Abstract

By making a series of wave-front observations that differ in angle and degree of collimation and using subaperture testing theory, the Zernike polynomial representation of several aberrating screens may be determined from external measurements of the optical system. In this Letter, the analytical basis is presented, limitations to the technique are explored, and some results of numerical evaluation are described.

© 1984 Optical Society of America

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References

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  1. W. W. Chow, G. N. Lawrence, Opt. Lett. 8, 468 (1983); Proc. Soc. Photo-Opt. Instrum. Eng. 440, 99 (1983); S. C. Jensen, W. W. Chow, G. N. Lawrence, Appl. Opt. 23, 740 (1984).
    [Crossref] [PubMed]
  2. C. Kim, J. Wyant, J. Opt. Soc, Am. 71, 1587 (1981); J. Thunen, O. Kwon, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Ariz., 1982).

1983 (1)

1981 (1)

C. Kim, J. Wyant, J. Opt. Soc, Am. 71, 1587 (1981); J. Thunen, O. Kwon, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Ariz., 1982).

Chow, W. W.

Kim, C.

C. Kim, J. Wyant, J. Opt. Soc, Am. 71, 1587 (1981); J. Thunen, O. Kwon, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Ariz., 1982).

Lawrence, G. N.

Wyant, J.

C. Kim, J. Wyant, J. Opt. Soc, Am. 71, 1587 (1981); J. Thunen, O. Kwon, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Ariz., 1982).

J. Opt. Soc, Am. (1)

C. Kim, J. Wyant, J. Opt. Soc, Am. 71, 1587 (1981); J. Thunen, O. Kwon, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Ariz., 1982).

Opt. Lett. (1)

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Figures (3)

Fig. 1
Fig. 1

Test configuration showing source plane, windows, and detector plane.

Fig. 2
Fig. 2

Coordinate system for source, window, and detector planes.

Fig. 3
Fig. 3

Minimum number of source points required versus the number of windows.

Tables (1)

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Table 1 Summary of Results for Example with Three Windows Located at 0.2, 0.4, and 0.6 cma

Equations (11)

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X i j k = X s i + ( X d j X s i ) Z k Z d , Y i j k = Y s i + ( Y d j Y s i ) Z k Z d ,
OPD i j = k = 1 K OPD i j k ,
OPD ( X i j k , Y i j k ) = n = 1 N a k n Z n ( X i j k , Y i j k ) ,
OPD i j = k = 1 K n = 1 N a k n Z n ( X i j k , Y i j k ) .
B p = OPD i j , p = j + ( i 1 ) J , i = 1 + p 1 J , j = p J ( p 1 J ) ,
B = [ OPD ( 1 , 1 ) OPD ( 1 , 2 ) OPD ( 1 , J ) OPD ( 2 , 1 ) OPD ( 1 , J ) ] .
A q = a k n , q = n + ( k 1 ) K , k = 1 + q 1 K , n = q K ( q 1 K ) .
H p q = Z n ( X i j k , Y i j k ) ,
P = I * J Q = K * N .
B = H A .
A = ( H t H ) 1 H t B ,

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