Abstract

A series of simulations were made for an ideal Twyman–Green interferogram of equally spaced straight fringes having tilt only about x. It was found that fitting polynomials to the interferometric data resulted in biased estimates of some of the fitting coefficients to the optical path difference. The acceptance of the Seidel aberrations grows with the noise level and diminishes when the number of fringes is increased.

© 1994 Optical Society of America

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References

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  1. D. Malacara, “Twyman–Green interferometer,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 69–76.
  2. D. Dutton, A. Cornejo, M. Latta, “A semiautomatic method for interpreting shearing interferograms,” Appl. Opt. 7, 125–131 (1968).
    [Crossref] [PubMed]
  3. M. P. Rimmer, “Evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974).
    [Crossref] [PubMed]
  4. A. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 298–302.
  5. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 340–346.
  6. G. E. Forsythe, “Generation and use of orthogonal polynomials for data-fitting on a digital computer,” J. Soc. Ind. Appl. Math. 5, 74–80 (1957).
    [Crossref]
  7. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980).
    [Crossref] [PubMed]
  8. R. C. Moore, “Automatic method of real time wavefront analysis,” Opt. Eng.18, 461–463 (1979).
  9. N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 164–167.
  10. V. S. Koroliuk, Manual de la Teoria de Probabilidades y Estadistica Matemática (Mir, Moscow, 1981), pp. 508–518.
  11. R. Berggren, “Analysis of interferograms,” Opt. Spectra 4, (11)22–25 (1970).
  12. R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Opt. Soc. 27, 94 (1925–1926).
  13. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.

1980 (1)

1979 (1)

R. C. Moore, “Automatic method of real time wavefront analysis,” Opt. Eng.18, 461–463 (1979).

1974 (1)

1970 (1)

R. Berggren, “Analysis of interferograms,” Opt. Spectra 4, (11)22–25 (1970).

1968 (1)

1957 (1)

G. E. Forsythe, “Generation and use of orthogonal polynomials for data-fitting on a digital computer,” J. Soc. Ind. Appl. Math. 5, 74–80 (1957).
[Crossref]

Berggren, R.

R. Berggren, “Analysis of interferograms,” Opt. Spectra 4, (11)22–25 (1970).

Cornejo, A.

D. Dutton, A. Cornejo, M. Latta, “A semiautomatic method for interpreting shearing interferograms,” Appl. Opt. 7, 125–131 (1968).
[Crossref] [PubMed]

A. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 298–302.

Draper, N. R.

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 164–167.

Dutton, D.

Forsythe, G. E.

G. E. Forsythe, “Generation and use of orthogonal polynomials for data-fitting on a digital computer,” J. Soc. Ind. Appl. Math. 5, 74–80 (1957).
[Crossref]

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 340–346.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.

Kingslake, R.

R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Opt. Soc. 27, 94 (1925–1926).

Koroliuk, V. S.

V. S. Koroliuk, Manual de la Teoria de Probabilidades y Estadistica Matemática (Mir, Moscow, 1981), pp. 508–518.

Latta, M.

Malacara, D.

D. Malacara, “Twyman–Green interferometer,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 69–76.

Moore, R. C.

R. C. Moore, “Automatic method of real time wavefront analysis,” Opt. Eng.18, 461–463 (1979).

Rimmer, M. P.

Silva, D. E.

Smith, H.

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 164–167.

Wang, J. Y.

Appl. Opt. (3)

J. Soc. Ind. Appl. Math. (1)

G. E. Forsythe, “Generation and use of orthogonal polynomials for data-fitting on a digital computer,” J. Soc. Ind. Appl. Math. 5, 74–80 (1957).
[Crossref]

Opt. Eng. (1)

R. C. Moore, “Automatic method of real time wavefront analysis,” Opt. Eng.18, 461–463 (1979).

Opt. Spectra (1)

R. Berggren, “Analysis of interferograms,” Opt. Spectra 4, (11)22–25 (1970).

Trans. Opt. Soc. (1)

R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Opt. Soc. 27, 94 (1925–1926).

Other (6)

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), p. 48.

D. Malacara, “Twyman–Green interferometer,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 69–76.

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 164–167.

V. S. Koroliuk, Manual de la Teoria de Probabilidades y Estadistica Matemática (Mir, Moscow, 1981), pp. 508–518.

A. Cornejo, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 298–302.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 340–346.

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Figures (7)

Fig. 1
Fig. 1

Number P of times that the aberration coefficients have to be accepted for (a) three fringes, (b) 11 fringes, (c) 21 fringes.

Fig. 2
Fig. 2

Mean values of the deviations of the aberration coefficient estimators for three fringes in the interference pattern.

Fig. 3
Fig. 3

Same as Fig. 2 but for 11 fringes in the interference pattern.

Fig. 4
Fig. 4

Same as Fig. 2 but for 21 fringes in the interference pattern.

Fig. 5
Fig. 5

Mean values of the deviations for only defocusing, tilt, and constant coefficients (aberration terms are not included) for three fringes in the interference pattern.

Fig. 6
Fig. 6

Same as Fig. 5 but for 11 fringes in the interference pattern.

Fig. 7
Fig. 7

Same as Fig. 5 but for 21 fringes in the interference pattern.

Equations (3)

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W 1 = d ( x 2 + y 2 ) + t x y + t y x + c t ,
W 2 = s ( x 2 + y 2 ) 2 + c y ( x 2 + y 2 ) + a ( x 2 + 3 y 2 ) + d ( x 2 + y 2 ) + t x y + t y x + c t .
W = t x y .

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