Abstract

We describe and experimentally demonstrate a phase shifting method based on the lateral displacement of a grating implemented with a twisted-nematic liquid-crystal spatial light modulator. This method allows an accurate implementation of the phase shift without requiring moving parts. The technique is implemented in a Mach–Zehnder digital holography setup in which the field transmitted by the sample object freely propagates to the hologram plane.

© 2009 Optical Society of America

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References

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2006 (1)

2004 (4)

2002 (3)

2000 (2)

L. Xu, J. Miao, and A. K. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610-612(2000).
[CrossRef]

1999 (3)

1998 (1)

1997 (1)

1994 (2)

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Arrizón, V.

Asundi, A. K.

L. Xu, J. Miao, and A. K. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Badizadegan, K.

Bevilacqua, F.

Cuche, E.

Dasari, R. R.

Deflores, L. P.

Depeursinge, C.

Devaney, A. J.

Dubois, F.

Feld, M. S.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Guo, C.

Guo, P.

Iwai, H.

Javidi, B.

Jüptner, W.

Kawai, H.

Kim, D.

Kischel, P.

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771-778 (2002).
[CrossRef]

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Legros, J.-C.

Liao, J.

Marquet, P.

Meneses-Fabian, C.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Miao, J.

L. Xu, J. Miao, and A. K. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Minetti, C.

Monnom, O.

Ohzu, H.

Popescu, G.

Rodriguez-Zurita, G.

Sánchez-de-la-Llave, D.

Schnars, U.

Tajahuerce, E.

Takaki, Y.

Vaughan, J. C.

Wang, H.

Xu, L.

L. Xu, J. Miao, and A. K. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Yourassowsky, C.

Zhang, L.

Zhang, T.

Zhu, Y.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771-778 (2002).
[CrossRef]

L. Xu, J. Miao, and A. K. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

Sov. Phys. Tech. Phys. (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

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Figures (8)

Fig. 1
Fig. 1

Optical setup for implementation of the two-step phase shift method.

Fig. 2
Fig. 2

Several periods of the gratings loaded to the SLM to generate phase shifts of (a) 0 and (b)  π / 2 .

Fig. 3
Fig. 3

Interference patterns obtained when both the object and the reference beams are plane waves. These patterns were obtained when the loaded gratings were those depicted in Fig. 2.

Fig. 4
Fig. 4

Partial views of holograms (a)  I c ( x , y ) and (b)  I s ( x , y ) obtained with the array of microlenses employed as the sample object.

Fig. 5
Fig. 5

Modulus of the computed Fourier spectrum of the function I L ( x , y ) = I c ( x , y ) + i I s ( x , y ) obtained for the array of microlenses.

Fig. 6
Fig. 6

Wrapped phase of the reconstructed array of microlenses.

Fig. 7
Fig. 7

Three-dimensional representation of the unwrapped phase of the reconstructed array of microlenses.

Fig. 8
Fig. 8

Normalized real values of holograms (a)  I c ( x , y ) and (b)  I s ( x , y ) for the bleached bar test pattern, and (c) corresponding to the three-dimensional image of the reconstructed unwrapped phase of this sample object.

Equations (10)

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g ( x ) = n = c n exp ( i 2 π n p x ) ,
g 1 ( x , y ) = c 1 b ( x , y ) exp ( i 2 π x / p ) ,
g ( x Δ x ) = n = c n exp ( i 2 π n p Δ x ) exp ( i 2 π n p x ) .
g 2 ( x , y ) = exp ( i 2 π Δ x / p ) g 1 ( x , y ) .
o ( x , y ) = a ( x , y ) exp [ i ϕ ( x , y ) ] .
r ( x , y ) = a r ( x , y ) exp { i [ 2 π ( u 0 x + v 0 y ) + δ ] } ,
I ( x , y ) = a r 2 ( x , y ) + a 2 ( x , y ) + 2 a r ( x , y ) a ( x , y ) cos [ ϕ ( x , y ) 2 π ( u 0 x + v 0 y ) δ ] .
I c ( x , y ) = a ( x , y ) cos [ ϕ ( x , y ) 2 π ( u 0 x + v 0 y ) ] ,
I s ( x , y ) = a ( x , y ) sin [ ϕ ( x , y ) 2 π ( u 0 x + v 0 y ) ] .
o ( x , y ) = [ I c ( x , y ) + i I s ( x , y ) ] exp [ i 2 π ( u 0 x + v 0 y ) ] .

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