Abstract

Multifocal spots in high numerical-aperture (NA) objectives has emerged as a rapid, parallel, and multi-location method in a multitude of applications. However, the typical method used for forming three-dimensional (3D) multifocal spots based on iterative algorithms limits the potential applications. We demonstrate a non-iterative method using annular subzone phases (ASPs) that are composed of many annular subareas in which phase-only distributions with different 3D displacements are filled. The dynamic 3D multifocal spots with controllable position of each focal spot in the focal volume of the objective are created using the ASPs. The experimental results of such dynamic tunable 3D multifocal spots offer the possibility of versatile process in laser 3D fabrication, optical trapping, and fast focusing scanned microscopic imaging.

© 2017 Optical Society of America

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References

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2017 (3)

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[PubMed]

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B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

2016 (1)

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

2014 (5)

2013 (5)

2012 (1)

2011 (4)

H. Lin, B. Jia, and M. Gu, “Dynamic generation of Debye diffraction-limited multifocal arrays for direct laser printing nanofabrication,” Opt. Lett. 36(3), 406–408 (2011).
[PubMed]

D. R. Burnham, T. Schneider, and D. T. Chiu, “Effects of aliasing on the fidelity of a two dimensional array of foci generated with a kinoform,” Opt. Express 19(18), 17121–17126 (2011).
[PubMed]

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

2010 (2)

2009 (2)

D. Engström, A. Frank, J. Backsten, M. Goksör, and J. Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express 17(12), 9989–10000 (2009).
[PubMed]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

2008 (1)

2007 (1)

2005 (1)

2003 (1)

2001 (1)

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(Pt 3), 368–376 (2001).
[PubMed]

2000 (1)

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A 253(1247), 349–357 (1959).

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1247), 358–379 (1959).

Andresen, P.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(Pt 3), 368–376 (2001).
[PubMed]

Antolini, R.

Arisaka, K.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

Backsten, J.

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Bengtsson, J.

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Burnham, D. R.

Cai, M.

Cao, H.

Cao, W.

Cha, J. W.

Chen, J.

Cheng, A.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

Chichkov, B. N.

Chiu, D. T.

Choudhury, A.

Chu, J.

J. Ni, C. Wang, C. Zhang, Y. Hu, L. Yang, Z. Lao, B. Xu, J. Li, D. Wu, and J. Chu, “Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material,” Light Sci. Appl. 6, e17011 (2017).

Clark, R. L.

Cole, D. G.

Cooper, J.

Courtial, J.

Dahan, M.

B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Di Leonardo, R.

Duadi, H.

Emiliani, V.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

Engström, D.

Fiche, J.-B.

B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

Fidelin, K.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

Fittinghoff, D.

Frank, A.

Fricke, M.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(Pt 3), 368–376 (2001).
[PubMed]

Froner, E.

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Gao, X.

Goksör, M.

Golshani, P.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

Gonçalves, J. T.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

Gu, M.

Hajj, B.

B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

Hellweg, D.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(Pt 3), 368–376 (2001).
[PubMed]

Hernandez, O.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

Hinze, U.

Hu, Y.

J. Ni, C. Wang, C. Zhang, Y. Hu, L. Yang, Z. Lao, B. Xu, J. Li, D. Wu, and J. Chu, “Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material,” Light Sci. Appl. 6, e17011 (2017).

Ianni, F.

Iwata, F.

Jenness, N. J.

Jia, B.

Jia, W.

Johannes, M. S.

Jordan, P.

Kim, H.-D.

H. S. Park, T.-T. Kim, H.-D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5(5435), 5435 (2014).
[PubMed]

Kim, K.

H. S. Park, T.-T. Kim, H.-D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5(5435), 5435 (2014).
[PubMed]

Kim, T.-T.

H. S. Park, T.-T. Kim, H.-D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5(5435), 5435 (2014).
[PubMed]

Koch, J.

Lao, Z.

J. Ni, C. Wang, C. Zhang, Y. Hu, L. Yang, Z. Lao, B. Xu, J. Li, D. Wu, and J. Chu, “Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material,” Light Sci. Appl. 6, e17011 (2017).

Li, H.

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[PubMed]

Li, J.

J. Ni, C. Wang, C. Zhang, Y. Hu, L. Yang, Z. Lao, B. Xu, J. Li, D. Wu, and J. Chu, “Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material,” Light Sci. Appl. 6, e17011 (2017).

Li, M.

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[PubMed]

Li, W.

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[PubMed]

Li, X.

Li, Y.

Lin, H.

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Lou, K.

Ma, J.

Ma, W.

Milkie, D. E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Min, B.

H. S. Park, T.-T. Kim, H.-D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5(5435), 5435 (2014).
[PubMed]

Morita, R.

Murakami, N.

Nakao, H.

Nedivi, E.

Ni, J.

J. Ni, C. Wang, C. Zhang, Y. Hu, L. Yang, Z. Lao, B. Xu, J. Li, D. Wu, and J. Chu, “Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material,” Light Sci. Appl. 6, e17011 (2017).

Nielsen, T.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(Pt 3), 368–376 (2001).
[PubMed]

Nollmann, M.

B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

Obata, K.

Oka, K.

Oudjedi, L.

B. Hajj, L. Oudjedi, J.-B. Fiche, M. Dahan, and M. Nollmann, “Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings,” Sci. Rep. 7(1), 5284 (2017).
[PubMed]

Padgett, M.

Padgett, M. J.

Papagiakoumou, E.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

Park, H. S.

H. S. Park, T.-T. Kim, H.-D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5(5435), 5435 (2014).
[PubMed]

Pavone, F. S.

Piestun, R.

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[PubMed]

Portera-Cailliau, C.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[PubMed]

Qian, S.

Ren, H.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1247), 358–379 (1959).

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Ruocco, G.

Sacconi, L.

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Sakamoto, M.

Schneider, T.

Schonbrun, E.

So, P. T. C.

Squier, J.

Subramanian, J.

Sun, M.

Taghizadeh, M. R.

Takai, T.

Tanese, D.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[PubMed]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Tu, C.

Tzeranis, D.

von Freymann, G.

E. H. Waller and G. von Freymann, “Multi foci with diffraction limited resolution,” Opt. Express 21(18), 21708–21713 (2013).
[PubMed]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[PubMed]

Waller, E. H.

Wang, C.

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Supplementary Material (6)

NameDescription
» Visualization 1       dynamic control multifocal spots in high NA objective
» Visualization 2       dynamic control multifocal spots in high NA objective
» Visualization 3       dynamic control multifocal spots in high NA objective
» Visualization 4       dynamic control multifocal spots in high NA objective
» Visualization 5       dynamic control multifocal spots in high NA objective
» Visualization 6       dynamic control multifocal spots in high NA objective

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Figures (11)

Fig. 1
Fig. 1 Schematic showing the geometry for the calculation of the focused field distribution of a high-NA objective.
Fig. 2
Fig. 2 (a) Phase pattern calculated using Eq. (4) with Δx = Δy = Δz = 3λ. (b) The 3D iso-intensity surface in the focal region with the surface intensity of I = 0.5Imax.
Fig. 3
Fig. 3 Example of simulation results with 3D displacement satisfying the cylindrical spiral equation: Δx = 5λcosφ, Δy = 5λsinφ, Δz = 5λφ/(2π) (see Visualization 1). (a) Phase pattern, (b) 3D iso-intensity surface distribution with I = 0.5Imax.
Fig. 4
Fig. 4 Schematic diagram of the ASP distributions. (a) The aperture stop plane of the objective. (b) A single annulus with M subareas. (c) The phase distribution in one of the M subareas. (d) An example of a procedure to show how to generate the desired phase pattern.
Fig. 5
Fig. 5 (a) ASP patterns filled with the 2D lateral phase-only data as described by Eq. (4) with M = 9, and (b) the corresponding intensity distribution in the focal plane (see Visualization 2).
Fig. 6
Fig. 6 The uniformity of the nine spots shown in Fig. 5 as a function of (a) number N of annular areas and (b) dynamic shift.
Fig. 7
Fig. 7 (a) An ASP filled with 3D phase-only data as described by Eq. (4) when M = 4, and (b) the 3D iso-intensity surfaces of the intensity distribution in the focal region with I = e−2Imax (see Visualization 3).
Fig. 8
Fig. 8 Schematic of the set-up in experiment, where PHF is a spatial pinhole filter, CL is a collimation lens, BS is a beam splitter, P is a polarizer, SLM is a spatial light modulator, PM is a plane mirror.
Fig. 9
Fig. 9 The corresponding experimental results of one focal spot with 3D displacement using the phase patterns of Fig. 3. The intensity distributions recorded by the CCD: (a) φ = 0°, (b) φ = 45°, (c) φ = 90°, (d) φ = 135°. (see Visualization 4)
Fig. 10
Fig. 10 Experimental results of nine sine-shaped multifocal spots with 2D phase modulation shown in Fig. 5(a). (see Visualization 5)
Fig. 11
Fig. 11 Experimental results of the 3D volumetric multifocal spots. (a) – (c) Radial position control; (d) – (f) Angular rotation control; (g)-(i) axial position control. The dynamic intensity distributions are shown in Visualization 6.

Equations (5)

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Ε(x,y,z)=A 0 α 0 2π P( θ ) Ε t ( θ,ϕ ) e ik x 2 + y 2 sinθcos( ta n 1 y x ϕ ) e ikzcosθ sinθdϕdθ,
Ε(x,y,z)= 0 α 0 2π P( θ ) Ε t ( θ,ϕ ) cosθ e i2π( ξx+ηyζz ) dξdη ,
Ε(x,y,z)= FT 3D { G( ξ,η,ζ ) },
ψ( x 0 , y 0 )= 2π λ [ x 0 Δx+ y 0 Δy R n t / NA +Δz 1 x 0 2 + y 0 2 ( R n t / NA ) 2 ],
u=1 max[ I m ]min[ I m ] max[ I m ]+min[ I m ] ,

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