Abstract

A circular null computer-generated hologram (CGH) was used to test a highly paraboloidal mirror (diameter, 90 mm; f number, 0.76). To verify the null CGH test a classic autocollimation test with a flat mirror was performed. Comparing the results, we show that the results of the null CGH test show good agreement with results of the autocollimation test.

© 2004 Optical Society of America

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References

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  1. J. M. Sassian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).
    [CrossRef]
  2. S. A. Lerner, J. M. Sassian, “Use of implicitly defined optical surfaces for the design of imaging and illumination systems,” Opt. Eng. 39, 1796–1801 (2000).
    [CrossRef]
  3. S. R. Clark, “Optical reference profilometry,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 2000).
  4. J. H. Burge, “Advanced techniques for measuring primary mirrors for astronomical telescopes,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).
  5. Y.-C. Chang, “Diffraction wavefront analysis of computer-generated holograms,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).
  6. J. H. Burge, “Measurement of large convex asphere,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 362–372 (1997).
    [CrossRef]
  7. 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, A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38, 1295–1301 (1999).
    [CrossRef]
  8. V. V. Cherkashin, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
    [CrossRef]

2000

S. A. Lerner, J. M. Sassian, “Use of implicitly defined optical surfaces for the design of imaging and illumination systems,” Opt. Eng. 39, 1796–1801 (2000).
[CrossRef]

1999

1988

J. M. Sassian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).
[CrossRef]

Burge, J. H.

J. H. Burge, “Measurement of large convex asphere,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 362–372 (1997).
[CrossRef]

J. H. Burge, “Advanced techniques for measuring primary mirrors for astronomical telescopes,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).

Chang, Y.-C.

Y.-C. Chang, “Diffraction wavefront analysis of computer-generated holograms,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).

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, 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, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

Churin, E. G.

Clark, S. R.

S. R. Clark, “Optical reference profilometry,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 2000).

Kharisov, A. A.

V. V. Cherkashin, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

Kharissov, A. A.

Kiryanov, A. V.

Kiryanov, V. P.

Kokarev, S. A.

Korl’kov, V. P.

V. V. Cherkashin, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

Korolkov, V. P.

Koronkevich, 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, 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, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

Lerner, S. A.

S. A. Lerner, J. M. Sassian, “Use of implicitly defined optical surfaces for the design of imaging and illumination systems,” Opt. Eng. 39, 1796–1801 (2000).
[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, 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, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

Sassian, J. M.

S. A. Lerner, J. M. Sassian, “Use of implicitly defined optical surfaces for the design of imaging and illumination systems,” Opt. Eng. 39, 1796–1801 (2000).
[CrossRef]

J. M. Sassian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).
[CrossRef]

Verhoglyad, A. G.

Appl. Opt.

Opt. Eng.

J. M. Sassian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).
[CrossRef]

S. A. Lerner, J. M. Sassian, “Use of implicitly defined optical surfaces for the design of imaging and illumination systems,” Opt. Eng. 39, 1796–1801 (2000).
[CrossRef]

Other

S. R. Clark, “Optical reference profilometry,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 2000).

J. H. Burge, “Advanced techniques for measuring primary mirrors for astronomical telescopes,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).

Y.-C. Chang, “Diffraction wavefront analysis of computer-generated holograms,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1993).

J. H. Burge, “Measurement of large convex asphere,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 362–372 (1997).
[CrossRef]

V. V. Cherkashin, A. A. Kharisov, V. P. Korl’kov, V. P. Koronkevich, A. G. Poleshchuk, “Accuracy potential of circular laser writing of DOEs,” in Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, A. L. Mikaelian, ed., Proc. SPIE3348, 58–68 (1998).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Geometry for defining a CGH such that it returns the same wave front as a perfect aspheric surface.

Fig. 2
Fig. 2

Layout with prescription of a null CGH test for a paraboloid mirror.

Fig. 3
Fig. 3

CGH function calculated at the CGH plane for paraboloid testing.

Fig. 4
Fig. 4

Layout for design of alignment CGHs: (a) adjustment of CGH position, (b) adjustment of distance from the CGH to the paraboloid.

Fig. 5
Fig. 5

CGH consisting of a main area for generating the paraboloidal test wave surrounded by six smaller diffractive sectors.

Fig. 6
Fig. 6

(a) Two-dimensional and (b) three-dimensional plots of the wave-front phase-difference map. Here and in Figs. 7 and 8, WV means wavelength.

Fig. 7
Fig. 7

Wave-front phase-difference map obtained from rotation of the CGH. Rotation angles were (a) 0°, (b) 120°, and (c) 240°.

Fig. 8
Fig. 8

Wave-front phase-difference map obtained from rotation of the paraboloid. Rotation angles were (a) 0°, (b) 120°, and (c) 240°. The dark shapes near the edges of the circles are fiducial marks that were used for alignment.

Fig. 9
Fig. 9

Autocollimation test for the paraboloid.

Fig. 10
Fig. 10

(a) Two-dimensional and (b) three-dimensional plots of the wave-front phase-difference map.

Tables (4)

Tables Icon

Table 1 Design Data for a Paraboloidal Mirror

Tables Icon

Table 2 Phase Coefficients of an Alignment CGH

Tables Icon

Table 3 CGH Structure Parametersa

Tables Icon

Table 4 Comparison of Null CGH and Autocollimation Testsa

Equations (8)

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

OHIr=OH+HI,
OH=Hx-Ox2+Hy-Oy2+Hz-Oz21/2,
HI=Ix-Hx2+Iy-Hy2+Iz-Hz21/2.
OHIr0=OH+HI,
OH=|Hz-Oz|,
HI=|Iz-Hz|.
ϕr=OHIr-OHIr0.
ϕr=1mC1r2+C2r4+C3r6+,

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