Abstract

A method for introducing phase steps in an interferogram based on translating a ruling at the input plane of a double aperture common-path interferometer is presented. The setup is built on a 4f optical system consisting of two apertures at the input plane and a Ronchi ruling in the Fourier plane, where at each aperture a Ronchi ruling is also placed. By filtering at the Fourier plane a single diffraction order of the spectrum from the rulings in the object plane, we demonstrate that a phase step is generated when one of the rulings in the input plane is translated. The principal advantage of this proposal lies in improving the resolution in the phase step. We develop a theoretical model and show experimental results.

© 2013 Optical Society of America

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References

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2013 (1)

2012 (1)

2011 (1)

2009 (1)

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-del-C. Encarnacion-Gutierrez, and N. I. Toto-Arellano, Opt. Commun. 282, 3063 (2009).
[CrossRef]

2008 (2)

2006 (1)

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizon, Opt. Commun. 264, 13 (2006).
[CrossRef]

2004 (1)

1994 (1)

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

1982 (1)

1966 (1)

Arrizon, V.

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizon, Opt. Commun. 264, 13 (2006).
[CrossRef]

Arrizón, V.

Diao, M.

Encarnacion-Gutierrez, M.-del-C.

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-del-C. Encarnacion-Gutierrez, and N. I. Toto-Arellano, Opt. Commun. 282, 3063 (2009).
[CrossRef]

Farrell, C. T.

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

Goodman, J. W.

Hao, B.

Itoh, K.

Ma, H.

Meneses-Fabian, C.

Player, M. A.

C. T. Farrell and M. A. Player, Meas. Sci. Technol. 5, 648 (1994).
[CrossRef]

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Sánchez-De-La-Llave, D.

Shan, M.

Toto-Arellano, N. I.

Vázquez-Castillo, J.

Vázquez-Castillo, J. F.

Weaver, C. S.

Zhang, Y.

Zhong, Z.

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Figures (4)

Fig. 1.
Fig. 1.

Schema of a DACPI: O, phase object; R, gratings; L, lenses.

Fig. 2.
Fig. 2.

Experimental interferograms for J=10, with phase step of π/5 achieved by ruling displacements of 10 μm.

Fig. 3.
Fig. 3.

Experimental measurement and theoretical prediction of αor in comparison to theoretical αd.

Fig. 4.
Fig. 4.

Phase extraction: (a) wrapped and (b) unwrapped phase.

Equations (20)

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tA(x,y)=wo(x,y)Ro(x,y)+wr(x,y)Rr(x,y),
ws(x,y)=w(x,yys)As(x,y)exp[iϕs(x,y)],
Rs(x,y)=xwxpksinc(xwxpk)ei2πkxsxpei2πkxpx,
t˜A(μ,ν)=w˜o(μ,ν)R˜o(μ,ν)+w˜r(μ,ν)R˜r(μ,ν),
R˜s(μ,ν)=xwxpksinc(xwxpk)ei2πkxsxpδ(μkxp,ν).
t˜A(μ,ν)=k{cokcw˜o(μkxp,ν)+crkcw˜r(μkxp,ν)},
cskc=xwxpsinc(xwxpk)ei2πkxsxp;
f˜I(μ,ν)=rect(xpμk),
t˜Ak(μ,ν)=cokcw˜o(μkxp,ν)+crkcw˜r(μkxp,ν).
t˜Ak(μ,ν)=t˜A(μ,ν)f˜I(μ,ν)R˜I(μ,ννd),
R˜I(μ,ννd)=vwvpnsinc(vwvpn)ei2πnvdvpei2πnλfvpν.
tk(x,y)=tAk(x,y)RI(x,y),
tAk(x,y)=[cokcwo(x,y)+crkcwr(x,y)]ei2πkxpx,
RI(x,y)=vwvpnsinc(vwvpn)ei2πnvdvpδ(x,yλfvpn).
tk(x,y)=vwvpnsinc(vwvpn)ei2πnvdvptAk(x,yλfvpn),
tk,n(x,y)=dnctAk(x,yy0n),
dnc=vwvpsinc(vwvpn)ei2πnvdvp.
tk,n=(cokcdn+1cAoeiϕo+crkcdncAreiϕr)ei2πkxpx.
I=c12[d12Ao2+d02Ar2+2d0d1AoArcos(ϕαorαd)],
αor=2πxoxrxp;αd=2πvdvp.

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