Abstract

We propose a technique to implement digital holography by means of a point diffraction interferometer. The device uses a liquid crystal television display and works under partially coherent illumination which makes it useful for 3D microscopy. We present the theory on which the method is based and the obtained results.

© 2005 Optical Society of America

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References

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Appl. Opt.

C. R. Acad. Sci. USSR

V. Linnik, �??Simple interferometer for the investigation of optical systems,�?? C. R. Acad. Sci. USSR, 1, 208- 210 (1933).

Flow Meas. Instrum.

B. Skarman, K. Wozniac, and J. Becker, �??Simultaneous 3D-PIV and temperature measurement using a new CCD based holographic interferometer,�?? Flow Meas. Instrum. 7, 1-6 (1996).
[CrossRef]

Opt. Eng.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, �??Quantitative predictions of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model, �?? Opt. Eng., 40, 2558-2564 (2001).
[CrossRef]

Opt. Lett.

Other

D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 1978).

Supplementary Material (2)

» Media 1: AVI (256 KB)     
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Figures (2)

Fig. 1.
Fig. 1.

Scheme of the optical set up, S is the source, O the object, Lś are convergent lenses, WPś are wave plates, Pś are polarizers and LCTV is the spatial light modulator that acts as phase filter. Π Represents the final plane

Fig. 2.
Fig. 2.

(a) (198 KB) Movie of the refocusing of the object computed from a digital hologram obtained when the CCD plane is -2 cm out of focus. (b) (231 KB) idem a) but the CCD plane is 6 cm out of focus. The size in the object plane is on the lower left part.

Equations (8)

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H ( u ) = 1 + δ ( u ) [ e i 2 π n N 1 ] .
A n ( x ) = o ( x ) e i Ψ ( x ) * h ( x ) = o ( x ) e i Ψ ( x ) + [ e i 2 π n N 1 ] K .
C = n = 0 N 1 ( A n A n * ) cos ( 2 π n N ) ; S = n = 0 N 1 ( A n A n * ) sin ( 2 π n N )
C = N K 2 + N K o ( x ) cos ( Ψ ( x ) + μ ) ; S = N K o ( x ) sin ( Ψ ( x ) + μ )
Ψ ( x ) = t g 1 ( S C C 0 ) μ .
O ( x ) = exp ( i k d ) i d λ exp [ i k 2 d x 2 ] 𝓕 [ exp ( i k 2 d x 2 ) O ( x ) ] ,
O ( x ) = exp ( i k d ) 1 [ exp ( i k d λ 2 2 ν x 2 ) [ O ( x ) ] ] .
O ( m Δ ) = exp ( i k d ) N 2 m , l = 0 N 1 exp [ i 2 π N ( m m 1 ) l ] exp [ i π λ d N 2 Δ 2 l 2 ] O ( m Δ )

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