Abstract

A digital phase-measuring interferometer with a laser-diode source has been developed that is based on a fringe-scanning technique with a stepwise wavelength change by variation of the laser injection current. The phase is changed to produce a relative phase difference between the beams in the two arms of the interferometer. Calibrated phase shifts used for a phase-extraction algorithm are derived from one-dimensional least-squares fits to cosine fringe functions to achieve accurate results. Experimental results are presented.

© 1987 Optical Society of America

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References

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  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
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1985

1984

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

1982

1981

1975

1974

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for measurements of the phase of the test lens and the current-tuning rate of the LD.

Fig. 2
Fig. 2

Interference signals (lower traces) introduced by a 100-Hz triangular wave (upper traces) of the injection current ranging from 60 to 70 mA. The figures correspond to the cases for the two path differences, l1 and l2.

Fig. 3
Fig. 3

(a) Interferogram of test lens having spherical aberration. Phase shifts are calibrated over the range marked by ol-12-4-233-i001. (b) Three-dimensional plot of discontinuous phase distribution. (c) Three-dimensional plot of the spherical aberration made by correcting 2π phase gaps in (b).

Equations (8)

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Δ ψ k = 2 π λ 0 2 l k Δ λ             ( k = 1 , 2 ) ,
Δ λ = ( m 2 - m 1 ) λ 0 2 l 2 - l 1 ,
I ( x , y , l ) = A ( x , y ) + B ( x , y ) cos { 2 π λ [ 2 w ( x , y ) + l ] } ,
Φ 0 + Δ Φ = 2 π λ 0 ( 2 w + l ) - ( 2 π l Δ λ λ 0 2 + 2 π 2 w Δ λ λ 0 2 ) .
δ j = 2 π l Δ λ λ 0 2 = j 2 π l α Δ i λ 0 2             ( j = 1 , , N ) ,
I j ( x , y , δ j ) = A ( x , y ) + B ( x , y ) cos ( Φ 0 - δ j )
X ( δ j ) [ A B cos Φ 0 B sin Φ 0 ] = C ( x , y , δ j ) ,
X = [ N Σ cos δ j Σ sin δ j Σ cos δ j Σ cos 2 δ j Σ sin δ j cos δ j Σ sin δ j Σ cos δ j sin δ j Σ sin 2 δ j ] , C = [ Σ I j * Σ I j * cos δ j Σ I j * sin δ j ] .

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