Diffuser with pseudorandom phase sequence

Yoshikazu Nakayama; Makoto Kato

doi:10.1364/JOSA.69.001367

Journal of the Optical Society of America
Vol. 69,
Issue 10,
pp. 1367-1372
(1979)
•https://doi.org/10.1364/JOSA.69.001367

Diffuser with pseudorandom phase sequence

Yoshikazu Nakayama and Makoto Kato

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Yoshikazu Nakayama and Makoto Kato, "Diffuser with pseudorandom phase sequence," J. Opt. Soc. Am. 69, 1367-1372 (1979)

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Abstract

A theoretical analysis of the power spectra of diffusers with a series of pseudorandom phase sequences is presented. General equations describing three typical cases of power spectra are derived by making use of the constraints assumed. Profiles of the power spectra showed good agreement with the results of numerical computation using the fast-Fourier-transform algorithm. The images of the diffusers through a double-diffraction optical system were also evaluated by computer simulation. The advantage of pseudorandom phase sequences over random phase sequences is discussed from the viewpoint of signal-to-noise ratio.

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Type of sequence	Phase sequence
4 - L - PRPS	0, $\frac{1}{2} π$ , 0, $\frac{1}{2} π$ , π, $\frac{3}{2} π$ , 0, $\frac{3}{2} π$
3 - L - PRPS	$\frac{2}{3} π$ , 0, $\frac{4}{3} π$ , $\frac{2}{3} π$ , 0, $\frac{2}{3} π, \frac{4}{3} π, \frac{2}{3} π$
6 - L - CPRPS	$\frac{2}{3} π, \frac{1}{3} π$ , 0, $\frac{5}{3} π, \frac{4}{3} π$ , π, $\frac{2}{3} π, \frac{1}{3} π$

	1	2	3	M
0	0	$\frac{1}{2}$	0	$\frac{1 + {(- 1)}^{M}}{4}$
1	$\frac{1}{2}$	0	$\frac{1}{2}$	$\frac{1 - {(- 1)}^{M}}{4}$
2	0	$\frac{1}{2}$	0	$\frac{1 + {(- 1)}^{M}}{4}$
3	$\frac{1}{2}$	0	$\frac{1}{2}$	$\frac{1 - {(- 1)}^{M}}{4}$

	1	2	3	M
0	0	$\frac{1}{2}$	$\frac{1}{4}$	$\sum_{k = 1}^{[M / 2]} 2^{- 2 k + 1} - \sum_{k = 1}^{[M - 1 / 2]} 2^{- 2 k}$
1	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{3}{8}$	$\sum_{k = 0}^{[M - 1 / 2]} 2^{- 2 k - 1} - \sum_{k = 1}^{[M / 2]} 2^{- 2 k}$
2	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{3}{8}$	$\sum_{k = 0}^{[M - 1 / 2]} 2^{- 2 k - 1} - \sum_{k = 1}^{[M / 2]} 2^{- 2 k}$

Type of sequence	Phase sequence
4 - L - PRPS	0, $\frac{1}{2} π$ , 0, $\frac{1}{2} π$ , π, $\frac{3}{2} π$ , 0, $\frac{3}{2} π$
3 - L - PRPS	$\frac{2}{3} π$ , 0, $\frac{4}{3} π$ , $\frac{2}{3} π$ , 0, $\frac{2}{3} π, \frac{4}{3} π, \frac{2}{3} π$
6 - L - CPRPS	$\frac{2}{3} π, \frac{1}{3} π$ , 0, $\frac{5}{3} π, \frac{4}{3} π$ , π, $\frac{2}{3} π, \frac{1}{3} π$

	1	2	3	M
0	0	$\frac{1}{2}$	0	$\frac{1 + {(- 1)}^{M}}{4}$
1	$\frac{1}{2}$	0	$\frac{1}{2}$	$\frac{1 - {(- 1)}^{M}}{4}$
2	0	$\frac{1}{2}$	0	$\frac{1 + {(- 1)}^{M}}{4}$
3	$\frac{1}{2}$	0	$\frac{1}{2}$	$\frac{1 - {(- 1)}^{M}}{4}$

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Equations (29)

Journal of the Optical Society of America