Abstract

The theory of speckle noise in a scanning beam is presented. The general formulas for the calculation of speckle contrast, which apply to any scanning display, are obtained. It is shown that the main requirement for successful speckle suppression in a scanning display is a narrow autocorrelation peak and low sidelobe level in the autocorrelation function of the complex amplitude distribution across a scanning light beam. The simple formulas for speckle contrast for a beam with a narrow autocorrelation function peak were obtained. It was shown that application of a diffractive optical element (DOE) with a Barker code phase shape could use only natural display scanning motion for speckle suppression. DOE with a Barker code phase shape has a small size and may be deposited on the light modulator inside the depth of the focus of the reflected beam area, and therefore, it does not need an additional image plane and complicated relay optics.

© 2008 Optical Society of America

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References

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  1. J. I. Trisnadi, C. B. Carlisle, and R. Monteverde "Overview and applications of grating light valve based optical write engines for high-speed digital imaging," Proc. SPIE 5348, 52-64 (2004).
    [CrossRef]
  2. M. W. Kowarz, J. C. Brazas, and J. G. Phalen, "Conformal grating electromechanical system (GEMS) for high-speed digital light modulation," in the Technical Digest of IEEE 15th International Conference on MEMS (IEEE, 2002), pp. 568-573.
  3. S. K. Yun, J. H. Song, I. J. Yeo, Y. J. Choi, V. I. Yurlov, S. D. An, H. W. Park, H. S. Yang, Y. G. Lee, K. B. Han, I. Shyshkin, A. S. Lapchuk, K. Y. Oh, S. W. Ryu, J. W. Jang, C. S. Park, C. G. Kim, S. K. Kim, E. J. Kim, K. S. Woo, J. S. Yang, E. J. Kim, J. H. Kim, S. H. Byun, S. W. Lee, O. K. Lim, J. P. Cheong, Y. N. Hwang, G. Y. Byun, J. H. Kyoung, S. K. Yoon, J. K. Lee, T. W. Lee, S. K. Hong, Y. S. Hong, D. H. Park, J. C. Kang, W. C. Shin, S. I. Lee, S. K. Oh, B. K. Song, H. Y. Kim, C. M. Koh, Y. H. Ryu, H. K. Lee, and Y. K. Raek, "Spatial optical modulator (SOM): high density diffractive laser projection display," Proc. SPIE 6487, 648710 (2007).
  4. S. K. Yun, "Open hole-based diffractive light modulator," U.S. patent Application 20060077526A1 (13 April 2006).
  5. J. W. Goodman, Statistical Optics (Wiley, 1985).
  6. L. Wang, T. Tschudi, T. Halldorsson, and P. R. Petursson, "Speckle reduction in laser projection systems by diffractive optical elements," Appl. Opt. 37, 1770-1775 (1998).
    [CrossRef]
  7. J. I. Trisnadi, "Speckle contrast reduction in laser projection displays," Proc. SPIE 4657, 131-137 (2002).
    [CrossRef]
  8. J. I. Trisnadi, "Method and apparatus for reducing laser speckle," U.S. patent 6,323,984 (27 November 2001).
  9. J. I. Trisnadi, "Method, apparatus and diffuser for reducing laser speckle," U.S. patent 6,747,781 (8 June 2004).
  10. M. W. Kovarz, F. H. Bonilla, B. E. Kruschwitz, and J. G. Phalen, "Speckle reduction for display system with electromechanical grating," U.S. patent 7,046,446 (16 May 2006).
  11. R. H. Barker, "Group synchronizing of binary digital sequences," in Communication Theory (Butterworth, 1953), pp. 273-287.
  12. I. M. Skolnik, Radar Handbook (McGraw-Hill, 1990), pp. 10-17.
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  14. A. Papoulis, Systems and Transforms with Applications in Optics (Mc-Graw Hill, 1968).

2004 (1)

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde "Overview and applications of grating light valve based optical write engines for high-speed digital imaging," Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

2002 (1)

J. I. Trisnadi, "Speckle contrast reduction in laser projection displays," Proc. SPIE 4657, 131-137 (2002).
[CrossRef]

1998 (1)

Appl. Opt. (1)

Proc. SPIE (2)

J. I. Trisnadi, "Speckle contrast reduction in laser projection displays," Proc. SPIE 4657, 131-137 (2002).
[CrossRef]

J. I. Trisnadi, C. B. Carlisle, and R. Monteverde "Overview and applications of grating light valve based optical write engines for high-speed digital imaging," Proc. SPIE 5348, 52-64 (2004).
[CrossRef]

Other (11)

M. W. Kowarz, J. C. Brazas, and J. G. Phalen, "Conformal grating electromechanical system (GEMS) for high-speed digital light modulation," in the Technical Digest of IEEE 15th International Conference on MEMS (IEEE, 2002), pp. 568-573.

S. K. Yun, J. H. Song, I. J. Yeo, Y. J. Choi, V. I. Yurlov, S. D. An, H. W. Park, H. S. Yang, Y. G. Lee, K. B. Han, I. Shyshkin, A. S. Lapchuk, K. Y. Oh, S. W. Ryu, J. W. Jang, C. S. Park, C. G. Kim, S. K. Kim, E. J. Kim, K. S. Woo, J. S. Yang, E. J. Kim, J. H. Kim, S. H. Byun, S. W. Lee, O. K. Lim, J. P. Cheong, Y. N. Hwang, G. Y. Byun, J. H. Kyoung, S. K. Yoon, J. K. Lee, T. W. Lee, S. K. Hong, Y. S. Hong, D. H. Park, J. C. Kang, W. C. Shin, S. I. Lee, S. K. Oh, B. K. Song, H. Y. Kim, C. M. Koh, Y. H. Ryu, H. K. Lee, and Y. K. Raek, "Spatial optical modulator (SOM): high density diffractive laser projection display," Proc. SPIE 6487, 648710 (2007).

S. K. Yun, "Open hole-based diffractive light modulator," U.S. patent Application 20060077526A1 (13 April 2006).

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. I. Trisnadi, "Method and apparatus for reducing laser speckle," U.S. patent 6,323,984 (27 November 2001).

J. I. Trisnadi, "Method, apparatus and diffuser for reducing laser speckle," U.S. patent 6,747,781 (8 June 2004).

M. W. Kovarz, F. H. Bonilla, B. E. Kruschwitz, and J. G. Phalen, "Speckle reduction for display system with electromechanical grating," U.S. patent 7,046,446 (16 May 2006).

R. H. Barker, "Group synchronizing of binary digital sequences," in Communication Theory (Butterworth, 1953), pp. 273-287.

I. M. Skolnik, Radar Handbook (McGraw-Hill, 1990), pp. 10-17.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

A. Papoulis, Systems and Transforms with Applications in Optics (Mc-Graw Hill, 1968).

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Figures (8)

Fig. 1
Fig. 1

(Color online) Optical diagram of speckle suppression in the projection display by using DOE.

Fig. 2
Fig. 2

(Color online) (a) Cross beam amplitude distribution and point-spread function of the human eye at the screen; (b) graphs of functions Q ( z ) and A ( D z ) / A ( 0 ) .

Fig. 3
Fig. 3

Speckle patterns. Experimental results: (a) stable wide beam without diffuser, (b) scanning beam.

Fig. 4
Fig. 4

(Color online) Calculated speckle parameters versus Barker code length N: (a) speckle contrast ratio versus Barker code length N; (b) degree of speckle contrast decreasing during the use of the Barker code diffuser.

Fig. 5
Fig. 5

(Color online) Fragment of SOM (three pixels).

Fig. 6
Fig. 6

(Color online) Optical diagram of the projection display using SOM technology and the Barker code DOE for speckle suppression.

Fig. 7
Fig. 7

(Color online) Deposition of the Barker code DOE on the outer facet of SOM cover glass.

Fig. 8
Fig. 8

(Color online) Deposition DOE relief on SOM ribbons and SOM bottom.

Equations (29)

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E ( ξ ) = Δ E 0 λ j a b r ( x ) H ( x V t ) e j k ( x 2 / 2 a ) × Sinc { 2 π D ( a b ξ + x ) } d x ,
r ( x ) = β ( x ) exp [ j ψ ( x ) ] ,
ψ ( x ) = { 2 k h ( x ) for   direct   projection   screen ( n 1 ) k h ( x ) for   rear   projection   screen ,
G ( x ) = 1 T T E ( x ) 2 d t = G 0 E 0 2 r ( x 1 ) r * ( x 2 )
× Sinc [ 2 π D ( x + x 1 ) ]  × Sinc [ 2 π D ( x + x 2 ) ]  × e j k [ ( x 1 2 x 2 2 ) / 2 a ] A ( x 1 x 2 ) d x 1 d x 2 ,
A ( x 1 x 2 ) = T H ( x 1 V t ) H * ( x 2 V t ) d t = 1 T V V T / 2 V T / 2 H ( x 1 x 2 + x ) H * ( x ) d x ,
A ( x 1 x 2 ) = δ ( x 1 x 2 ) ,
G ( x ) = G 0 E 0 2 r ( x 1 ) 2 Sinc 2 [ 2 π D ( x + x 1 ) ] d x 1 = A E 0 2 ,
C = σ I I = I 2 I 2 I ,
I 2 = G ( x ) 2 = E 0 2 ( G 0 f ( x 1 x 2 ) A ( x 1 x 2 ) × Sinc [ 2 π D x 1 ] Sinc [ 2 π D x 2 ] × e j k [ ( x 1 2 x 2 2 ) / 2 a ] d x 1 d x 2 ) 2 ,
I 2 = 1 4 E 0 2 R 2 G 0 2 A 2 ( 0 ) D 2 ,
Sinc 2 ( 2 π D x ) d x = D 2 π Sinc 2 ( x ) d x = D 2 ;
I 2 = { E 0 2 G 0 r ( x 1 ) r * ( x 2 ) Sinc [ 2 π D ( x + x 1 ) ] × Sinc [ 2 π D ( x + x 2 ) ] e j k [ ( x 1 2 x 2 2 ) / 2 a ] A ( x 1 x 2 ) d x 1 d x 2 } 2 = E 0 4 G 0 2 F ( x 1 , x 2 , x 3 , x 4 ) A ( x 1 x 2 ) A ( x 3 x 4 ) × Sinc [ 2 π D x 1 ] Sinc [ 2 π D x 2 ] Sinc [ 2 π D x 3 ] Sinc [ 2 π D x 4 ] × e j k [ ( x 1 2 x 2 2 + x 3 2 x 4 2 ) / 2 a ] d x 1 d x 2 d x 3 d x 4 ,
σ r 2 2 = ( r ( x ) 2 ) 2 r ( x ) 2 2 = r ( x ) 2 2 = R 2 ;
F ( x 1 , x 2 , x 3 , x 4 ) = R 2 δ ( x 1 x 2 ) δ ( x 3 x 4 ) [ 1 δ ( x 1 x 3 ) ] + R 2 δ ( x 2 x 3 ) δ ( x 1 x 4 ) × [ 1 δ ( x 2 x 4 ) ] + 2 R 2 δ ( x 1 x 2 ) × δ ( x 3 x 4 ) δ ( x 1 x 3 ) = R 2 [ δ ( x 1 x 2 ) δ ( x 3 x 4 ) + δ ( x 2 x 3 ) δ ( x 1 x 4 ) ] .
δ ( x 1 x 2 ) δ ( x 3 x 4 ) δ ( x 1 x 3 ) = δ ( x 2 x 3 ) δ ( x 1 x 4 ) × δ ( x 2 x 4 ) .
I 2 = In 1 + In 2 ,
In 1 = R 2 E 0 4 G 0 2 δ ( x 1 x 2 ) δ ( x 3 x 4 ) A ( x 1 x 2 ) × A ( x 3 x 4 ) Sinc [ 2 π D x 1 ] Sinc [ 2 π D x 2 ] Sinc [ 2 π D x 3 ] × Sinc [ 2 π D x 4 ] e j k [ ( x 1 2 x 2 2 + x 3 2 x 4 2 ) / 2 a ] d x 1 d x 2 d x 3 d x = R 2 E 0 4 G 0 2 [ A ( 0 ) ] 2 [ Sinc 2 ( 2 π D x 2 ) d x ] 2 = R 2 E 0 4 G 0 2 [ A ( 0 ) D 2 ] 2 = I 2 ;
In 2 = R 2 E 0 4 G 0 2 δ ( x 2 x 3 ) δ ( x 1 x 4 ) A ( x 1 x 2 ) × A ( x 3 x 4 ) Sinc [ 2 π D x 1 ] Sinc [ 2 π D x 2 ] Sinc [ 2 π D x 3 ] × Sinc [ 2 π D x 4 ] e j k [ ( x 1 2 x 2 2 + x 3 2 x 4 2 ) / 2 a ] d x 1 d x 3 d x 3 d x 4 = R 2 E 0 4 G 0 2 A ( x 3 x 4 ) 2 Sinc 2 [ 2 π D x 3 ] × Sinc 2 [ 2 π D x 4 ] d x 3 d x 4 .
C = A ( x 3 x 4 ) 2 Sinc 2 [ 2 π D x 3 ] Sinc 2 [ 2 π D x 4 ] d x 3 d x 4 A 2 ( 0 ) [ Sinc 2 [ 2 π D x ] d x ] 2 .
I n 2 = R 2 E 0 4 G 0 2 d v A ( y ) 2 Sinc 2 [ 2 π D ( y + v ) ] × Sinc 2 [ 2 π D v ] d y = R 2 E 0 4 G 0 2 A ( y ) 2 d y Sinc 2 [ 2 π D ( y + v ) ] × Sinc 2 [ 2 π D v ] d v = R 2 E 0 4 G 0 2 D 2 A ( D v ) 2 Q ( v ) d v ,
Q ( v ) = Sinc 2 [ 2 π ( v + x ) ] Sinc 2 ( 2 π x ) d x , = 1 8 π 2 ( 1 Sinc ( 4 π v ) v 2 ) .
C 2 = 2 | A ( D z ) A ( 0 ) | 2 Q ( z ) d z = 1 4 π 2 | A ( D z ) A ( 0 ) | 2 ( 1 Sinc ( 4 π z ) z 2 ) d z .
C 2 = 2 Q ( 0 ) [ 1 / 2 N 0 ( 1 + 2 N x ) 2 d x + 0 1 / 2 N ( 1 2 N x ) 2 d x ]
= 2 Q ( 0 ) 3 D / T = 2 Q ( 0 ) 3 N 0 ,
C = 2 9 N 0 .
C = 2 9 N .
D = D 0 S S 0 ,
C = C 0 S 0 S ,

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