Abstract

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.

© 2012 Optical Society of America

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References

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2010 (1)

2009 (1)

2008 (1)

2000 (1)

Hettwer, J. Kranz, and J. Schwider, Opt. Eng. 39, 960 (2000).
[CrossRef]

1999 (1)

J. A. Quiroga, D. Crespo, and E. Bernabeu, Opt. Eng. 38, 974 (1999).
[CrossRef]

1997 (1)

1996 (1)

M. D. Pritt, IEEE Trans. Geosci. Remote Sens. 34, 728 (1996).
[CrossRef]

1990 (1)

1985 (1)

O. Kafri and I. Glatt, Opt. Eng. 24, 944 (1985).

1984 (1)

1983 (1)

Bar-Ziv, E.

Bernabeu, E.

J. A. Quiroga, D. Crespo, and E. Bernabeu, Opt. Eng. 38, 974 (1999).
[CrossRef]

Carpio, M.

Chen, Y.

Crespo, D.

J. A. Quiroga, D. Crespo, and E. Bernabeu, Opt. Eng. 38, 974 (1999).
[CrossRef]

Glatt, I.

O. Kafri and I. Glatt, Opt. Eng. 24, 944 (1985).

He, A.

Hettwer,

Hettwer, J. Kranz, and J. Schwider, Opt. Eng. 39, 960 (2000).
[CrossRef]

Kafri, O.

Keren, E.

Kranz, J.

Hettwer, J. Kranz, and J. Schwider, Opt. Eng. 39, 960 (2000).
[CrossRef]

Kwon, Y.

Martínez-García, A.

Meneses-Fabian, C.

Montes-Perez, A.

Morales, A.

Pritt, M. D.

M. D. Pritt, IEEE Trans. Geosci. Remote Sens. 34, 728 (1996).
[CrossRef]

Quiroga, J. A.

J. A. Quiroga, D. Crespo, and E. Bernabeu, Opt. Eng. 38, 974 (1999).
[CrossRef]

Rayas-Álvarez, J. A.

Rodriguez-Vera, R.

Rodriguez-Zurita, G.

Rodríguez-Zurita, G.

Schreiber, H.

Schwider, J.

Hettwer, J. Kranz, and J. Schwider, Opt. Eng. 39, 960 (2000).
[CrossRef]

H. Schreiber and J. Schwider, Appl. Opt. 36, 5321 (1997).
[CrossRef]

Servin, M.

Sgulim, S.

Song, Y.

Toto-Arellano, N.-I.

Vázquez-Castillo, J. F.

Zhao, Z.

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Figures (4)

Fig. 1.
Fig. 1.

Optical configuration of the triple grating interferometry.

Fig. 2.
Fig. 2.

Frequency spectrum distribution.

Fig. 3.
Fig. 3.

Moiré patterns and phase distribution.

Fig. 4.
Fig. 4.

The final phase distribution.

Equations (13)

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

u1(x,y)exp[ikφ(x,y)],
I0=2a02a14[1+cos(4πdysinα2+kP1ξ+η2πb1d)],I1=2a04a12[1+cos(4πdysinα2+kP1+η2πb1d)],I2=2a02a14[1+cos(4πdysinα2+kP1+ξ+η2πb1d)],I3=2a02a14[1+cos(4πdysinα2+kP1ξη2πb1d)],I4=2a04a12[1+cos(4πdysinα2+kP1η2πb1d)],I5=2a02a14[1+cos(4πdysinα2+kP1+ξη2πb1d)].
kP1=2πd[φ(x,y)xΔ1cosα2φ(x,y)y(Δ1+2Δ2)sinα2].
ξ=kP22πλd2(Δ1cosαβ2+2Δ2sinα2sinβ2),η=kP3πλΔ1d2,
I0=I(x,y)[1+V(x,y)cos(ψξ+η)],I2=I(x,y)[1+V(x,y)cos(ψ+ξ+η)],I3=I(x,y)[1+V(x,y)cos(ψξη)],I5=I(x,y)[1+V(x,y)cos(ψ+ξη)],
ψ=4πdysinα2+φ(x,y)x2πΔ1dcosα22πb1d.
ψ=tan1[(I0I2+I3+I5I0I2I3+I5)tanξ],
ψ=tan1[(I0I2+I3I5I0I2I3+I5)tanη].
Ii=0,2,3,5=I(x,y)(1+κi)[1+V(x,y)cos(ψi+ωi)],
ψ=tan1[(I0I2+I3+I5I0I2I3+I5)tan(ξ+σ)].
Δψκ=14sinηsin2ξ[(κ0+κ2)sin(ψ+η)+(κ3κ5)sin(ψη)(κ0+κ5)sin(ξη)+(κ2+κ3)sin(ξ+η)].
Δψω=14sinηsin2ξ[(ω0+ω2)cos(ψ+η2)+(ω3ω5)cos(ψη2)+(ω0+ω5)cos(ξη2)+(ω2ω3)cos(ξ+η2)].
Δψσ=σsin2ψ.

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