Abstract

The extreme alignment sensitivity of nonlinear diamond-turned reflaxicons makes them difficult to test and analyze. To evaluate the wave front it is necessary to know what portion results from alignment errors. This paper describes the setup, alignment, and testing of a nonlinear diamond-turned independent-element reflaxicon manufactured at the Union Carbide, Oak Ridge Y-12 plant. Interferograms taken with the center cone misaligned a known amount are analyzed using the axicon preprocessing option in fringe [ J. S. Loomis ( ASTM Report STP 666 and Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 ( 1979)]. The results show that fringe correctly removes the cone and decenter errors introduced by the misalignments. It is also shown how the resulting interferograms are unfolded to give the OPD errors as seen on the outer cone.

© 1981 Optical Society of America

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References

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  1. J. S. Loomis, “A Computer Program for Analysis of Interferometric Data,” in Optical Interferograms—Reduction and Interpretation (American Society for Testing and Materials, Philadelphia, 1978), ASTM STP 666, A. H. Guenther, D. H. Liebenberg, Eds., pp.71–86.
    [CrossRef]
  2. J. S. Loomis, Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 (1979).
  3. P. W. Scott, Rocketdyne Division of Rockwell International, Internal Letter No. G-0-79-2062, 1Mar.1979.

1979

J. S. Loomis, Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 (1979).

P. W. Scott, Rocketdyne Division of Rockwell International, Internal Letter No. G-0-79-2062, 1Mar.1979.

Loomis, J. S.

J. S. Loomis, Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 (1979).

J. S. Loomis, “A Computer Program for Analysis of Interferometric Data,” in Optical Interferograms—Reduction and Interpretation (American Society for Testing and Materials, Philadelphia, 1978), ASTM STP 666, A. H. Guenther, D. H. Liebenberg, Eds., pp.71–86.
[CrossRef]

Scott, P. W.

P. W. Scott, Rocketdyne Division of Rockwell International, Internal Letter No. G-0-79-2062, 1Mar.1979.

Proc. Soc. Photo-Opt. Instrum. Eng.

J. S. Loomis, Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 (1979).

Rocketdyne Division of Rockwell International, Internal Letter No. G-0-79-2062

P. W. Scott, Rocketdyne Division of Rockwell International, Internal Letter No. G-0-79-2062, 1Mar.1979.

Other

J. S. Loomis, “A Computer Program for Analysis of Interferometric Data,” in Optical Interferograms—Reduction and Interpretation (American Society for Testing and Materials, Philadelphia, 1978), ASTM STP 666, A. H. Guenther, D. H. Liebenberg, Eds., pp.71–86.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Axicon optical systems.

Fig. 2
Fig. 2

The four possible alignment errors in the reflaxicon system.

Fig. 3
Fig. 3

Hyperbolic fringes formed by the moiré between two circular fringe patterns. This is the same aberration formed by a linear reflaxicon with a small amount of decenter between the elements.

Fig. 4
Fig. 4

Schematic diagram of the test setup.

Fig. 5
Fig. 5

The test setup: (A) Twyman-Green interferometer, (B) folding flat, (C) collimating lens, (D) reflaxicon outer cone, (E) re-flaxicon inner cone, (F) large flat mirror.

Fig. 6
Fig. 6

Double-pass interferograms showing different amount of decenter.

Fig. 7
Fig. 7

OPD maps generated from the interferograms.

Fig. 8
Fig. 8

Geometry used to unfold the OPD maps to show the surface errors on the outer cone.

Fig. 9
Fig. 9

OPD maps as seen at the solid output (top) and on the outer cone (bottom).

Tables (1)

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Table I Experimental Results a

Equations (9)

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ϕ 1 = ( θ y b sin ϕ - θ x b cos ϕ ) a 1 r ;
ϕ 2 = ( θ y i sin ϕ - θ x i cos ϕ ) ( a 2 r + a 3 r 2 ) ;
ϕ 3 = δ z i ( a 4 + a 5 r + a 6 r 2 ) ;
ϕ 4 = ( δ y i cos ϕ + δ x i sin ϕ ) ( a 7 + a 8 r ) ;
B 1 cos ϕ + B 2 sin ϕ = constant .
ϕ 5 = ( θ y f sin ϕ - θ x f cos θ ) ( a 9 + a 10 r ) ,
x 2 = ( f 0 / f i ) x 1
r 1 = x 0 - x 1 ,             r 2 = x 0 - x 2 .
r 2 = 1 m r 1 + A ,

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