Abstract

We proposed a valid method with a novel computer-generated hologram (CGH) to test large-aperture convex aspheric. The CGH consisted of two zones with different amounts of power: the central zone has a larger amount of power than the marginal zone. Compared with other CGHs used for convex aspheric testing [SPIE.2576.258 (1995)], it could overcome the difficulty of measuring the central region of the convex surface under test, while relaxing the requirement for the illumination optics and CGH of the test system. We have designed an optical test system with the novel CGH to test a 150 mm-diameter convex surface with full aperture by using optical design software Zemax. The simulated result verified the efficiency of the novel CGH. It is believed that this kind of CGHs can be used to measure any large and deep convex surface with full aperture.

© 2007 Optical Society of America

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References

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  1. J. C. Wyant, "Interferometric testing of aspheric surfaces," SPIE 816, 19-39 (1987).
  2. W. Silvertooth, "A Modification of th Hindle Test for Cassegrain Secondaries," J. Opt.Soc Am 30,140 (1940).
  3. W. E. James and M. D. Waterworth, "A Method for testing aspheric surfaces," Opt. Acta 12, 223-227 (1965)
    [CrossRef]
  4. J. H. Burge, "Applications of computer-generated holograms for interferometric measurement of large aspheric optics," SPIE 2576, 258-269 (1995).
    [CrossRef]
  5. J. H. Burge and D. S. Anderson, "Full aperture interferometeric test of convex secondary mirrors using holographic test plates," SPIE 2199, 181-192 (1994).
    [CrossRef]
  6. J. H. Burge, "Fizeau interferometery for large convex surface," SPIE 2536, 127-137 (1995).
    [CrossRef]
  7. J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
    [CrossRef]
  8. H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
    [CrossRef]
  9. Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
    [PubMed]
  10. Y. J. Xie, Z. W. Lu, and F. Y. Li, "Fabrication of large diffractive optical elements in thick film on a concave lens surface," Opt. Express 11,992-995 (2003).
    [CrossRef] [PubMed]
  11. Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
    [CrossRef]
  12. H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
    [CrossRef] [PubMed]
  13. R. Mercier, "Holographic testing of aspherical surfaces," SPIE 163,208-214 (1977).

2004 (3)

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
[CrossRef]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

1998 (1)

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

1995 (2)

J. H. Burge, "Fizeau interferometery for large convex surface," SPIE 2536, 127-137 (1995).
[CrossRef]

J. H. Burge, "Applications of computer-generated holograms for interferometric measurement of large aspheric optics," SPIE 2576, 258-269 (1995).
[CrossRef]

1994 (1)

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

1987 (1)

J. C. Wyant, "Interferometric testing of aspheric surfaces," SPIE 816, 19-39 (1987).

1977 (1)

R. Mercier, "Holographic testing of aspherical surfaces," SPIE 163,208-214 (1977).

1965 (1)

W. E. James and M. D. Waterworth, "A Method for testing aspheric surfaces," Opt. Acta 12, 223-227 (1965)
[CrossRef]

1940 (1)

W. Silvertooth, "A Modification of th Hindle Test for Cassegrain Secondaries," J. Opt.Soc Am 30,140 (1940).

Anderson, D. S.

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

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

Burge, J. H.

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

J. H. Burge, "Fizeau interferometery for large convex surface," SPIE 2536, 127-137 (1995).
[CrossRef]

J. H. Burge, "Applications of computer-generated holograms for interferometric measurement of large aspheric optics," SPIE 2576, 258-269 (1995).
[CrossRef]

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

James, W. E.

W. E. James and M. D. Waterworth, "A Method for testing aspheric surfaces," Opt. Acta 12, 223-227 (1965)
[CrossRef]

Kan, S. S.

Li, F. Y.

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
[CrossRef]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Fabrication of large diffractive optical elements in thick film on a concave lens surface," Opt. Express 11,992-995 (2003).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

Liu, H

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Lu, Z. W.

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
[CrossRef]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Fabrication of large diffractive optical elements in thick film on a concave lens surface," Opt. Express 11,992-995 (2003).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

Mercier, R.

R. Mercier, "Holographic testing of aspherical surfaces," SPIE 163,208-214 (1977).

Milster, T. D.

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

Shun, Q.

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Silvertooth, W.

W. Silvertooth, "A Modification of th Hindle Test for Cassegrain Secondaries," J. Opt.Soc Am 30,140 (1940).

Vernold, C. L.

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

Wang, S. R.

Waterworth, M. D.

W. E. James and M. D. Waterworth, "A Method for testing aspheric surfaces," Opt. Acta 12, 223-227 (1965)
[CrossRef]

Weng, Z. C.

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

Wyant, J. C.

J. C. Wyant, "Interferometric testing of aspheric surfaces," SPIE 816, 19-39 (1987).

Xie, Y. J.

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
[CrossRef]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Fabrication of large diffractive optical elements in thick film on a concave lens surface," Opt. Express 11,992-995 (2003).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

Zhao, J. L.

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

J. Opt.Soc Am (1)

W. Silvertooth, "A Modification of th Hindle Test for Cassegrain Secondaries," J. Opt.Soc Am 30,140 (1940).

Opt. Acta (1)

W. E. James and M. D. Waterworth, "A Method for testing aspheric surfaces," Opt. Acta 12, 223-227 (1965)
[CrossRef]

Opt. Commu (1)

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, and Q. Shun, "Full-aperture measurement of convex surfaces in interferometric test using holographic test plate," Opt. Commu 241, 231-236 (2004).
[CrossRef]

Opt. Express (4)

Y. J. Xie, Z. W. Lu, F. Y. Li, J. L. Zhao and Z. C. Weng, "Lithographic fabrication of large diffractive optical elements on a concave lens surface," Opt. Express 10,1043-1047 (2002).
[PubMed]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Fabrication of large diffractive optical elements in thick film on a concave lens surface," Opt. Express 11,992-995 (2003).
[CrossRef] [PubMed]

Y. J. Xie, Z. W. Lu, and F. Y. Li, "Lithographic fabrication of large curved hologram by laser writer," Opt. Express 12,1180-1184 (2004).
[CrossRef]

H Liu, Z. W. Lu, F. Y. Li, Y. J. Xie, S. S. Kan and S. R. Wang, "Using curved hologram to test large-aperture convex surface," Opt. Express 12,3251-3255 (2004).
[CrossRef] [PubMed]

SPIE (6)

R. Mercier, "Holographic testing of aspherical surfaces," SPIE 163,208-214 (1977).

J. H. Burge, "Applications of computer-generated holograms for interferometric measurement of large aspheric optics," SPIE 2576, 258-269 (1995).
[CrossRef]

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

J. H. Burge, "Fizeau interferometery for large convex surface," SPIE 2536, 127-137 (1995).
[CrossRef]

J. H. Burge, D. S. Anderson, T. D. Milster, C. L. Vernold, "Measurement of a convex secondary mirror using a holographic test plate," SPIE 2199, 193-198 (1998).
[CrossRef]

J. C. Wyant, "Interferometric testing of aspheric surfaces," SPIE 816, 19-39 (1987).

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Figures (4)

Fig. 1.
Fig. 1.

Layout for measuring convex surface with diffractive optical element.

Fig. 2.
Fig. 2.

(a). Slope error in illumination system (b) Wavefront slope of the adjacent order (c) Wavefront slope of the adjacent order inside the radius 13 mm.

Fig. 3.
Fig. 3.

Line frequency vs Aperture of the two-zone hologram.

Fig. 4.
Fig. 4.

Interferogram corresponding to (a) the central zone of the surface under test (b) the marginal zone of the surface under test.

Equations (11)

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v c max { v ill ( r ) }
v ( r ) = v CGH ( r ) + v ill ( r )
for all r r 1 , v ( r ) v c
ϕ CGH ( r ) = 2 [ ϕ out ( r ) ϕ in ( r ) ]
= 2 [ ϕ sph ( r ) ϕ asph ( r ) ]
= 2 [ ( a sph 1 r 2 + a sph 2 r 4 + a sph 3 r 6 + ) ( a asph 1 r 2 + a asph 2 r 4 + a asph 3 r 6 + ) ]
= 2 ( a sph 1 a asph 1 ) r 2 + 2 ( a sph 2 a asph 2 ) r 4 + 2 ( a sph 3 a asph 3 ) r 6 +
a asph 1 = 1 2 ( 1 + k ) R asph 1
a sph 1 = 1 2 R sph
= 1 2 ( 1 + k ) ( R asph + d )
a CGH = 1 R aph 1 ( k + 1 ) ( R asph + d )

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