Abstract

Speckle is a major source of noise in holographic projection. Time averaging of multiple holograms may be used to reduce speckle contrast, but multiple holograms must be calculated per each frame, costing in computational power. We show that a single hologram may be used to generate a fully speckle-free reconstruction, by cyclic shifting and time averaging. We demonstrate the concept experimentally, and discuss its application for high-rate holographic projection systems.

© 2009 Optical Society of America

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2008

2007

2005

J. E. Curtis, C. H. Schmitz, and J. P. Spatz, "Symmetry dependence of holograms for optical trapping," Opt. Lett. 30, 2086-2088 (2005).
[CrossRef] [PubMed]

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

2004

2001

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

2000

1997

1996

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

1995

1990

1988

1976

1972

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Jena) 35, 237-246 (1972).

Aagedal, H.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

Abe, Y.

Amako, J.

Arrizón, V.

Beth, T.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

Bonas, I. G.

Bryngdahl, O.

Charpak, S.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Chu, H. H.

Clark, R. L.

Cole, D. G.

Cotter, L. K.

Crossland, W. A.

Croucher, J.

Curtis, J. E.

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

DeSars, V.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Di Leonardo, R.

DiGregorio, D. A.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Dillon, R. J.

Drabik, T. J.

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

Emiliani, V.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Franklin, R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Jena) 35, 237-246 (1972).

Goodman, J. W.

Grier, D. G.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

Handerek, V. A.

Handschy, M. A.

Henshall, G.

Holmes, M. J.

Ianni, F.

Ito, T.

Jenness, N. J.

Johannes, M. S.

Kazo, Y.

Kunugi, T.

Lutz, C.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Manolis, I. G.

Masuda, N.

Miura, H.

Miura, J.

O'Connor, D. H.

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

Otis, T. S.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Padgett, M. J.

Parker, T. R.

Redmond, M. M.

Robertson, B.

Ruocco, G.

Sarkisov, D. V.

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

Satake, S.-i.

Sato, K.

Sato, Y.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Jena) 35, 237-246 (1972).

Schmid, M.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

Schmitz, C. H.

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

Shimobaba, T.

Shoham, S.

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

Sonehara, T.

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

Spatz, J. P.

Stace, C.

Takenouchi, M.

Tan, K. L.

Teiwes, S.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

Testorf, M.

Trisnadi, J. I.

Wakabayashi, H.

Wang, S. S.-H.

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

Warr, S. T.

White, H. J.

Wilkinson, T. D.

Woolley, R. A.

Wulff, K. D.

Wyrowski, F.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

F. Wyrowski and O. Bryngdahl, "Iterative Fourier-transform algorithm applied to computer holography," J. Opt. Soc. Am. A 5, 1058-1065 (1988).
[CrossRef]

Appl. Opt.

J. Lightwave Technol.

J. Mod. Opt.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409 - 1421 (1996).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nat. Meth.

C. Lutz, T. S. Otis, V. DeSars, S. Charpak, D. A. DiGregorio, and V. Emiliani, "Holographic photolysis of caged neurotransmitters," Nat. Meth. 5, 821-827 (2008).
[CrossRef]

Nat. Methods

S. Shoham, D. H. O'Connor, D. V. Sarkisov, and S. S.-H. Wang, "Rapid neurotransmitter uncaging in spatially defined patterns," Nat. Methods 2, 837-843 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Jena)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Jena) 35, 237-246 (1972).

Rev. Sci. Instrum.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72,1810-1816 (2001).
[CrossRef]

Other

E. Buckley, "Holographic Laser Projection Technology," in SID 08 Digest, (Society for Information Display, 2008), 1074-1079.

H. Aagedal, J. Turunen, and M. Schmid, "Paraxial Beam Splitting and Shaping," in Diffractive Optics for Industrial and Commercial Applications, J. Turunen and F. Wyrowski, eds., (Wiley-VCH 1997).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert & Company, 2005).

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed., (McGraw-Hill, 1986).

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Figures (6)

Fig. 1.
Fig. 1.

The intensity at the point (u,v) is approximated by the sum of nearby sampling points contained within a square. In this case, the choice of c=4 results in the square containing a total of 16 sampling points. The contribution of 4 PSFs is shown as an example.

Fig. 2.
Fig. 2.

An illustration of the different terms contributing to a simple 3-pixel reconstruction.

Fig. 3.
Fig. 3.

Ilustration of two different shifts on the (g,h) plane. The red circle marks a distinct area of the hologram, which serves as a reference point.

Fig. 4.
Fig. 4.

Different choices of shifts, illustrated in the (g, h) plane.

Fig. 5.
Fig. 5.

Outline of the experimental system. BE – Beam expander, PBS – Polarizing Beam Splitter, Lenses L1 and L2 form the de-magnifying telescope, S is a rectangular slit that blocks the zero order, Lenses L3 and L4 are microscope objectives.

Fig. 6.
Fig. 6.

Comparison of speckle averaging methods. Only a small part of the reconstruction is shown, containing a 10-pixel diameter circular patch. Scale bars are 10 μm. Figure 6(a) shows a typical result of the 8-iteration GSW that yields high uniformity. Figure 6(b) shows the system PSF. In Fig. 6(c) we can see severe speckle, when no averaging is performed. In Fig. 6(d) we can see the effect of conventional time averaging, produced by sequentially displaying 16 independently-calculated holograms. In Fig. 6(e) we see that shift-averaging with 16 random shifts of a single calculated hologram produces similiar results. Finally, a sequence of 16 deterministic shifts chosen according to Eq. (22) (with c = 4) eliminates the speckle and produces a smooth, uniformly-illuminated spot.

Equations (25)

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

F m n = exp ( i ϕ m n ) ; m , n = 1,2 , . . , M .
f k l = I k l · exp ( i ψ k l ) = m , n = 0 M 1 F m n exp [ 2 π i ( m k M + n l M ) ] .
t ( x , y ) = rect ( x , y ) { [ m , n = 1 M exp ( i ϕ m n ) δ ( x m d , y n d ) ] rect ( x d , y d ) } ,
E ( u , υ ) = F ( t ( x , y ) ) = k = l = f k l S k l ( u , υ ) ,
S k l ( u , υ ) = sinc ( u k , υ l ) · sinc ( u M , υ M ) ,
sinc ( x ) = sin ( π x ) π x
E ( u , υ ) k = 1 c l = 1 c f k l · S k l ( u , υ ) .
I ( u , υ ) = E ( u , υ ) 2 = k = 1 c l = 1 c r = 1 c s = 1 c f k l f r s * S k l ( u , υ ) S r s ( u , υ ) .
I ( u , υ ) = k = 1 c l = 1 c I k l S k l 2 ( u , υ ) + k = 1 c l = 1 c r = 1 k 1 s = 1 l 1 2 I k l I r s cos ( ψ k l ψ r s ) S k l ( u , υ ) S r s ( u , υ ) .
I coherent = ( k = 1 c l = 1 c I k l S k l ) 2 .
I ( u , υ ) = 1 N a = 1 N I a ( u , υ ) = 1 N a = 1 N k = 1 c l = 1 c I k l a S k l 2 ( u , υ )
+ 1 N a = 1 N k = 1 c l = 1 c r = 1 k 1 s = 1 l 1 2 I k l a I r s a cos ( ψ k l a ψ r s a ) S k l ( u , υ ) S r s ( u , υ ) ,
F m n a = F ( m g a ) , ( n h a ) ; a = 1,2 , , N ,
F m n = F ( m + M ) , n = F m , ( n + M ) .
f k l a = f k l exp [ 2 π i ( k · g a M + l · h a M ) ] .
ψ k l a ψ r s a = ( ψ k l ψ r s ) + 2 π ( k r ) g a + ( l s ) h a M .
I ( u , υ ) = 1 N a = 1 N k = 1 c l = 1 c r = 1 c s = 1 c f k l a f r s a S k l ( u , υ ) S r s ( u , υ )
= k = 1 c l = 1 c r = 1 c s = 1 c S k l ( u , υ ) S r s ( u , υ ) [ 1 N a = 1 N f k l a f r s a * ] .
1 N a = 1 N f k l a f r s a * = δ k r δ l s I k l .
1 N a = 1 N f k l a f r s a * = 1 N f k l f r s * a = 1 N exp { 2 π i M [ ( k r ) g a + ( l s ) h a ] } .
1 n k = 1 n exp ( 2 π i k l n ) = { 1 l = 0 0 l = 1,2 , n 1 ,
N = c , g a = M c , h a = 0 ,
1 N a = 1 N f k l a f r s a * = 1 c f k l f r s * a = 1 c exp [ 2 π i c ( k r ) ] = f k l f r s * δ k r .
N = c 2 , g a b = a M c , h a b = b M c ,
1 c 2 a = 1 c b = 1 c f k l a b f r s a b * = 1 c 2 f k l f r s * a = 1 c b = 1 c exp [ 2 π i ( k r ) a c ] exp [ 2 π i ( l s ) b c ] = I k l δ k r δ l s .

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