Abstract

The condition for a diffuser to produce the maximum speckle contrast reduction with the minimum number of distinct phase patterns is derived. A binary realization of this optimum diffuser is obtained by mapping the rows or columns of a Hadamard matrix to the phase patterns. The method is experimentally verified in the Grating Light Valve laser projection display.

© 2004 Optical Society of America

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References

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  1. J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).
  2. J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).
  3. J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.
  4. S. Lowenthal and D. Joyeux, J. Opt. Soc. Am. 61, 847 (1971).
  5. L. Wang, T. Tschudi, T. Halldorsson, and P. R. Petursson, Appl. Opt. 37, 1770 (1998).
    [CrossRef]
  6. A. S. Hedayat, N. J. A. Sloan, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, New York, 1999).
    [CrossRef]
  7. D. T. Amm and R. W. Corrigan, Proc. SPIE 3634, 71 (1999).
    [CrossRef]
  8. J. I. Trisnadi, Proc. SPIE 4657, 131 (2002).
    [CrossRef]

2002 (1)

J. I. Trisnadi, Proc. SPIE 4657, 131 (2002).
[CrossRef]

1999 (1)

D. T. Amm and R. W. Corrigan, Proc. SPIE 3634, 71 (1999).
[CrossRef]

1998 (1)

1976 (1)

1971 (1)

1962 (1)

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Amm, D. T.

D. T. Amm and R. W. Corrigan, Proc. SPIE 3634, 71 (1999).
[CrossRef]

Corrigan, R. W.

D. T. Amm and R. W. Corrigan, Proc. SPIE 3634, 71 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

Gordon, E. I.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Halldorsson, T.

Hedayat, A. S.

A. S. Hedayat, N. J. A. Sloan, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, New York, 1999).
[CrossRef]

Joyeux, D.

Lowenthal, S.

Petursson, P. R.

Rigden, J. D.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Sloan, N. J. A.

A. S. Hedayat, N. J. A. Sloan, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, New York, 1999).
[CrossRef]

Stufken, J.

A. S. Hedayat, N. J. A. Sloan, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, New York, 1999).
[CrossRef]

Trisnadi, J. I.

J. I. Trisnadi, Proc. SPIE 4657, 131 (2002).
[CrossRef]

Tschudi, T.

Wang, L.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Proc. IRE (1)

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Proc. SPIE (2)

D. T. Amm and R. W. Corrigan, Proc. SPIE 3634, 71 (1999).
[CrossRef]

J. I. Trisnadi, Proc. SPIE 4657, 131 (2002).
[CrossRef]

Other (2)

A. S. Hedayat, N. J. A. Sloan, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, New York, 1999).
[CrossRef]

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

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Figures (5)

Fig. 1
Fig. 1

(a) Detector resolution spot partitioned into M=N1N2 cells, (b) phase pattern with M phase cells superimposed upon the resolution spot.

Fig. 2
Fig. 2

Mapping from the ath row of H to the ath phase pattern.

Fig. 3
Fig. 3

Batik pattern of Sylvester type H16.

Fig. 4
Fig. 4

(a) Sixteen batik phase patterns from Sylvester type H16, (b) the effect of negating the sixth column of H16.

Fig. 5
Fig. 5

Images and samples of intensity fluctuation of (a) the original speckle and (b) the reduced speckle.

Equations (9)

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

I0=i=1N1j=1N2Eij2.
I=1Aa=1Ai=1N1j=1N2hijaEij2,
a=1Ahija*hkla=Aδikδjl,
I=1Aa=1Ai=1N1j=1N2k=1N1l=1N2hija*Eij*hklaEkl=i=1N1j=1N2Eij2.
a=1Mhija*hkla=Mδikδjl.
HTMHM=MIM,
H1=1,  H2M=HMHMHM-HM.
hija=Ha,i-1N2+j,
a=1Mhijahkla=a=1MHa,i-1N2+jHa,k-1N2+l=Mδikδjl.

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