Abstract

It is shown that phase-extraction algorithms in phase-measurement interferometry can be developed from the principle of least-squares estimation. It is then demonstrated that this view can be taken to develop algorithms that estimate the phase in the presence of external perturbations. To illustrate, an algorithm is developed that extracts the phase in the presence of a linear time-dependent drift.

© 1982 Optical Society of America

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References

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  1. J. H. Bruning, “Fringe scanning interferometers,” Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 409.
  2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wave-front measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  3. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14, 2622 (1975).
    [CrossRef] [PubMed]
  4. R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1962), p. 510.

1975 (1)

1974 (1)

Brangaccio, D. J.

Bruning, J. H.

Gallagher, J. E.

Hamming, R. W.

R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1962), p. 510.

Herriott, D. R.

Rosenfeld, D. P.

White, A. D.

Wyant, J. C.

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Figures (1)

Fig. 1
Fig. 1

Twyman–Green interferometer with piezoelectric translator in reference arm.

Tables (1)

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Table 1 Iterative Solutions

Equations (17)

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I ( X , Y , t ) = 1 + γ cos { 4 π λ [ W ( X , Y ) Δ L ] } ,
Q = j = 1 N { I j * 1 γ cos [ 4 π W ( X , Y ) λ 2 π N j ] } 2 .
j = 1 N { I j * 1 γ cos [ 4 π W ( X , Y ) λ 2 π N j ] } × sin [ 4 π W ( X , Y ) λ 2 π N j ] = 0 .
j = 1 N sin ( 2 π N j ) cos ( 2 π N j ) = 0
j = 1 N sin 2 ( 2 π N j ) = j = 1 N cos 2 ( 2 π N j ) .
W ( X , Y ) = λ 4 π tan 1 [ j = 1 N I j * sin ( 2 π N j ) / j = 1 N I j * cos ( 2 π N j ) ] .
M ( τ ) = T 0 T 0 + τ d t [ 1 + γ cos ( 2 π N τ t + ϕ ) ] ,
( T 8 , T 8 ) , ( T 8 , 3 T 8 ) , ( 3 T 8 , 5 T 8 ) , ( 5 T 8 , 7 T 8 ) ,
T 0 = j τ τ 2 ,
M j = τ + N γ τ π sin ( π N ) cos ( ϕ + 2 π N j ) .
ϕ = tan 1 [ j = 0 N 1 M j * sin ( 2 π N j ) j = 0 N 1 M j * cos ( 2 π N j ) ] .
ϕ = tan 1 [ ( M 1 * M 3 * ) ( M 0 * M 2 * ) ]
= π 2 + tan 1 ( M 0 * M 2 * M 1 * M 3 * ) .
Q = j = 1 N [ I j * 1 γ cos ( θ j ) ] 2 ,
θ j = 4 π W ( X , Y ) λ 2 π N ( 1 + F ) j .
j = 1 N I j * sin ( θ j ) = j = 1 N [ sin ( θ j ) + 1 2 γ sin ( 2 θ j ) ] ,
j = 1 N j I j * sin ( θ j ) = j = 1 N j [ sin ( θ j ) + 1 2 γ sin ( 2 θ j ) ] ,

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