Abstract

We propose using a two-level (1 and +1 as variables) orthogonal array (OA) to generate a binary phase diffuser for speckle reduction in laser projection displays. Compared with the Hadamard matrix, the diffuser generated from OA is more flexible. The speckle contrast ratio (CR) when introducing the binary phase diffuser at an intermediate image plane within the projector is calculated, and the minimum speckle CR can be achieved by finite step change of the diffuser patterns. With Kronecker algebra, the two-dimensional diffuser can also be replaced by two one-dimensional diffusers with the same function, and it can be implemented into the laser projector electronically and easily.

© 2010 Optical Society of America

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References

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  1. K. E. Jachimowicz, “Projection display technologies: laser projection displays,” in M.A.Karim, ed., Electro-Optical Displays (Marcel Dekker, 1992), pp. 255–265.
  2. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).
  3. J. I. Trisnadi, “Speckle contrast reduction in laser projection displays,” Proc. SPIE 4657, 131–137 (2002).
    [CrossRef]
  4. J. I. Trisnadi, “Hadamard speckle contrast reduction,” Opt. Lett. 29, 11–13 (2004).
    [CrossRef] [PubMed]
  5. F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
    [CrossRef]
  6. B. Dingel and S. Kawata, “Speckle-free image in a laser-diode microscope by using the optical feedback effect,” Opt. Lett. 18, 549–551 (1993).
    [CrossRef] [PubMed]
  7. C. Saloma, S. Kawata, and S. Minamiet, “Laser-diode microscope that generates weakly speckled images,” Opt. Lett. 15, 203–205 (1990).
    [CrossRef] [PubMed]
  8. L. Wang, T. Tschudi, T. Halldorsson, and P. R. Pétursson, “Speckle reduction in laser projection systems by diffractive optical elements,” Appl. Opt. 37, 1770–1775 (1998).
    [CrossRef]
  9. L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
    [CrossRef]
  10. K. J. Horadam, Hadamard Matrices and Their Applications (Princeton U. Press, 2006).
  11. A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics (Springer, 1999).
  12. S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
    [CrossRef]
  13. A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
    [CrossRef]

2008 (1)

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

2006 (1)

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

2004 (1)

2003 (1)

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

2002 (1)

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

2000 (1)

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

1998 (1)

1993 (1)

1990 (1)

Akio, F.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Boeddinghaus, M.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

Daisuke, I.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Dingel, B.

Elbert, A.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

Gehner, A.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

Gruber, H.

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

Halldorsson, T.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

L. Wang, T. Tschudi, T. Halldorsson, and P. R. Pétursson, “Speckle reduction in laser projection systems by diffractive optical elements,” Appl. Opt. 37, 1770–1775 (1998).
[CrossRef]

Hedayat, A. S.

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics (Springer, 1999).

Horadam, K. J.

K. J. Horadam, Hadamard Matrices and Their Applications (Princeton U. Press, 2006).

Jachimowicz, K. E.

K. E. Jachimowicz, “Projection display technologies: laser projection displays,” in M.A.Karim, ed., Electro-Optical Displays (Marcel Dekker, 1992), pp. 255–265.

Kallmeyer, F.

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

Kawata, S.

Kazuya, W.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Knobbe, J.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

Komenda, O.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

Koshi, T.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Krüger, S.

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

Minamiet, S.

Neumann, H.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

Norihiro, O.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Pétursson, P.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

Pétursson, P. R.

Saloma, C.

Satoshi, I.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Shoji, H.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Sloane, N. J. A.

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics (Springer, 1999).

Steinhoff, A.

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

Stufken, J.

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics (Springer, 1999).

Trisnadi, J. I.

J. I. Trisnadi, “Hadamard speckle contrast reduction,” Opt. Lett. 29, 11–13 (2004).
[CrossRef] [PubMed]

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

Tschudi, T.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

L. Wang, T. Tschudi, T. Halldorsson, and P. R. Pétursson, “Speckle reduction in laser projection systems by diffractive optical elements,” Appl. Opt. 37, 1770–1775 (1998).
[CrossRef]

Wang, L.

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

L. Wang, T. Tschudi, T. Halldorsson, and P. R. Pétursson, “Speckle reduction in laser projection systems by diffractive optical elements,” Appl. Opt. 37, 1770–1775 (1998).
[CrossRef]

Wernicke, G.

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

Wildenhain, M.

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

Yoshifumi, S.

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (1)

L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T. Halldorsson, and P. Pétursson, “Speckle reduction in laser projections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (4)

S. Krüger, A. Steinhoff, F. Kallmeyer, G. Wernicke, and H. Gruber, “Spatial light modulator system as dynamic diffractive element,” Proc. SPIE 5003, 142–149 (2003).
[CrossRef]

A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, “MEMS analog light processing—an enabling technology for adaptive optical phase control,” Proc. SPIE 6113, 61130K (2006).
[CrossRef]

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

F. Akio, O. Norihiro, S. Yoshifumi, I. Daisuke, W. Kazuya, I. Satoshi, T. Koshi, and H. Shoji, “Effective speckle reduction in laser projection displays,” Proc. SPIE 6911, 69110T (2008).
[CrossRef]

Other (4)

K. E. Jachimowicz, “Projection display technologies: laser projection displays,” in M.A.Karim, ed., Electro-Optical Displays (Marcel Dekker, 1992), pp. 255–265.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

K. J. Horadam, Hadamard Matrices and Their Applications (Princeton U. Press, 2006).

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics (Springer, 1999).

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Figures (3)

Fig. 1
Fig. 1

Picking up the mth row of OA C to generate a u × v phase mask.

Fig. 2
Fig. 2

Example of using two 1D diffusers to replace a 2D diffuser.

Fig. 3
Fig. 3

Digital micromirror device-based laser projector using two OAs to generate the 1D diffusers, referring to the optical system in [3, 4].

Equations (16)

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R = σ I ¯ = I 2 ¯ I ¯ 2 I ¯ ,
R = M + K 1 K M ,
m = 1 M P k ( m ) P l ( m ) * = β δ k , l ,
I = β k = 1 K | A k | 2 ,
B T B = N 1 I N 2 ,
I = m = 1 N 1 I m = m = 1 N 1 k = 1 N 2 l = 1 N 2 A k A l * P k ( m ) P l ( m ) * = k = 1 N 2 l = 1 N 2 A k A l * m = 1 N 1 P k ( m ) P l ( m ) * ,
m = 1 N 1 P k ( m ) P l ( m ) * = N 1 δ k , l .
I = N 1 k = 1 N 2 | A k | 2 .
I ¯ = N 1 k = 1 N 2 | A k | 2 ¯ = N 1 N 2 J A , I 2 ¯ = ( N 1 k = 1 N 2 | A k | 2 ) 2 ¯ = N 1 2 k = 1 N 2 | A k | 4 + k = 1 , l = 1 N 2 | A k | 2 | A l | 2 | k l ¯ = N 1 2 [ 2 N 2 J A 2 + ( N 2 2 N 2 ) J A 2 ] = N 1 2 ( N 2 2 + N 2 ) J A 2 ,
R = 1 N 2 .
D = B C = [ B 1 , 1 C 1 , 1 B 1 , 1 C 1 , N 4 B 1 , j C 1 , y B 1 , N 2 C 1 , 1 B 1 , N 2 C 1 , N 4 B i , 1 C x , 1 B i , 1 C x , N 4 B i , j C x , y B i , N 2 C x , 1 B i , N 2 C x , N 4 B N 1 , 1 C N 3 , 1 B N 1 , 1 C N 3 , N 4 B N 1 , j C N 3 , y B N 1 , N 2 C N 3 , 1 B N 1 , N 2 C N 3 , N 4 ] ,
( B C ) T = B T C T , ( B T C T ) ( B C ) = B T B C T C ,
D T D = ( B C ) T ( B C ) = ( B T C T ) ( B C ) = B T B C T C = N 1 I N 2 N 3 I N 4 = N 1 N 3 I N 2 N 4 ,
D m = [ B i , 1 C x , 1 B i , 1 C x , y B i , 1 C x , N 4 B i , j C x , 1 B i , j C x , y B i , j C x , N 4 B i , N 2 C x , 1 B i , N 2 C x , y B i , N 2 C x , N 4 ] = [ B i , 1 B i , j B i , N 2 ] [ C x , 1 C x , y C x , N 4 ] = B i C x ,
D T D = B T B C T C = B B T C C T = ( B C ) ( B C ) T = D D T ,
B T B = B B T , C T C = C C T .

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