Abstract

A new method based on pseudo-Wigner-Hough transform is proposed for the simultaneous measurement of the in-plane and out-of-plane displacements using digital holographic moiré. Multiple interference phases corresponding to the in-plane and out-of-plane displacement components are retrieved from a single moiré fringe pattern. The segmentation of the interference field allows us to approximate it with a multicomponent linear frequency modulated signal. The proposed method accurately and simultaneously estimates all the phase parameters of the signal components without the use of any signal separation techniques. Simulation and experimental results demonstrate the efficacy of the proposed method and its robustness against the variations in object beam intensity.

© 2014 Optical Society of America

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References

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2013

R. Kulkarni, P. Rastogi, “Multiple phase estimation in digital holographic interferometry using product cubic phase function,” Opt. Laser Eng. 51, 1168–1172 (2013).
[CrossRef]

2012

2011

2010

2008

L. Cirillo, A. Zoubir, M. Amin, “Parameter estimation for locally linear fm signals using a time-frequency hough transform,” IEEE T. Signal Process. 56, 4162–4175 (2008).
[CrossRef]

P. Picart, D. Mounier, J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33, 276–278 (2008).
[CrossRef] [PubMed]

2007

D. S. Pham, A. M. Zoubir, “Analysis of multicomponent polynomial phase signals,” IEEE T. Signal Process. 55, 56–65 (2007).
[CrossRef]

2005

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

2003

1995

S. Barbarossa, “Analysis of multicomponent lfm signals by a combined wigner-hough transform,” IEEE T. Signal Process. 43, 1511–1515 (1995).
[CrossRef]

Albertazzi, A. G.

Amin, M.

L. Cirillo, A. Zoubir, M. Amin, “Parameter estimation for locally linear fm signals using a time-frequency hough transform,” IEEE T. Signal Process. 56, 4162–4175 (2008).
[CrossRef]

Barbarossa, S.

S. Barbarossa, “Analysis of multicomponent lfm signals by a combined wigner-hough transform,” IEEE T. Signal Process. 43, 1511–1515 (1995).
[CrossRef]

Cirillo, L.

L. Cirillo, A. Zoubir, M. Amin, “Parameter estimation for locally linear fm signals using a time-frequency hough transform,” IEEE T. Signal Process. 56, 4162–4175 (2008).
[CrossRef]

Desse, J. M.

Fujigaki, M.

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

Gorthi, S. S.

Kohler, C.

Kulkarni, R.

R. Kulkarni, P. Rastogi, “Multiple phase estimation in digital holographic interferometry using product cubic phase function,” Opt. Laser Eng. 51, 1168–1172 (2013).
[CrossRef]

Matui, T.

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

Moisson, E.

Morimoto, Y.

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

Mounier, D.

Okazawa, S.

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

Patorski, K.

Pham, D. S.

D. S. Pham, A. M. Zoubir, “Analysis of multicomponent polynomial phase signals,” IEEE T. Signal Process. 55, 56–65 (2007).
[CrossRef]

Picart, P.

Pokorski, K.

Rajshekhar, G.

Rastogi, P.

Viotti, M. R.

Zoubir, A.

L. Cirillo, A. Zoubir, M. Amin, “Parameter estimation for locally linear fm signals using a time-frequency hough transform,” IEEE T. Signal Process. 56, 4162–4175 (2008).
[CrossRef]

Zoubir, A. M.

D. S. Pham, A. M. Zoubir, “Analysis of multicomponent polynomial phase signals,” IEEE T. Signal Process. 55, 56–65 (2007).
[CrossRef]

Appl. Mech. Mater.

S. Okazawa, M. Fujigaki, Y. Morimoto, T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” Appl. Mech. Mater. 3–4, 223–228 (2005).
[CrossRef]

Appl. Opt.

IEEE T. Signal Process.

S. Barbarossa, “Analysis of multicomponent lfm signals by a combined wigner-hough transform,” IEEE T. Signal Process. 43, 1511–1515 (1995).
[CrossRef]

L. Cirillo, A. Zoubir, M. Amin, “Parameter estimation for locally linear fm signals using a time-frequency hough transform,” IEEE T. Signal Process. 56, 4162–4175 (2008).
[CrossRef]

D. S. Pham, A. M. Zoubir, “Analysis of multicomponent polynomial phase signals,” IEEE T. Signal Process. 55, 56–65 (2007).
[CrossRef]

Opt. Express

Opt. Laser Eng.

R. Kulkarni, P. Rastogi, “Multiple phase estimation in digital holographic interferometry using product cubic phase function,” Opt. Laser Eng. 51, 1168–1172 (2013).
[CrossRef]

G. Rajshekhar, P. Rastogi, “Fringe analysis: Premise and perspectives,” Opt. Laser Eng. 50, iii–x (2012).
[CrossRef]

Opt. Lett.

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Figures (5)

Fig. 1:
Fig. 1:

(a) Δφ1(x, y) (b) Δφ2(x, y) (c) moiré fringe pattern (d) Fourier spectrum of interference field. The phase values are in radians.

Fig. 2:
Fig. 2:

cosine fringes corresponding to the estimated (a) Δφ1(x, y) (b) Δφ2(x, y). Error in estimation of (a) Δφ1(x, y) (b) Δφ2(x, y). All values are in radians.

Fig. 3:
Fig. 3:

Experimental set up: BS1-BS2, beam splitters; BE1-BE3, beam expanders; M1-M5, mirrors; OB1-OB2, object beams; RB, reference beam; IF, beam intensity filter.

Fig. 4:
Fig. 4:

(a) Moiré fringe pattern (b) Fourier spectrum of interference field (c) Estimated Δφ1(x, y) (d) Estimated Δφ2(x, y). The phase values are in radians.

Fig. 5:
Fig. 5:

(a) Sum of phases (b) wrapped form of sum of phases (c) Difference of phases (d) wrapped form of difference of phases. The phase values are in radians.

Tables (1)

Tables Icon

Table 1: Phase estimation error in radians at different amplitude ratio

Equations (10)

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Γ ( x , y ) = A 1 ( x , y ) exp [ j Δ φ 1 ( x , y ) ] + A 2 ( x , y ) exp [ j Δ φ 2 ( x , y ) ] + η ( x , y )
Γ l ( y ) = A l 1 ( y ) exp [ j Δ φ l 1 ( y ) ] + A l 2 ( y ) exp [ j Δ φ l 2 ( y ) ] + η l ( y )
Δ φ l 1 ( y ) = a l 1 + b l 1 y + c l 1 y 2
Δ φ l 2 ( y ) = a l 2 + b l 2 y + c l 2 y 2
PWHT ( θ ) = y = M N L M 1 l = M M Γ l ( y + l ) Γ l * ( y l ) exp ( j 2 ω ( y ; θ ) )
Δ b = π 1.4 W
Δ c = π ( 1.19 M 2 + 1.2 M N L 3 M + 0.4 N L + 17.5 )
a ^ l k = angle { 1 N L y = N L 1 2 N L 1 2 Γ l ( y ) exp [ j ( b ^ l k y + c ^ l k y 2 ) ] }
A ^ l k = | 1 N L y = N L 1 2 N L 1 2 Γ l ( y ) exp [ j ( b ^ l k y + c ^ l k y 2 ) ] |
Γ r ( x , y ) = A 1 ( x , y ) cos [ Δ φ 1 ( x , y ) ] + A 2 ( x , y ) cos [ Δ φ 2 ( x , y ) ] + η r ( x , y )

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