Abstract

A new method for construction of complex pseudorandom phase sequence diffusers for diffraction-limited holography is presented. The irradiance fluctuation in the reconstructed image can be suppressed by modifying the size of the sampling area associated with the specific phase terms. The advantage of this diffuser is discussed in terms of the power spectrum and the signal to noise ratio.

© 1980 Optical Society of America

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References

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  1. M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” Appl. Opt. 14, 1093–1099 (1975).
    [CrossRef] [PubMed]
  2. Y. Torii, “Synthesis of Deterministic Phase Codes for Phase Shifter in Holography,” Opt. Commun. 24, 157–180 (1978).
    [CrossRef]
  3. Y. Nakayama and M. Kato, “Diffusor with psoudorandom phase sequence,” J. Opt. Soc. Am. 69, 1367–1372 (1979).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 13.

1979 (1)

1978 (1)

Y. Torii, “Synthesis of Deterministic Phase Codes for Phase Shifter in Holography,” Opt. Commun. 24, 157–180 (1978).
[CrossRef]

1975 (1)

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

Y. Torii, “Synthesis of Deterministic Phase Codes for Phase Shifter in Holography,” Opt. Commun. 24, 157–180 (1978).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 13.

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Figures (5)

FIG. 1
FIG. 1

Double diffraction optical system. An object at the plane P1 is imaged through an aperture of the size DH onto the plane P2.

FIG. 2
FIG. 2

Schematic model of the one-dimensional WMD. A phase sequence {ϕN, ϕN+2,⋯, ϕo. ⋯, ϕN−2,. ϕN} corresponds to the original PRPS and another sequence {ϕN+1, ϕN+3, ⋯, ϕ−1, ϕ1, ⋯. ϕN−3, ϕN−1} is the remainder in the CPRPS.

FIG. 3
FIG. 3

Normalized forms of the power spectra; (a) the six-level WMD (S = 6) and (b) the eight-level WMD (S = 8). M indicates the degree of modulation. The WMD reduces to the CPRD when M = 0, and also to the PRD when M = 1. The size of the holograms ξ is calculated in the case of P = 25 μ, λ = 488 nm, and f = 70 mm.

FIG. 4
FIG. 4

Calculated signal to noise ratio versus hologram size for six-level WMD’s with five values of M. Other parameters are also the same as in Fig. 3.

FIG. 5
FIG. 5

Calculated signal to noise ratio versus hologram size for eight-level WMD’s with five values of M. Other parameters are also the same as in Fig. 3.

Tables (2)

Tables Icon

TABLE I Examples of the PRPS

Tables Icon

TABLE II Sizes of the main lobes of the calculated power spectra. Other parameters are the same as in Fig. 2

Equations (35)

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g ( x ) = n = N / 2 N / 2 rect ( x 2 n P ( 1 + M ) P ) exp ( i ϕ 2 n ) + n = N / 2 N / 2 rect ( x ( 2 n + 1 ) P ( 1 M ) P ) exp ( i ϕ 2 n + 1 ) ,
M = ( L m L s ) / 2 P
E [ I ( ξ ) ] = P 2 ( ( N + 1 ) ( 1 + M ) 2 sinc 2 ( ( 1 + M ) P ξ λ f ) + N ( 1 M ) 2 sinc 2 ( ( 1 M ) P ξ λ f ) + K = 1 N { ( N K + 1 ) [ h = 0 S / 2 1 P r ( 2 h , 2 K ) cos ( 4 h S π ) ] × cos ( 4 π K P ξ ) ( 1 + M ) 2 sinc 2 ( ( 1 + M ) P ξ λ f ) + ( N K ) [ h = 0 S / 2 1 P r ( 2 h , 2 K ) cos ( 4 h S π ) ] × cos ( 4 π K P ξ ) ( 1 M ) 2 sinc 2 ( ( 1 M ) P ξ λ f ) + 2 ( N K + 1 ) [ h = 0 S / 2 1 P r ( 2 h + 1 , 2 K 1 ) cos ( 2 h + 1 S 2 π ) ] × cos ( 2 π ( 2 K 1 ) P ξ λ f ) [ sinc 2 ( P ξ λ f ) M 2 sinc 2 ( M P ξ λ f ) ] } ) ,
P r ( 2 h , 2 K ) = ( 1 / 2 ) [ P r ( 2 h 2 , 2 K 2 ) + P r ( 2 h + 2 , 2 K 2 ) ] ,
P r ( 2 h , 2 K ) = ( 1 / 2 ) [ P r ( 2 h 1 , 2 K 1 ) + P r ( 2 h + 1 , 2 K 1 ) ] ,
P r ( 2 h + 1 , 2 K 1 ) = ( 1 / 2 ) [ P r ( 2 h , 2 K 2 ) + P r ( 2 h + 2 , 2 K 2 ) ] ,
P r ( 2 h + 1 , 1 ) = { 1 / 2 2 h + 1 = 1 or S 1 0 otherwise ,
P r ( 2 h , 2 ) = { 1 / 2 2 h = 2 or S 2 0 otherwise .
ϕ 2 n ϕ 2 n 2 K = 2 π 2 h / S ,
ϕ 2 n + 1 ϕ 2 n + 1 2 K = 2 π 2 h / S ,
ϕ 2 n ϕ 2 n ( 2 K 1 ) = 2 π ( 2 h + 1 ) / S .
ϕ 2 n ϕ 2 n 1 = 2 π / S or 2 π ( S 1 ) / S ,
ϕ 2 n ϕ 2 n 2 = 2 π 2 / S or 2 π ( S 2 ) / S .
2 3 π
4 3 π
2 3 π
2 3 π
4 3 π
2 3
1 2 π
3 2 π
3 2 π
1 2 π
2 3 π
1 3 π
5 3 π
4 3 π
2 3 π
1 3 π
1 4 π
1 2 π
1 4 π
7 4 π
3 2 π
5 4 π