Abstract

Clustered speckle patterns are a particular type of speckles that appear when a coherently illuminated diffuser is imaged through a multiple aperture pupil mask attached to a lens. The cluster formation is the result of the complex speckle modulations of the multiple interferences produced by the apertures. In this paper, a three-dimensional analytical approach to simulate cluster speckles everywhere after the lens is presented. This approach has the possibility of including multiple aperture masks at the lens and at the diffuser, in contrast to previous works which were also limited to the description of the patterns only at the image plane. This model contributes to the development of tailor made speckle patterns that can be used in diverse optical applications, including those lying in the focus region. The approach is validated under different conditions by comparing experimental results with simulations on a statistical basis. Some aspects of possible uses of these clusters are briefly revised, such as optical trapping, manipulation and metrology.

© 2012 OSA

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    [CrossRef]
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2012 (1)

2011 (1)

2010 (5)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (4)

L. Ángel, M. Tebaldi, and N. Bolognini, “Multiple rotation assessment through isothetic fringes in speckle photography,” Appl. Opt.46, 2676–2682 (2007).
[CrossRef] [PubMed]

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

2006 (2)

T.M. Grzegorczyk, B.A. Kemp, and J.A. Kong, Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field, J. Opt. Soc. Am. A.23, 2324–2330 (2006).
[CrossRef]

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, and M. Takeda, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express14, 120–127 (2006).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

M. Tebaldi, A. Lencina, and N. Bolognini, “Analysis and applications of the speckle patterns registered in a photorefractive BTO crystal,” Opt. Commun.202, 257–270 (2002).
[CrossRef]

2000 (3)

G. Grynberg, P. Horak, and C. Mennerat-Robilliard, “Spatial diffusion of atoms cooled in a speckle field,” Europhys. Lett.49, 424–430 (2000).
[CrossRef]

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

1999 (1)

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

1995 (1)

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun.114, 203–210 (1995).
[CrossRef]

1990 (1)

1979 (1)

1976 (1)

1971 (1)

J. N. Butters and J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E4, 277–279 (1971).
[CrossRef]

1962 (1)

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. TheoryIT-8, 194–195 (1962).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, (Dover Publications, 1965) p. 297.

Ahufinger, V.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Allard, B.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Ángel, L.

L. Ángel, M. Tebaldi, and N. Bolognini, “Multiple rotation assessment through isothetic fringes in speckle photography,” Appl. Opt.46, 2676–2682 (2007).
[CrossRef] [PubMed]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

Ángel Toro, L.

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

Arizaga, R.

Asakura, T.

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun.114, 203–210 (1995).
[CrossRef]

Aspect, A.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Boiron, D.

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Bolognini, N.

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

L. Ángel, M. Tebaldi, and N. Bolognini, “Multiple rotation assessment through isothetic fringes in speckle photography,” Appl. Opt.46, 2676–2682 (2007).
[CrossRef] [PubMed]

A. Lencina, P. Vaveliuk, M. Tebaldi, and N. Bolognini, “Modulated speckle simulations based on the random-walk model,” Opt. Lett.28, 1748–1750 (2003).
[CrossRef] [PubMed]

M. Tebaldi, A. Lencina, and N. Bolognini, “Analysis and applications of the speckle patterns registered in a photorefractive BTO crystal,” Opt. Commun.202, 257–270 (2002).
[CrossRef]

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

Bourdel, T.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Bouyer, P.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Brantut, J. P.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Brito, J. M.

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

Butters, J. N.

J. N. Butters and J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E4, 277–279 (1971).
[CrossRef]

Chian, F.P.

Chiang, F. P.

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).

Damski, B.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Delande, D.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

Fienup, J. R.

Fournier, J. M.

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Françon, M.

M. Françon, Laser Speckle and Applications in Optics (Academic Press, 1979).

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: theory and applications (Roberts&Company, 2007).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), Ch 3.

Grynberg, G.

G. Grynberg, P. Horak, and C. Mennerat-Robilliard, “Spatial diffusion of atoms cooled in a speckle field,” Europhys. Lett.49, 424–430 (2000).
[CrossRef]

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Grzegorczyk, T.M.

T.M. Grzegorczyk, B.A. Kemp, and J.A. Kong, Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field, J. Opt. Soc. Am. A.23, 2324–2330 (2006).
[CrossRef]

Guidoni, L.

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Guizar-Sicairos, M.

Horak, P.

G. Grynberg, P. Horak, and C. Mennerat-Robilliard, “Spatial diffusion of atoms cooled in a speckle field,” Europhys. Lett.49, 424–430 (2000).
[CrossRef]

Ishijima, R.

Izdebskaya, Y. V.

Izdebskaya, Ya. V.

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

Kelly, D. P.

Kemp, B.A.

T.M. Grzegorczyk, B.A. Kemp, and J.A. Kong, Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field, J. Opt. Soc. Am. A.23, 2324–2330 (2006).
[CrossRef]

Khetan, R. P.

Khetan, R.P.

Kirchner, M.

Kivshar, Y. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

Kong, J.A.

T.M. Grzegorczyk, B.A. Kemp, and J.A. Kong, Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field, J. Opt. Soc. Am. A.23, 2324–2330 (2006).
[CrossRef]

Krolikowski, W.

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

Kuhn, R. C.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Leendertz, J. A.

J. N. Butters and J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E4, 277–279 (1971).
[CrossRef]

Lencina, A.

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

A. Lencina, P. Vaveliuk, M. Tebaldi, and N. Bolognini, “Modulated speckle simulations based on the random-walk model,” Opt. Lett.28, 1748–1750 (2003).
[CrossRef] [PubMed]

M. Tebaldi, A. Lencina, and N. Bolognini, “Analysis and applications of the speckle patterns registered in a photorefractive BTO crystal,” Opt. Commun.202, 257–270 (2002).
[CrossRef]

Leushacke, L.

Lewenstein, M.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Li, D.

Li, Y.

Mennerat-Robilliard, C.

G. Grynberg, P. Horak, and C. Mennerat-Robilliard, “Spatial diffusion of atoms cooled in a speckle field,” Europhys. Lett.49, 424–430 (2000).
[CrossRef]

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Miniatura, C.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Miyamoto, Y.

Mosso, F.

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

Müller, C. A.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Pezzé, L.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Plisson, T.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Rabal, H. J.

Reed, I. S.

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. TheoryIT-8, 194–195 (1962).
[CrossRef]

Robert-de-Saint-Vincent, M.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Rode, A. V.

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

Salomon, C.

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Sanchez-Palencia, L.

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Sanpera, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Sen, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Sen, U.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Sendra, G. H.

Sheridan, J. T.

Shvedov, V. G.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Selective trapping of multiple particles by volume speckle field,” Opt. Express18, 3137–3142 (2010).
[CrossRef] [PubMed]

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

Sigwarth, O.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Solano, P.

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

Staforelli, J. P.

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, (Dover Publications, 1965) p. 297.

Takeda, M.

Tebaldi, M.

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

L. Ángel, M. Tebaldi, and N. Bolognini, “Multiple rotation assessment through isothetic fringes in speckle photography,” Appl. Opt.46, 2676–2682 (2007).
[CrossRef] [PubMed]

A. Lencina, P. Vaveliuk, M. Tebaldi, and N. Bolognini, “Modulated speckle simulations based on the random-walk model,” Opt. Lett.28, 1748–1750 (2003).
[CrossRef] [PubMed]

M. Tebaldi, A. Lencina, and N. Bolognini, “Analysis and applications of the speckle patterns registered in a photorefractive BTO crystal,” Opt. Commun.202, 257–270 (2002).
[CrossRef]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

Thurman, S. T.

Trivi, M.

G. H. Sendra, H. J. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A26, 2634–2639(2009).
[CrossRef]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

Uno, K.

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun.114, 203–210 (1995).
[CrossRef]

Uozumi, J.

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun.114, 203–210 (1995).
[CrossRef]

Vaveliuk, P.

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

A. Lencina, P. Vaveliuk, M. Tebaldi, and N. Bolognini, “Modulated speckle simulations based on the random-walk model,” Opt. Lett.28, 1748–1750 (2003).
[CrossRef] [PubMed]

Vera, E.

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

Wada, A.

Wang, W.

Wu, Z.

Yokozeki, T.

Zhang, G.

Adv. Phys. (1)

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243–379 (2007).
[CrossRef]

Appl. Opt. (3)

Eur. Phys. J. D (1)

D. Boiron, C. Mennerat-Robilliard, J. M. Fournier, L. Guidoni, C. Salomon, and G. Grynberg, “Trapping and cooling cesium atoms in a speckle Field,” Eur. Phys. J. D7, 373–377 (1999).
[CrossRef]

Europhys. Lett. (1)

G. Grynberg, P. Horak, and C. Mennerat-Robilliard, “Spatial diffusion of atoms cooled in a speckle field,” Europhys. Lett.49, 424–430 (2000).
[CrossRef]

IRE Trans. Inf. Theory (1)

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. TheoryIT-8, 194–195 (1962).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

T.M. Grzegorczyk, B.A. Kemp, and J.A. Kong, Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field, J. Opt. Soc. Am. A.23, 2324–2330 (2006).
[CrossRef]

J. Phys. E (1)

J. N. Butters and J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E4, 277–279 (1971).
[CrossRef]

New J. Phy. (1)

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phy.9, 1–39 (2007).

Opt. Commun. (5)

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun.114, 203–210 (1995).
[CrossRef]

F. Mosso, M. Tebaldi, A. Lencina, and N. Bolognini, “Cluster speckle structures through multiple apertures forming a closed curve,” Opt. Commun.283, 1285–1290 (2010).
[CrossRef]

J. P. Staforelli, J. M. Brito, E. Vera, P. Solano, and A. Lencina, “A clustered speckle approach to optical trapping,” Opt. Commun.283, 4722–4726 (2010).
[CrossRef]

M. Tebaldi, A. Lencina, and N. Bolognini, “Analysis and applications of the speckle patterns registered in a photorefractive BTO crystal,” Opt. Commun.202, 257–270 (2002).
[CrossRef]

M. Tebaldi, L. Ángel, M. Trivi, and N. Bolognini, “New multiple aperture arrangements for speckle photography,” Opt. Commun.182, 95–105 (2000).
[CrossRef]

Opt. Eng. (1)

M. Tebaldi, L. Ángel Toro, M. Trivi, and N. Bolognini, “Optical processing by fringed speckles registered in a BSO crystal,” Opt. Eng.39, 3232–3238 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. Robert-de-Saint-Vincent, J. P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D Diffusive Expansion of Ultracold Atoms in a Disordered Potential,” Phys. Rev. Lett.104, 220602 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

V. G. Shvedov, A. V. Rode, Ya. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Speckle field as a multiple particle trap,” Proc. SPIE7715, 77150K (2010).
[CrossRef]

Waves in Random and Complex Media (1)

A. Lencina, M. Tebaldi, P. Vaveliuk, and N. Bolognini, “Dynamic behaviour of speckle cluster formation,” Waves in Random and Complex Media17, 29–42 (2007).
[CrossRef]

Other (5)

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).

M. Françon, Laser Speckle and Applications in Optics (Academic Press, 1979).

J. W. Goodman, Speckle Phenomena in Optics: theory and applications (Roberts&Company, 2007).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), Ch 3.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, (Dover Publications, 1965) p. 297.

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Figures (9)

Fig. 1
Fig. 1

Magnified images of different kinds of speckle patterns. a) Clustered speckles; b) Standard speckles. Speckle patters were obtained on air by using a frequency doubled Nd:YAG laser with λ = 532 nm, Z0 = 75 mm, ZC = 400 mm, f = 50 mm. For clustered speckles a lens pupil mask consisting of sixteen apertures of about 1 mm diameter evenly distributed on a circumference of 30 mm diameter was employed. See Sec. 2.1 for parameters details.

Fig. 2
Fig. 2

Clustered speckle field propagation sketch. A plane wave impinges normally on a diffuser. A diffuser pupil mask with several apertures is placed behind it. After this, the speckles propagate towards a lens which also has a lens pupil mask. Then, clustered speckles are obtained in the semi-space after the lens and recorded at the observation plane. The apertures in the diffuser pupil mask are centered at the (xs, ys), whereas the apertures in the lens pupil mask are centered at (uh, vh).

Fig. 3
Fig. 3

Experimental setup employed to study the 3D clustered speckle features. An inverted microscope is modified to obtain and to record clustered speckles at different planes. Computer display: reconstruction of the longitudinal intensity profile of the laser beam around the focal plane employed to set the focal plane position.

Fig. 4
Fig. 4

Simulated and experimental speckle images for the cases of diffuser pupil masks with one, six and ten apertures of 0.46 mm and 0.90 mm diameter. In the case of one aperture, this is centered on the optical axis of the system. For the cases of six and ten apertures, they are evenly distributed on a circumference of 4 mm diameter. For all cases the |μA| is calculated by means of Eq. (5). All images display a square region of 12 μm × 12 μm.

Fig. 5
Fig. 5

Radial profiles of the modulus of the complex coherence factor calculated from Fig. 4 by using Eq. (7).

Fig. 6
Fig. 6

Clustered speckle around the focal plane of Fig.3. Simulated and experimental intensity contours at half-intensity are displayed. A doubled Nd:YAG laser, λ = 532 nm is employed and the gap between the objectives is filled with oil. The diffuser pupil mask has six apertures of approximately 0.46mm diameter distributed in a circumference of 4 mm diameter.

Fig. 7
Fig. 7

Comparison between experimental and simulated images taken from pupil image formation to the lens focal plane. All ZC-distances are measured respect to the second principal plane of the objective in the approximation of a thin lens (see Appendix). The gap between objectives is filled with and without immersion oil which constitutes the two cases to be compared. A He-Ne laser with λ = 632.8 nm is used. The diffuser pupil mask is the same as in Fig. 6. All images display a square region of 160 μm × 160 μm.

Fig. 8
Fig. 8

Experimental and simulated clustered speckle pattern formation at the focal plane. Images are a X10 magnified region extracted from Fig. 7 displaying an area of 16 μm × 16 μm.

Fig. 9
Fig. 9

Scheme used for calculation of principal planes. O I ¯ = 195 m m, and S I ¯ = 45 m m. F indicates the focal plane, PP1 and PP2 refer to the first and second principal planes, respectively. ZC and Z0 are the image and object distances, respectively. For the Edmund Optics 40X semi-plan objective, the working distance is E I ¯ = 0.6 m m and f = 4.39 mm is the objective focal distance. Note that the scheme is not to scale.

Equations (7)

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E ( x , y , z ) = 1 Z n 0 Z n C E ( x , y , 0 ) P ( u , v ) exp { i 2 π ( X u ) 2 + ( Y v ) 2 2 Z n C } × exp { i 2 π ( u x ) 2 + ( v y ) 2 2 Z n 0 } exp { i 2 π u 2 + v 2 2 f } d x d y d u d v ,
E C S = 1 Z n 0 Z n C s , q , h P , M , N a h ( u u h , v v h ) exp { i ϕ q s } E q s ( x x s x q , y y s y q ) × exp { i 2 π [ ( x Z n 0 + X Z n C ) u + ( y Z n 0 + Y Z n C ) v ] } exp { i π w ( u 2 + v 2 ) } d x d y d u d v ,
E C S = 1 Z n 0 Z n C s , q , h P , M , N exp { i 2 π [ ( x s + x q Z n 0 + X Z n C ) u h + ( y s + y q Z n 0 + Y Z n C ) v h w ( u h 2 + v h 2 ) / 2 ] + i ϕ q s } × exp { i 2 π [ ( x s + x q Z n 0 + X Z n C w u h ) u 0 + ( y s + y q Z n 0 + Y Z n C w v h ) v 0 ] } × U q s ( u 0 + u h Z n 0 , v 0 + v h Z n 0 ) a h ( u 0 , v 0 ) exp { i π w ( u 0 2 + v 0 2 ) } d u 0 d v 0 .
E C S = 1 Z n 0 Z n C s , q , h P , M , N exp { i 2 π [ ( x s + x q Z n 0 + X Z n C ) u h + ( y s + y q Z n 0 + Y Z n C ) v h w ( u h 2 + v h 2 ) / 2 ] + i ϕ q s } × 1 a u h a v h w exp { i π w [ ( x s + x q Z n 0 + X Z n C w u h ) 2 + ( y s + y q Z n 0 + Y Z n C w v h ) 2 ] } × ( erf { π 2 w ( 1 i ) [ x s + x q Z n 0 + X Z n C w ( u h a u h 2 ) ] } erf { π 2 w ( 1 i ) [ x s + x q Z n 0 + X Z n C w ( u h + a u h 2 ) ] } ) × ( erf { π 2 w ( 1 i ) [ y s + y q Z n 0 + Y Z n C w ( v h a v h 2 ) ] } erf { π 2 w ( 1 i ) [ y s + y q Z n 0 + Y Z n C w ( v h + a v h 2 ) ] } )
| μ A ( x 1 , x 2 ; y 1 , y 2 ) | = R I ( x 1 , x 2 ; y 1 , y 2 ) R I ( x 1 , x 1 ; y 1 , y 1 ) 1 ,
R I ( Δ x , Δ y ) = 1 { | { I } | 2 }
R P μ ( r ) = 1 2 π 0 2 π | μ A ( r , θ ) | d θ ,

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