Abstract

We propose a fast calculation method for diffraction to nonplanar surfaces using the fast-Fourier transform (FFT) algorithm. In this method, the diffracted wavefront on a cylindrical surface is expressed as a convolution between the point response function and the spatial distribution of objects wherein the convolution is calculated using FFT. The principle of the fast calculation and the simulation results are presented.

© 2005 Optical Society of America

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References

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Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

N. Yoshikawa, M. Itoh, and T. Yatagai, �??Interpolation of reconstructed image in Fourier transform computer-generated hologram,�?? Opt. Commun. 119, 33�??40 (1995).
[CrossRef]

Opt. Express (1)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the geometrical relation between the object and observation surfaces.

Fig. 2.
Fig. 2.

Amplitude distribution of the Fourier spectrum of PRF.

Fig. 3.
Fig. 3.

The interference patterns on the cylindrical surface.

Fig. 4.
Fig. 4.

Object distribution on the cylindrical surface.

Fig. 5.
Fig. 5.

Top views of the geometrical relations (a) between the object surface and the CGH surface and (b) between the CGH surface and the observation plane.

Fig. 6.
Fig. 6.

The reconstructed images in the sectional planes of (a) z=1 cm where “x” is in focus and (b) z=-1 cm where “O” is in focus.

Equations (9)

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g R ( ϕ , y 0 ) = C f r ( θ , y ) exp ( ikL ) L d θ dy ,
L = [ R 2 + r 2 2 Rr cos ( θ ϕ ) + ( y y 0 ) 2 ] 1 2 ,
h ( θ , y ) = exp [ ik ( R 2 + r 2 2 Rr cos θ + y 2 ) 1 2 ] ( R 2 + r 2 2 Rr cos θ + y 2 ) 1 2 .
g R ( ϕ , y 0 ) = C f r ( θ , y ) h ( θ ϕ , y y 0 ) d θ d y
= C f r * h ( ϕ , y 0 ) ,
ν θ ( θ , y ) = 1 2 π h ( θ , y ) θ ,
ν θ max = k 𝓛 2 π , W θ = k 𝓛 π ,
ν y ( θ , y ) = 1 2 π h ( θ , y ) y .
ν y max = k Δ y 4 π 1 [ ( R r ) 2 + ( Δ y 2 ) 2 ] 1 2 , W y = k Δ y 2 π 1 [ ( R r ) 2 + ( Δ y 2 ) 2 ] 1 2 ,

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