Abstract

We present a new method for recording off-axis digital Fourier holograms of three-dimensional objects under spatially incoherent illumination. The method is implemented by modifying the optical configuration of triangular interferometer. The recording properties and 3D reconstruction ability of the proposed method are investigated theoretically and experimentally. Multicolor holographic recording and reconstruction of spatially incoherent illuminated object are achieved by using the proposed off-axis Fourier triangular interferometer and monochromatic digital camera. Only three holograms are sufficient to rebuild a color image without zero-order and twin image disturbing effect. Combining with some image fusion skills during reconstruction, the reconstructed color images with satisfied quality are demonstrated.

© 2014 Optical Society of America

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References

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2013 (2)

2012 (5)

2009 (1)

2008 (2)

2007 (2)

1997 (1)

1985 (1)

1966 (1)

1965 (1)

Alfieri, D.

Barada, D.

Brooker, G.

Cochran, G.

Di, J. L.

Faridian, A.

Ferraro, P.

Finizio, A.

Grilli, S.

Hayasaki, Y.

Javidi, B.

Jiang, H. Z.

Kelner, R.

Kiire, T.

Kim, E. S.

Kim, M. K.

Kim, S. G.

Lee, B.

Li, H.

Lohmann, A. W.

Memmolo, P.

Miccio, L.

Naik, D. N.

Nicola, S. D.

Osten, W.

Paturzo, M.

Pedrini, G.

Psaltis, D.

Rosen, J.

Ryeom, J.

Sirat, G.

Sugisaka, J. I.

Yatagai, T.

Zhao, J. L.

Appl. Opt. (2)

J. Display Technol. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Korea (1)

Opt. Express (4)

Opt. Lett. (6)

Other (2)

L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of the ICO Conf. Opt. Instr., London, 305–310 (1961).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005), Chap. 9, pp. 374–375.

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Figures (6)

Fig. 1
Fig. 1

Schematic of an IFTCH system (a) Basic Optical set-up, (b) optical configuration for detail analysis.

Fig. 2
Fig. 2

Schematic of an Incoherent digital Fourier Triangular Color holography (IFTCH) system. L0, L1, L2, L3, lens with focal length f0, f1, f2, f3; M1, M2 mirrors; P1, P2, polarizers; PBS, polarizing beam splitter; D, recording distance.

Fig. 3
Fig. 3

Typical experimental results of IFTCH. (a) Part of a digital hologram captured by IFTCH (b) Reconstructed image of the hologram. (c) Improved reconstructed image. (d) Dependence of SNR on the number of reconstructed images being superposed.

Fig. 4
Fig. 4

Demonstration of 3D imaging capability of IFTCH. (a) Part of the hologram recorded with a die positioned at zs = 50 mm. (b) 2D FT of the hologram. (c) Reconstructed image at the best focus plane of the real image and (d) its twin image, respectively.

Fig. 5
Fig. 5

Variation of CC depends on the shift value along (a) horizontal and (b) vertical direction respectively for Green – Red overlapping. Variation of CC depends on the shift value along (c) horizontal and (d) vertical direction respectively for Green – Red overlapping.

Fig. 6
Fig. 6

Reconstruction results of two color dices by using IFTCH with three different wavelengths illumination. (a) λ1 = 650nm at distance D1 = 66mm. (b) λ2 = 533nm at distance D2 = 68mm. (c) λ3 = 465nm at distance D3 = 70mm. (d) The color fusion of (a), (b) and (c) after optimized by correlation coefficient method.

Equations (11)

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T(x,y; r s , z s )= A s z s exp( j2π z s λ )exp{ jπ λ z s [ (x x s ) 2 + (y y s ) 2 ]} = A s c( r s , z s )Q(1/ z s )L( r s / z s ),
u i (x,y; r s , z s )=T(x,y; r s , z s )Q(1/ f 0 )Q(1/ f 0 ) = c ' (x,y; r s , z s )Q( 1 f s + f 0 )L[ r s f s z s ( f s + f 0 ) ],
u c (x,y; r s , z s )= A s c '' (x,y; r s , z s )Q[ α 2 f s + f 0 ]L[ α r s f s z s ( f s + f 0 ) ]L( r c , r s ),
u cc (x,y; r s , z s )= A s c ''' (x,y; r s , z s )Q[ 1 α 2 ( f s + f 0 ) ]L[ r s f s α z s ( f s + f 0 ) ]L( r cc , r s ),
I(x,y; r s , z s )=| u c + u cc | 2 = A s 2 (| c 1 | 2 +| c 2 | 2 )+{ c 1 c 2 * A s 2 Q[( α 2 1 α 2 ) 1 f s + f 0 ] L[(α 1 α )( r s f s z s ( f s + f 0 ) )] L c ( r , r s )+c.c.},
H(x,y)= I(x,y; r s , z s )d x s d y s d z s .
I(x,y; r s , f 0 )= A s 2 (| c 1 | 2 +| c 2 | 2 )+{ c 1 c 2 * A s 2 L[(α 1 α )( r s f 0 )] L c ( r , r s )+c.c.}.
O(x,y, z r )= F -1 [(H(βx,βy))]*Q(1/ z r ),
z r =± f 2 4 f 1 4 f 1 2 f 2 2 f 0 z s f 0 2 .
N 1 : N 2 : N 3 = λ 1 D 1 : λ 2 D 2 : λ 3 D 3 ,
r= 1 n1 i=1 n [ I v 1 (i)E(I v 1 ) σ(I v 1 ) ][ I v 2 (i)E(I v 2 ) σ(I v 2 ) ] ,

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