Abstract

In digital holography (DH) the numerical reconstruction of the whole wavefront allows one to extract the wrapped phase map mod, 2π. It can occur that the reconstructed wrapped phase map in the image plane is undersampled because of the limited pixel size in that plane. In such a case the phase distribution cannot be retrieved correctly by the usual unwrapping procedures. We show that the use of the digital lateral-shearing interferometry approach in DH provides the correct reconstruction of the phase map in the image plane, even in extreme cases where the phase profile changes very rapidly. We demonstrate the effectiveness of the method in a particular case where the profile of a highly curved silicon microelectromechanical system membrane has to be reconstructed.

© 2007 Optical Society of America

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References

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2006 (8)

2005 (2)

2004 (1)

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, and G. Pierattini, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

2003 (2)

2002 (2)

J. H. Massig, Opt. Lett. 27, 2179 (2002).
[CrossRef]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

2001 (2)

1987 (1)

Appl. Opt. (4)

Appl. Phys. Lett. (2)

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, and G. Pierattini, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. Kühn, E. Cuche, Y. Emery, T. Colomb, F. Charrière, F. Montfort, M. Botkine, N. Aspert, and C. Depeursinge, Proc. SPIE 6188, 618804 (2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) DH experimental setup. BS, beam splitter; MO, microscope objective; S, sample. (b) scanning electron microscope picture of the MEMS.

Fig. 2
Fig. 2

Wrapped phase maps of the MEMS from the original hologram with (a) 1024 × 1024   pixels and (b) 1024 × 1024   pixels padded to 2048 × 2048   pixels . (c) and (d) Unwrapped phase along the x direction for the original and the padded hologram, respectively. (e) Incorrect surface profile due to the US as obtained from the wrapped phase map (a). (f) Correct retrieved surface profile as obtained from wrapped phase map (b) Profile obtained by the padding procedure.

Fig. 3
Fig. 3

(a) Derivate of the phase map of the MEMS (shearogram). (b) Derivate of the phase map of the MEMS without the linear term. (c) Profile of the phase of the MEMS along a central row of the phase map. (d) Phase map of the MEMS as obtained by the DH–LSI approach.

Equations (5)

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y 1 2 R x 2 + ( θ 0 + θ 1 ) x ,
y ( x ) = λ 4 π ϕ ( x , y ) .
x max = R [ N Δ ξ 4 d ( θ 0 + θ 1 ) ] .
Δ ϕ x = ϕ ( x , y ) ϕ ( x s x , y ) .
Δ ϕ x s x ϕ x x .

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