Abstract

The principle of unconventional holography, called coherence holography, is proposed and experimentally demonstrated for the first time. An object recorded in a hologram is reconstructed as the three-dimensional distribution of a complex spatial coherence function, rather than as the complex amplitude distribution of the optical field itself that usually represents the reconstructed image in conventional holography. A simple optical geometry for the direct visualization of the reconstructed coherence image is proposed, along with the experimental results validating the proposed principle. Coherence holography is shown to be applicable to optical coherence tomography and profilometry.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

J. Rosen and M. Takeda, �??Longitudinal spatial coherence applied for surface profilometry,�?? Appl. Opt. 39, 4107-4111 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

P. J. Peters, �??Incoherent holography with mercury light source,�?? Appl. Phys. Lett. 8, 209-210 (1966).
[CrossRef]

J. Opt. Soc. Am. (7)

J. Opt. Soc. Am. A (3)

Nature (1)

D. Gabor, �??A new microscopic principle,�?? Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Acta (1)

W. H. Carter and E. Wolf, �??Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,�?? Opt. Acta 28, 227-244 (1981).
[CrossRef]

Opt. Lett. (1)

Optical Instruments and Techniques 1961 (1)

L. Mertz and N. O. Young, �??Fresnel transformations of images,�?? in Proceedings of Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall, London 1961) p.305.

Other (2)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), Chap. 10.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985), Chap. 5.

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Figures (4)

Fig. 1.
Fig. 1.

Optical fields reconstructed from a conventional hologram with a phase-conjugated reference beam.

Fig. 2.
Fig. 2.

Direct visualization of a coherence image reconstructed from a coherence hologram. The coherence image is directly observable as the contrast and the phase of a fringe pattern.

Fig. 3.
Fig. 3.

Special geometry for spatial coherence tomography and profilometry. A coherence hologram is placed in the front focal plane of a lens. Seen through the lens from the side of the interferometer, the hologram looks like an infinitely large hologram located at infinity.

Fig. 4.
Fig. 4.

(a) Object; (b) Image reconstructed from phase-only hologram; (c) Modulus of spatial coherence function; (d) Coherence hologram representing spatially incoherent source distribution; (e) Coherence image visualized as a fringe contrast.

Equations (11)

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u r Q r R = I A ( r S ) u R * ( r S ) exp ( i k r Q r S ) r Q r S d r S
= I A ( r S ) exp [ i k ( r Q r S r R r S ) ] r Q r S r R r S d r S ,
J r Q r R = I I ( r S ) exp [ i k ( r Q r S r R r S ) ] r Q r S r R r S d r S ,
J r Q r R = J r S r S exp [ i k ( r Q r S r R r S ) ] r Q r S r R r S d r S d r S ,
J r Q r R = μ ( Δ r S ) { I I ( r S ) exp [ i k ( r Q r S ( r R Δ r S ) r S ) ] r Q r S ( r R Δ r S ) r S d r S } d ( Δ r S ) .
J r Q r R = μ ( Δ r S ) u ( r Q , r R Δ r S ) d ( Δ r S ) ,
I r Δz I S ( r S ) { 1 + cos [ k ( Δ z z ) r r S 2 z + α ( Δ z ) ] } d r S
= [ I S ( r S ) d r S ] { 1 + μ r Δz cos [ α ( Δz ) β r Δz ] } ,
μ r Δz = μ ( r , Δz ) exp [ i β ( r , Δz ) ]
= I S ( r S ) exp { i k Δz r r S 2 z 2 } d r S I S ( r S ) d r S .
μ ( r , Δz ) = I S ( r ̂ S ) exp { i k Δz tan 2 θ r r S Max r ̂ S 2 } d r ̂ S I S ( r ̂ S ) d r ̂ S ,

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