Abstract

Speckle fringe patterns of ESPI are full of high-level speckle noise and normally are processed by phase shifting methods that require multi speckle fringe patterns. We propose a novel method to generate a speckle-noise-free fringe pattern from a single speckle fringe pattern and to extract the phase field from the new pattern. With the new method, the correlation between two speckle patterns is performed only within contour windows instead of rectangular windows and this contoured correlation results in a smooth, normalized fringe pattern without speckle noise. The new ESPI fringe patterns are speckle-noise-free and of comparable quality to that of moiré and hologram, which is unimaginable with traditional ESPI methods. In addition to the smoothness, the resultant fringe pattern is normalized automatically so that the full phase field can be extracted from this single fringe pattern by the single-image phase-shifting method.

© 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.

FRINGE

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

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]

Optical Testing Digest

G. Kaufmann, A. Davila and D. Kerr, �??Interview-Smoothing of speckle interferometry fringe-patterns,�?? Optical Testing Digest, Vol. 2(4), 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).

K. Andresen and Qifeng Yu, �??Robust phase unwrapping by spin filtering combined with a phase direction map,�?? Optik 94, 145-9 (1993).

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Figures (9)

Fig.1.
Fig.1.

Comparison of three kind resultant fringe patterns by subtraction, correlation with rectangular windows, contoured correlation, respectively.

Fig. 2.
Fig. 2.

The fringe contour windows.

Fig. 3.
Fig. 3.

Experimental results. The upper part is a speckle fringe pattern with subtraction and the lower part is the contoured correlation fringe pattern with a window size of 67×7 pixels for the same original speckle patterns.

Fig. 4.
Fig. 4.

The intensity distribution of an intersection of the contoured correlation fringe pattern of Fig. 3.

Fig. 5.
Fig. 5.

The phase field results. The upper part is the saw-tooth phase field from the lower part of Fig. 3 and the lower part is its unwrapped phase field result.

Fig. 6.
Fig. 6.

The saw-tooth phase distribution of an intersection of the upper part of Fig. 5.

Fig. 7.
Fig. 7.

The full phase field distribution of an intersection of the lower part of Fig. 5.

Fig. 8.
Fig. 8.

Experimental results. The upper left part, upper right part and lower parts are the resultant fringe patterns by subtraction, direct correlation with rectangular windows of 17×17 pixels and the contour correlation with window size of 67×5 pixels, respectively.

Fig. 9.
Fig. 9.

The resultant patterns of the effects of window sizes. The upper and lower parts are the results by direct correlation and contoured correlation, respectively The window sizes are 3×3 and 9×1 (a), 7×7 and 15×3(b), 13×13 and 55×3(c), 19×19 and 73×5 pixels(d), respectively, for the upper and lower parts.

Equations (21)

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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 ) ]
C ( 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
< I 2 > m × n = 2 < I > m × n 2
< cos β > m × n = < cos ( β + Δ θ ) > m × n = 0
< f 1 > = 2 < I > m × n , < f 2 > = 2 < I > m × n
< f 1 f 2 > m × n = < ( I 1 + I 2 ) 2 + 2 ( I 1 + I 2 ) I 1 I 2 cos β
+ 2 ( I 1 + I 2 ) I 1 I 2 cos ( β + Δ θ ) + 4 I 1 I 2 cos β cos ( β + Δ θ ) > m × n
= < ( I 1 + I 2 ) 2 + 4 I 1 I 2 cos ( β + Δ θ ) > m × n
= 6 < I > m × n 2 + < 2 I 1 I 2 ( cos ( 2 β + Δ θ ) + cos Δ θ ) > m × n
= 6 < I > m × n 2 + 2 < I > m × n 2 cos Δ θ
< ( f 1 < f 1 > m × n ) ( f 2 < f 2 > m × n ) > m × n = < f 1 f 2 > m × n < f 1 > m × n < f 2 > m × n
= 2 < I > m × n 2 + 2 < I > m × n 2 cos Δ θ
< ( f 1 < f 1 > m × n ) 2 > m × n = < f 1 2 2 f 1 < f 1 > m × n + < f 1 > m × n 2 > m × n = 4 < I > m × n 2
< ( f 2 < f 2 > m × n ) 2 > m × n = < f 2 2 2 f 2 < f 2 > m × n + < f 2 > m × n 2 > m × n = 4 < I > m × n 2
C = 2 < I > m × n 2 + 2 < I > m × n 2 cos Δ θ 4 < I > m × n 2 = ( cos Δ θ + 1 ) 2
I ( x , y ) = I 0 c + I 1 c cos ( φ ( x , y ) )
J ( x , y ) = I 0 c + I 1 c 2 ( I I 0 c ) 2 = I 0 c × I 1 c sin φ ( x , y )
cos φ ( x , y ) x = sin φ ( x , y ) φ ( x , y ) x
J ( x , y ) = I oc + I 1 c sin ( φ ( x , y ) )
φ ( x , y ) = arctan ( J ( x , y ) I 0 c I ( x , y ) I 0 c ) = arctan ( sin [ φ ( x , y ) ] cos [ φ ( x , y ) ] )

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