Abstract

We employ the Fourier-transform graphic representation of a set of antisymmetrical and symmetrical sampling reference harmonics to obtain new symmetrical phase-shifting algorithms tailored to specific characteristics. As an example, a new detuning-insensitive seven-point algorithm, with a third signal harmonic insensitivity and which is detuning insensitive at this frequency, is derived.

© 2000 Optical Society of America

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References

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  1. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).
  2. K. G. Larkin and B. F. Oreb, J. Opt. Soc. Am. A 9, 1740 (1992).
    [CrossRef]
  3. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 12, 761 (1995).
    [CrossRef]
  4. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, Appl. Opt. 22, 3421 (1983).
    [CrossRef]
  5. P. Hariharan, B. F. Oreb, and T. Eiju, Appl. Opt. 26, 2504 (1987).
    [CrossRef] [PubMed]

1995 (1)

1992 (1)

1987 (1)

1983 (1)

Burow, R.

Eiju, T.

Elssner, K. E.

Farrant, D. I.

Grzanna, J.

Hariharan, P.

Hibino, K.

Larkin, K. G.

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Merkel, K.

Oreb, B. F.

Schwider, J.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Spolaczyk, R.

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Figures (3)

Fig. 1
Fig. 1

Fourier-transform amplitudes of antisymmetrical HkAf and symmetrical HkSf sampling reference harmonics for a relative phase-shift increment α of π/6 rad.

Fig. 2
Fig. 2

Fourier-transform sampling reference function amplitudes, GAf and GSf, for the new seven-sample PSA.

Fig. 3
Fig. 3

Detuning sensitivity of (a) our tailored seven-sample PSA compared with the detuning sensitivities of (b) the Schwider–Hariharan PSA and (c) the Larkin–Oreb PSA.

Equations (7)

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hkAx=δx-xk-δx+xk,
hkSx=-δx-xk+2δx-δx+xk,
xk=kα/2πfr=αk/2πfr,
GAf=k=1KwkAHkAf,
GSf=k=1KwkSHkSf.
gAx=k=1KwkAhkAx,
gSx=k=1KwkShkSx.

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