Abstract

This paper investigates, through simulation and experiment, the behavior of two dimensional foci arrays generated via phase-only holography where an iterative algorithm was used to produce the kinoforms. Specifically, we studied how aliasing of the signal on a spatial light modulator affects the quality of the foci array as the density and size of the array are varied. This study provides a reference for applications where it is important to understand how the fidelity and overall quality of the foci array changes as the number of foci increases and as the spacing between foci decreases.

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2009 (1)

2008 (1)

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (3)

2004 (1)

2002 (1)

2001 (1)

1999 (1)

1997 (1)

1995 (1)

1970 (1)

1969 (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. and Dev. 13, 150–155 (1969).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Amako, J.

Carberry, D. M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Chang, B.

Chang, Y.

Chiang, S.

Chou, L.

Clark, R. L.

Cole, D. G.

Cooper, J.

Courtial, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” N. J. Phys. 7, 117 (2005).
[CrossRef]

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12, 5475–5480 (2004).
[CrossRef] [PubMed]

Crossland, W. A.

Curtis, J. E.

di Leonardo, R.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Gibson, G.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

K. D. Wulff, D. G. Cole, R. L. Clark, R. Di Leonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14, 4169–4174 (2006).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (Roberts and Company Publishers, 2005).

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. and Dev. 13, 150–155 (1969).
[CrossRef]

Hojo, J.

Ianni, F.

Jackson, J. C.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Jericho, M. H.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. and Dev. 13, 150–155 (1969).
[CrossRef]

Jordan, P.

Kohler, C.

Kreuzer, H. J.

Laczik, Z. J.

Leach, J.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

K. D. Wulff, D. G. Cole, R. L. Clark, R. Di Leonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14, 4169–4174 (2006).
[CrossRef] [PubMed]

Lee, W. H.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. and Dev. 13, 150–155 (1969).
[CrossRef]

Love, G. D.

Mears, R. J.

Meinertzhagen, I. A.

Miles, M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Miura, H.

Osten, W

Padgett, M.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12, 5475–5480 (2004).
[CrossRef] [PubMed]

Padgett, M. J.

Robert, D.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

Ruocco, G.

Schmitz, C. H. J.

Schwab, X.

Sinclair, G.

Sonehara, T.

Spatz, J. P.

Takaki, Y.

Tan, K. L.

Whyte, G.

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” N. J. Phys. 7, 117 (2005).
[CrossRef]

Wulff, K. D.

Xu, W.

Appl. Opt. (6)

IBM J. Res. and Dev. (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. and Dev. 13, 150–155 (1969).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

G. Gibson, D. M. Carberry, G. Whyte, J. Leach, J. Courtial, J. C. Jackson, D. Robert, M. Miles, and M. Padgett, “Holographic assembly workstation for optical manipulation,” J. Opt. A, Pure Appl. Opt. 10, 044009 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

N. J. Phys. (1)

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” N. J. Phys. 7, 117 (2005).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (Roberts and Company Publishers, 2005).

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Figures (7)

Fig. 1
Fig. 1

The holography apparatus is constructed with a 4f system. L 1 is the Fourier transform lens, L 2 is a second lens, f 1 = 300 mm, f 2 = 500 mm. Inset shows our definitions of maximum spatial frequency, fmax , and inter-foci spacing, dx , within the microscope focal plane (MFP).

Fig. 2
Fig. 2

Root mean square residual difference between original kinoforms with N o r i g = 100 P and N o r i g = 100 ( P 1 ) where P are integers between 1 and 21. Here Nfoci = 100 and dx is varied between 5δx and 30δx .

Fig. 3
Fig. 3

Left panel: A 100 × 100 pixel section of original kinoform with N o r i g = 2000 . Right panel: Same section of the original kinoform aliased to N a l _ p i x = 500 pixels . One pixel in the right panel has the same physical dimension as 16 pixels in the left panel. Both white grids in the upper right corner of the panel display boxes that are 4 × 4 original pixels in size.

Fig. 4
Fig. 4

Simulated relative standard deviation of foci intensities (rel. σ) versus increasing number of foci (Nfoci ) for kinoforms with varying numbers of aliased pixels (Nal_pix ) and dx = 10δx . The legend indicates Nal_pix for each curve. Inset shows the effect of aliasing on rel. σ for Nfoci = 400.

Fig. 5
Fig. 5

Simulated relative standard deviation of foci intensities (rel. σ) plotted as a function of the density of foci (ρfoci ) for kinoforms with varying numbers of aliased pixels (Nal_pix ) and for fmax (maximum spatial frequency) = 30δx . The legend indicates Nal_pix for each curve. Inset shows the effects of aliasing on pattern quality for a single ρfoci = 0.071 foci μm−2.

Fig. 6
Fig. 6

Experimentally measured relative standard deviation of foci intensities (rel. σ) plotted as a function of the number of foci (Nfoci ) for Nal_pix (number of aliased pixels) = 200 and 1080; dx = 10δx . Inset shows the effect of aliasing on rel. σ for Nfoci = 400. Error bars represent standard deviation; n = 20.

Fig. 7
Fig. 7

Experimentally measured relative standard deviation of foci intensities (rel. σ) for varying foci density (ρfoci ); Nal_pix (number of aliased pixels) = 200 and 1080; fmax (maximum spatial frequency) = 30δx . Inset shows the effect of aliasing on rel. σ for ρfoci = 0.071 foci μm−2. Error bars represent standard deviation; n = 20.

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