE the disturbing diffraction patterns look worse than with the sliced one.

Fig. 8
Fig. 8

Alignment structure is a linear reflection grating around the transmitting structure for a spherical or aspheric wave.

Fig. 9
Fig. 9

To calculate the misalignment aberrations in the DOE plane, the normal vector field n(x, y) of the surface has to be transferred to the DOE plane, giving n ( x ˜ , y ˜ ) . It is n that has to be used for the following calculations.

Fig. 10
Fig. 10

Absolute deviations (in waves) of the asphere for the striped combo-DOE. In (b) the asphere is rotated clockwise by 90° with respect to (a).

Fig. 11
Fig. 11

Absolute deviations (in waves) of the asphere for the superposed combo-DOE. In (b) the asphere is rotated clockwise by 90° with respect to (a).

Fig. 12
Fig. 12

Difference between the two absolute deviations (in waves) for the (a) striped and (b) superposed combo-DOE. The 90° measurement has been rotated back by the software.

Fig. 13
Fig. 13

Effect of a small tilt of the mirror in the cat's eye position.

Tables (3)

Tables Icon

Table 1 Residual Aberrations After Misalignment Elimination

Tables Icon

Table 2 Repeatability of Single Measurements and Reproducibilities of Single with Respect to Absolute Measurements

Tables Icon

Table 3 Residual Aberrations of a Misaligned Test Object a

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

Φ meas = Φ obj + Φ mis + Φ sys .
N .A . max , in   air = sin θ max = λ p min .
W normal   pos. ( x , y ) = W R ( x , y ) + W S ( x , y ) + W O ( x , y ) ,
W rot .  pos . ( x , y ) = W R ( x , y ) + W S ( x , y ) + W O ( x , y ) ,
W cat's   eye   pos . ( x , y ) = W R ( x , y ) + W S ( x , y ) + W S ( x , y ) 2 .
W O ( x , y ) = 1 2 { W normal   pos . ( x , y ) + W rot .   pos . ( x , y ) [ W cat's   eye   pos . ( x , y ) + W cat's   eye   pos. ( x , y ) ] } .
Φ mis = 2 k ( n d ) ,
d = T + Ω × r ,
Φ mis ( x , y ) = i T i M T i + j Ω j M Ω j .
n ( x ˜ , y ˜ ) = λ 2 π [ Φ / x ˜ , Φ / y ˜ , ( 2 π / λ ) 2 ( Φ / x ˜ ) 2 ( Φ / y ˜ ) 2 ] .
W rot .  pos . ( r , φ ) = W R ( r , φ ) + W S ( r , φ ) + W O ( r , φ + π + Δ φ ) .
W O ( r , φ + π + Δ φ ) = W O ( r , φ + π ) + Δ φ W O ( r , φ + π ) ( φ + π ) .
Δ W O = 2 π 100,000 .
W cat's   eye   pos . ( x , y ) = W R ( x , y ) + W S ( x + Δ x , y ) + W S ( x , y ) 2 .
W S ( x + Δ x , y ) = W S ( x , y ) + Δ x W S ( x , y ) x .
Δ W S = 2 π 500 .

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