Abstract

The implementation of a new type of phase-shifting, self-referencing interferometer that simultaneously achieves the phase shift and separation of beams with a stationary diffraction grating is described. The capabilities of stroboscopic interferometry are demonstrated with results from an experiment in which the rapidly varying surface deformations of a sonically activated pellicle mirror are measured in a time-sliced fashion at 50-μsec intervals.

© 1987 Optical Society of America

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References

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  1. J. C. Wyant, Laser Focus 18 (5), 65 (1982).
  2. O. Y. Kwon, Opt. Lett. 9, 59 (1984).
    [CrossRef] [PubMed]
  3. O. Y. Kwon, D. M. Shough, Proc. Soc. Photo-Opt. Instrum. Eng. 599, 273 (1985).

1985

O. Y. Kwon, D. M. Shough, Proc. Soc. Photo-Opt. Instrum. Eng. 599, 273 (1985).

1984

1982

J. C. Wyant, Laser Focus 18 (5), 65 (1982).

Kwon, O. Y.

O. Y. Kwon, D. M. Shough, Proc. Soc. Photo-Opt. Instrum. Eng. 599, 273 (1985).

O. Y. Kwon, Opt. Lett. 9, 59 (1984).
[CrossRef] [PubMed]

Shough, D. M.

O. Y. Kwon, D. M. Shough, Proc. Soc. Photo-Opt. Instrum. Eng. 599, 273 (1985).

Wyant, J. C.

J. C. Wyant, Laser Focus 18 (5), 65 (1982).

Laser Focus

J. C. Wyant, Laser Focus 18 (5), 65 (1982).

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

O. Y. Kwon, D. M. Shough, Proc. Soc. Photo-Opt. Instrum. Eng. 599, 273 (1985).

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Figures (4)

Fig.1
Fig.1

Mach–Zehnder radial-shear grating interferometer.

Fig. 2
Fig. 2

Stroboscopic laser interferometry experiment: schematic of the apparatus.

Fig. 3
Fig. 3

Data reduction of interferograms measured from resting pellicle mirror: (a) raw intensity interferograms with 90° relative phase shift recorded at the three focal planes; (b) modulo 2π phase map generated from interferograms in (a) using Eq. (3); (c) unwrapped phase map generated by resolving the 2π phase ambiguities in (b).

Fig. 4
Fig. 4

Three-dimensional surface plots of stroboscopically measured, high-speed surface deformation of a pellicle mirror. Frames are shown at 50-μsec intervals following the sonic impact.

Equations (5)

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I ( x , y ) = I b ( x , y ) + I m ( x , y ) cos [ ϕ ( x , y ) + δ ] ,
I A ( x , y ) = I b ( x , y ) + I m ( x , y ) cos [ ϕ ( x , y ) + π / 4 ] , I B ( x , y ) = I b ( x , y ) + I m ( x , y ) cos [ ϕ ( x , y ) + 3 π / 4 ] , I C ( x , y ) = I b ( x , y ) + I m ( x , y ) cos [ ϕ ( x , y ) + 5 π / 4 ] .
ϕ ( x , y ) = tan 1 [ I C ( x , y ) I B ( x , y ) I A ( x , y ) I B ( x , y ) ] .
G ( x x g , y ) = n g n exp [ i 2 π n ξ 0 ( x x g ) ] ,
δ n = 2 π n ξ 0 x g + P ( g n ) ,

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