Abstract

Work on orthogonal polynomials by Tatian has been incorporated into a computer program for interferogram analysis. For obscured-aperture optical systems, the data reduction is far more accurate than with programs based only on Zernike polynomials. Results are shown for spherical aberration, coma, and astigmatism.

© 1980 Optical Society of America

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References

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  1. B. Tatian, J. Opt. Soc. Am. 64, 1083 (1974).
    [Crossref]
  2. In the University of Arizona program fringe, written by J. Loomis, Zernike polynomials are used as a basis, but the interpolating polynomial is computed from a Gram-Schmidt orthogonalization of the basis on the data set.

1974 (1)

J. Opt. Soc. Am. (1)

Other (1)

In the University of Arizona program fringe, written by J. Loomis, Zernike polynomials are used as a basis, but the interpolating polynomial is computed from a Gram-Schmidt orthogonalization of the basis on the data set.

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Figures (4)

Fig. 1
Fig. 1

The OPD error function for W040 = 1; = ¼,½,¾.

Fig. 2
Fig. 2

The OPD error function for W131 = 1; = ¼,½,¾.

Fig. 3
Fig. 3

The error function for rms wave-front error; W040 = 1, W131 = 1.

Fig. 4
Fig. 4

Data points for double-pass interferogram of OPD = 5y − 6r2 + 4.77028r4.

Tables (2)

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Table I OPDs with rms = 0.2

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Table II Root-Mean-Square Wave-Front Error with rms = 0.2

Equations (8)

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W = W 040 r 4 + W 020 r 2 .
σ W 2 = W 2 - W 2 , W 2 = 0 2 π 1 ( W 040 r 4 + W 020 r 2 ) 2 r d r d θ 0 2 π 1 r d r d θ .
OPD ( r ) = W 040 [ r 4 - ( 1 + 2 ) r 2 + ( 1 + 4 2 + 4 ) ] ,
σ W 2 = ( 1 - 2 ) 4 180 W 040 2 .
OPD ( x , y ) = W 131 × y ( r 2 - 2 3 1 - 6 1 - 4 ) ,
σ W 2 = ( 1 - 2 ) ( 1 + 4 2 + 4 ) 72 ( 1 + 2 ) , W 131 , 2
OPD ( x , y ) = W 222 2 ( y 2 - x 2 ) ,
σ W 2 = 1 + 2 + 4 24 W 222 2 .

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