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Full-color computer-generated holograms using 3-D Fourier spectra

Yusuke Sando, Masahide Itoh, and Toyohiko Yatagai

Open Access Open Access

Abstract

A new method for synthesizing a full-color computer-generated hologram (CGH) of real-existing objects has been proposed. In this method, the synthesizing process of CGHs and the adjustments of magnifications for each wavelength are considered based on parabolic sampling of three-dimensional (3-D) Fourier spectra. Our method requires only one-dimensional (1-D) azimuth scanning of objects, does not require any approximations in the synthesizing process, and can perform efficient magnification adjustments required for color reconstruction. Experimental results have been presented to verify the principle and validity of this method.

©2004 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. A virtual optical system for 3-D objects.

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Fig. 2.
Fig. 2. Schematics of the principle of 3-D CST. (a) Orthogonal projection in the real space and (b) a sectional plane in the 3-D Fourier space obtained from a projection image.

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Fig. 3.
Fig. 3. Paraboloid of revolution. (a) Components identical to objects waves and (b) intersections between the paraboloid of revolution and a sectional Fourier plane.

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Fig. 4.
Fig. 4. Extractive area on the u-v plane from (a) one projection image and (b) a series of projection images.

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Fig. 5.
Fig. 5. A recording optical system.

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Fig. 6.
Fig. 6. Adjustments of magnifications.

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Fig. 7.
Fig. 7. Color projection images at θ=17°.

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Fig. 8.
Fig. 8. Numerical reconstructed images.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

g ( x 0 , y 0 ) = ∭ O ( x , y , z ) exp { − i 2 π λ [ x 0 x + y 0 y f − ( x 0 2 + y 0 2 ) z 2 f 2 ] } dxdydz ,
g ( u , v ) = ∭ O ( x , y , z ) exp { − i 2 π [ u x + v y − λ 2 ( u 2 + v 2 ) z ] } dxdydz
= { ∭ O ( x , y , z ) exp [ − i 2 π ( u x + vy + w z ) ] dxdydz } ∣ w = − λ ( u 2 + v 2 ) ⁄ 2
= 퓕 [ O ( x , y , z ) ] ∣ w = − λ ( u 2 + v 2 ) ⁄ 2 ,
w cos ⁡ θ + u sin ⁡ θ = 0
w = − λ 2 ( u 2 + v 2 ) .
( u − tan ⁡ θ λ ) 2 + v 2 = ( tan ⁡ θ λ ) 2 , w = − u tan ⁡ θ .
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