Abstract

Mechanical vibrations in the frame of an interferometer can introduce a space-dependent factor throughout an interferogram, making its analysis quite difficult. This factor is formally equivalent to the modulus of the complex degree of coherence in the case of quasimonochromatic light. A simple method for retrieving the underlying phase distribution and detecting small perturbations is presented. Introducing an appropriate correction for the above-mentioned factor, good sensitivity is also achievable in noisy environments.

© 1989 Optical Society of America

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References

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  1. S. Nakadate, H. Saito, “Fringe Scanning Speckle-Pattern Interferometry,” Appl. Opt. 24, 2172 (1985).
    [CrossRef] [PubMed]
  2. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  3. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-Pattern Analysis Using a 2-D Fourier Transform,” Appl. Opt. 25, 1653 (1986).
    [CrossRef] [PubMed]
  4. J. B. Schemm, C. M. Vest, “Fringe Pattern Recognition and Interpolation Using Nonlinear Regression Analysis,” Appl. Opt. 22, 2850 (1983).
    [CrossRef] [PubMed]
  5. L. Crescentini, G. Fiocco, “Automatic Fringe Recognition and Detection of Subwavelength Phase Perturbations with a Michelson Interferometer,” Appl. Opt. 27, 118 (1988).
    [CrossRef] [PubMed]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

1988 (1)

1986 (1)

1985 (1)

1983 (1)

1982 (1)

Bachor, H.-A.

Bone, D. J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Crescentini, L.

Fiocco, G.

Ina, H.

Kobayashi, S.

Nakadate, S.

Saito, H.

Sandeman, R. J.

Schemm, J. B.

Takeda, M.

Vest, C. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Analog–digital read out for a single line of the interferogram: a, interference image; b, illumination pattern of one arm; c,illumination pattern of the other arm.

Fig. 3
Fig. 3

Computed phase distribution; unsmoothed results.

Fig. 4
Fig. 4

Two-dimensional map of the computed phase distribution in radians.

Fig. 5
Fig. 5

Same as Fig. 4 but for a different interferogram.

Fig. 6
Fig. 6

Number of events vs observed discrepancy between computed values of δθ(x,y) and the best-fit linear distribution a + bx + cy.

Equations (11)

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I ( x , y , t ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 I 1 I 2 cos [ ϕ 0 ( x , y ) + ϕ 1 ( x , y , t ) ]  ,
I ( x , y , t ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 I 1 I 2 cos [ ϕ 0 ( x , y ) + ϕ 1 ( x , y , t ) ]  ,
F ( t ) = 1 T t T / 2 t + T / 2 F ( τ ) d τ .
I ( x , y , t ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 β ( x , y , t ) I 1 I 2 cos [ ϕ 0 ( x , y ) ]  ,
cos Φ 1 ( x , y , t ) = a 0 ( t ) + a 1 ( t ) x + a 2 ( t ) y + a 3 ( t ) x y + a 4 ( t ) x 2 + a 5 ( t ) y 2 ,
a 0 ( t ) = cos Φ 0 ( t ) ; a 1 ( t ) = Φ 1 ( t ) sin Φ 0 ( t ) ; a 2 ( t ) = Φ 2 ( t ) sin Φ 0 ( t ) ; a 3 ( t ) = Φ 1 ( t ) Φ 2 ( t ) cos Φ 0 ( t ) ; a 4 ( t ) = Φ 1 ( t ) 2 cos Φ 0 ( t ) / 2 ; a 5 ( t ) = Φ 2 ( t ) 2 cos Φ 0 ( t ) / 2.
I ( x , y ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 β I 1 I 2 cos ϕ 0 ( x , y )  ,
[ V V 1 V 2 ] ( 1 δ ) / γ 0 = [ V 1 V 1 V 2 ] ( 1 δ ) / γ 0 + [ V 2 V 1 V 2 ] ( 1 δ ) / γ 0 + 2 β cos ϕ 0 .
R = υ υ 1 υ 2 2 υ 1 υ 2 ,
R 1 2 [ υ υ 1 υ 2 ln υ υ 1 υ 2 υ 1 υ 1 υ 2 ln υ 1 υ 1 υ 2 υ 2 υ 1 υ 2 ln υ 2 υ 1 υ 2 ] δ + β cos ϕ 0 .
R ( ± 1 ) 1 2 [ υ υ 1 υ 2 ln υ υ 1 υ 2 υ 1 υ 1 υ 2 ln υ 1 υ 1 υ 2 υ 2 υ 1 υ 2 ln υ 2 υ 1 υ 2 ] δ ( ± ) ,

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