Abstract

We present a novel method for obtaining the phase distribution of an object spectrum by using a fringe-scanning phase-conjugate interferometer. A detailed analysis of the proposed technique is provided, and experimental demonstrations for validating this technique are also given. The major advantages of this method are its potentially high accuracy and its low space–bandwidth-product requirement for the detection system.

© 1989 Optical Society of America

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References

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  1. K. Xu, Opt. Commun. 67, 21 (1988).
    [CrossRef]
  2. A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).
  3. S. Wu, C. Xu, Z. Wang, in ICO-13 Conference Digest (ICO Organizing Committee, Sapporo, Japan, 1984), p. 458.
  4. J. H. Brunning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 409.

1988

K. Xu, Opt. Commun. 67, 21 (1988).
[CrossRef]

A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).

Brunning, J. H.

J. H. Brunning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 409.

Chion, A. E.

A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).

Khoshnevisan, M.

A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).

Wang, Z.

S. Wu, C. Xu, Z. Wang, in ICO-13 Conference Digest (ICO Organizing Committee, Sapporo, Japan, 1984), p. 458.

Wu, S.

S. Wu, C. Xu, Z. Wang, in ICO-13 Conference Digest (ICO Organizing Committee, Sapporo, Japan, 1984), p. 458.

Xu, C.

S. Wu, C. Xu, Z. Wang, in ICO-13 Conference Digest (ICO Organizing Committee, Sapporo, Japan, 1984), p. 458.

Xu, K.

K. Xu, Opt. Commun. 67, 21 (1988).
[CrossRef]

Yeh, P.

A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).

Opt. Commun.

K. Xu, Opt. Commun. 67, 21 (1988).
[CrossRef]

Opt. Eng.

A. E. Chion, P. Yeh, M. Khoshnevisan, Opt. Eng. 27, 385 (1988).

Other

S. Wu, C. Xu, Z. Wang, in ICO-13 Conference Digest (ICO Organizing Committee, Sapporo, Japan, 1984), p. 458.

J. H. Brunning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 409.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for phase measurement. M’s, mirrors; BS’s, beam splitters; PBS, polarizing beam splitter; L’s, lenses; Q, quarter-wave plate; A, analyzer; MS, microscope; CCD, charge-coupled device camera.

Fig. 2
Fig. 2

Orientation of polarizing components: P, P//, S and P polarization, respectively; Qs, Qf, slow and fast axes, respectively, of the quarter-wave plate; A, analyzer.

Fig. 3
Fig. 3

Output fringe shift with respect to the analyzer orientation angle.

Fig. 4
Fig. 4

Implementation of an electro-optic birefringence modulator (E-O BM). Other abbreviations as in Fig. 1.

Equations (9)

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[ O ( x , y ) O ( x , y ) ] FT [ | O ˜ ( u , υ ) | exp [ j ϕ ( u , υ ) ] | O ˜ ( u , υ ) | exp [ j ϕ ( u , υ ) ] ] .
[ j 1 1 j ] | O ˜ ( u , υ ) | [ exp [ j ϕ ( u , υ ) ] exp [ j ϕ ( u , υ ) ] ] = 2 | O ˜ ( u , υ ) | exp ( j π 4 ) { cos [ ϕ ( u , υ ) + π 4 ] sin [ ϕ ( u , υ ) + π 4 ] } .
I ( u , υ , Ө ) = 2 | O ˜ ( u , υ ) | 2 { 1 sin [ 2 ϕ ( u , υ ) 2 Ө ] } ,
2 ϕ ( u , υ ) = tan 1 [ B ( u , υ ) A ( u , υ ) ] ,
A ( u , υ ) = n π | O ( u , υ ) | 2 cos [ 2 ϕ ( u , υ ) ] = 0 n π I ( u , υ , Ө ) sin 2 Ө d Ө , B ( u , υ ) = n π | O ( u , υ ) | 2 sin [ 2 ϕ ( u , υ ) ] = 0 n π I ( u , υ , Ө ) cos 2 Ө d Ө ,
A ( u , υ ) = i = 1 m I ( u , υ , Ө i ) sin 2 Ө i , B ( u , υ ) = i = 1 m I ( u , υ , Ө i ) cos 2 Ө i ,
σ ϕ = 1 m s / n ,
( | O ˜ ( u , υ ) | exp [ j ϕ ( u , υ ) ] | O ˜ ( u , υ ) | exp { j ϕ [ ( u , υ ) + α ] } ) .
I ( u , υ , Ө , α ) = 2 | O ˜ ( u , υ ) | 2 { 1 sin [ 2 ϕ ( u , υ ) 2 Ө α ] } .

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