Abstract

We present a novel technique of variable tomographic scanning capable of reconstructing tomographic images of an object volume along any arbitrarily tilted plane. The method is based on wavelength scanning digital interference holography, using a series of holograms generated with a range of scanned wavelengths. From each hologram, the object field is reconstructed in a number of selected tilted planes. The desired tomographic images are then reconstructed from the numerical superposition of the object fields. Thus the tomographic images can be generated along variable planes without the need for physically repeating the scanning and recording processes. Experimental results are presented to verify the proposed concept.

© 2005 Optical Society of America

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References

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Appl. Opt.

Opt. Express

Opt. Lett.

Science

D.Huang, E.A.Swanson, C.P.Lin, J.S.Schuman,W.G.Stinson, W.Chang, M.R.Hee, T.Flotte, K. Gregory, C.A.Puliafito, and J.G.Fujimoto, �??Optical coherence tomography,�?? Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other

J. W. Goodman. Introduction to Fourier Optics. McGraw-Hill, 1996.

Supplementary Material (4)

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Figures (4)

Fig. 1.
Fig. 1.

Reconstruction of the wavefield on a tilted xo - yo plane for a given wave distribution on the x-y plane (hologram plane). See text for details.

Fig. 2.
Fig. 2.

Optical apparatus used in the digital interference holography experiments. The Ls are various lenses; BS is a beamsplitter; AP is an aperture and REF is a mirror. The CCD camera captures the interference pattern at the plane S.

Fig. 3.
Fig. 3.

Contour images of a dime in a 2.25 × 2.25 × 0.6 mm3 volume: (a) (QuickTime, 1.40MB) The animation shows xo-yo cross sections with normal tomographic scanning by the Fresnel diffraction formula; (b) (QuickTime, 0.98MB) The animation shows xo-yo cross sections with tilted tomographic scanning by the proposed algorithm; (c) and (d) are flat views of the yo-z cross sections from (a) and (b).

Fig. 4.
Fig. 4.

Contour images of a chick embryo in a 2.26 × 2.26 mm2 area: (a) (QuickTime, 1.12MB) The animation shows normal tomographic scanning with the Fresnel diffraction formula; (b) (QuickTime, 1.12MB) The animation shows tilted tomographic scanning with the proposed algorithm.

Equations (9)

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E ( r ) A ( r p ) exp ( ik r r p ) d 3 r p ,
E ( r ) k A ( r p ) exp ( ik r r p ) d 3 r p A ( r p ) δ ( r r p ) d 3 r p
A ( r ) ,
E x o y o z o = i E 0 λ o x y exp [ ikr x y x o y o ] r x y x o y o χ x y x o y o dxdy ,
r = ( z o y o sin θ ) 2 + ( x x o ) 2 + ( y y o cos θ ) 2 ,
E ξ η z o = i E 0 λ r o exp [ i k ( r o z o y o sin θ r o ) ]
× o x y exp [ i k 2 z o ( x 2 + y 2 ) ] exp [ i 2 π ( ξ x + η y ) ] dxdy ,
ξ = x o λ r o , and η = y o cos θ λ r o .
Δ x o = λ z N Δ x , Δ y o = λ z N Δ y cos θ

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