Abstract

We describe a method and algorithm for reducing the sensitivity of phase-shifting interferometry to external vibrations. Using an interline-transfer camera, a shutter, and a fast phase shifter, we acquire a series of paired interferograms in quadrature, with the pairs spaced to maximize residual phase-error cancellation. The rapid acquisition of quadrature pairs significantly improves resistance of interferometry to low-frequency vibrations.

© 1998 Optical Society of America

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References

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1996 (1)

1995 (1)

P. de Groot, J. Opt. Soc. Am. 12, 354 (1995).
[CrossRef]

1991 (1)

C. L. Koliopoulos, Proc.??SPIE 1531, 119 (1991).

1990 (1)

1984 (1)

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).
[CrossRef]

1983 (1)

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

P. de Groot, J. Opt. Soc. Am. 12, 354 (1995).
[CrossRef]

Opt. Eng. (1)

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).
[CrossRef]

Proc.??SPIE (1)

C. L. Koliopoulos, Proc.??SPIE 1531, 119 (1991).

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Figures (4)

Fig. 1
Fig. 1

Timing diagrams for PQ-PSI, showing π/2 phase intervals, camera frames, and the shutter state. Each shaded π/2 phase interval represents half of an acquired quadpair. Phase intervals acquired in the same frame (e.g., 2 and 6) are added by the camera.

Fig. 2
Fig. 2

Theoretical vibration-sensitivity spectra for PQ-PSI, the traditional five-frame PSI, and the 2+1 technique for a 60-Hz camera.

Fig. 3
Fig. 3

Experimental verification of improved resistance to vibration for PQ-PSI compared with the traditional five-frame PSI. The vibrational frequency is normalized to the effective camera frame rate.

Fig. 4
Fig. 4

Segmented phase-shift profile for four-quadpair PQ-PSI that provides the same performance as a linear profile but with reduced total phase excursion. The bold regions indicate quadpair acquisitions (see Fig.  1).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

tanφ=i6-i16i1-i11,
tanφ=i2-i12i7-i17.
tanϕ=I2-I4I3-I1-I5,
I1=i1, I2=i2+i6, I3=i7+i11, I4=i12+i16, I5=i17.

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