Abstract

Speckle fringe patterns of electronic speckle pattern interferometry (ESPI) are full of high-level speckle noise and are mainly processed by phase-shifting methods that normally require three speckle fringe patterns or more. The author proposes a novel method, the contoured correlation-fringe-pattern (CCFP) method, by which speckle-noise-free fringe patterns can be generated for ESPI. The application of this novel method is extended to the phase-shifting or phase-stepping for ESPI after its improvement. It generates speckle-noise-free phase fringes and remains valid for single phase-step condition, thus eliminates the two main disadvantages of the phase-shifting (stepping) methods of ESPI.

© 2004 Optical Society of America

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References

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    [CrossRef]
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Acta Photonica Sinica

Yuming He, �??Digital shearing speckle corelation fringes pattern formed by using linear correlation calculating method,�?? Acta Photonica Sinica 24, 13-17 (1995).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

Qifeng Yu, X. Sun and X. Liu, �??Removing speckle noise and skeleton extraction from a single speckle fringe pattern,�?? Opt. Eng. 42, 68-74 (2003).
[CrossRef]

Opt. Express

Optical Testing Digest

G. Kaufmann, A. Davila and D. Kerr, �??Interview-Smoothing of speckle interferometry fringe-patterns,�?? Optical Testing Digest, 2, 1997.

Optik

Qifeng Yu, Xiaolin Liu, Xiangyi Sun and Zhihui Lei, �??Double-image and single-image phase-shifting methods for phase measurement,�?? Optik 109, 89-95 (1998).

Proc. FRINGE

K. Creath, �??Speckle: Signal or Noise?�?? in Proc. FRINGE 93, W. Jueptner and W. Osten, ed. (Akademie Verlag GmgH, Berlin, 1993), pp. 97-102.

Progress in Optics

K. Creath, �??Phase-measurement interferometry techniques,�?? Progress in Optics, XXVI, 349-393(1988).
[CrossRef]

Other

J.C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975), Chap.2.

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Figures (7)

Fig. 1.
Fig. 1.

The resultant fringe patterns of a ESPI derived by subtraction (top left), direct correlation with window size of 17×17(top right) and contoured correlation with window size of 67×5 pixels (bottom), respectively.

Fig. 2.
Fig. 2.

The top is a simulated speckle fringe pattern and the bottom is the saw-tooth phase fringe pattern for the same pattern achieved by our new method.

Fig. 3.
Fig. 3.

The phase distributions of the simulated ideal phase and the result derived by our new method for the same cross-section in Fig. 2.

Fig. 4.
Fig. 4.

The top is a practical speckle fringe pattern with common subtraction without post-processing, the bottom is its SFOM.

Fig. 5.
Fig. 5.

The phase fringe patterns derived by (top) the common four image phase-shifting method, (bottom) the proposed single-phase-step method with a window size of 51×3 pixels.

Fig. 6.
Fig. 6.

The phase fringe patterns derived by the proposed methods with contoured correlation fringe patterns with a window size of 51×3 pixels, (top) by the single-phase-step method, (bottom) by the three-phase-step method.

Fig. 7.
Fig. 7.

The phase distributions of the same cross-section in the phase pattern derived by (a) subtraction method in the top of Fig. 5, (b) the single-phase-step method with contoured correlation fringe patterns in the bottom of Fig. 5 and (c) the three-phase-step method with contoured correlation fringe patterns in the bottom of Fig. 6.

Equations (10)

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f 1 ( x , y ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 I 1 I 2 cos [ Ψ 1 ( x , y ) Ψ 2 ( x , y ) ]
f 2 ( x , y ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 I 1 I 2 cos [ Ψ 1 ( x , y ) Ψ 2 ( x , y ) + Δ θ ( x , y ) ]
< f 1 > = 2 < I > m × n , < f 2 > = 2 < I > m × n
< cos β > m × n = < cos ( β + Δ θ ) > m × n = 0
C 1 ( x , y ) = < ( f 1 < f 1 > m × n ) ( f 2 < f 2 > m × n ) > m × n [ < ( f 1 < f 1 > m × n ) 2 > m × n ] 1 2 [ < ( f 2 < f 2 > m × n ) 2 > m × n ] 1 2
= 2 < I > m × n 2 + 2 < I > m × n 2 cos Δ θ 4 < I > m × n 2 = ( cos Δ θ + 1 ) 2
f 3 ( x , y ) = I 1 ( x , y ) + I 2 ( x , y ) + 2 I 1 I 2 cos [ Ψ 1 ( x , y ) Ψ 2 ( x , y ) + Δ θ ( x , y ) + π 2 ]
C 2 ( x , y ) = < ( f 1 < f 1 > m × n ) ( f 3 < f 3 > m × n ) > m × n [ < ( f 1 < f 1 > m × n ) 2 > m × n ] 1 2 [ < ( f 3 < f 3 > m × n ) 2 > m × n ] 1 2
= ( cos ( Δ θ + π 2 ) + 1 ) 2 = ( 1 sin Δ θ ) 2
Δ θ ( x , y ) = arctan ( 1 2 C 2 ( x , y ) 2 C 1 ( x , y ) 1 ) = arctan ( sin [ Δ θ ( x , y ) ] cos [ Δ θ ( x , y ) ] )

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