Abstract

We present a novel design approach for a binary phase mask with depth-of-focus (DoF) extension ability. Our method considers that the binarized version of an axisymmetric continuous phase pupil generates twin-intensity profiles that are symmetric with respect to the focal plane, each of which resembles the focal behavior of its continuous original. The DoF extension is realized by repositioning and coherently summing the twin foci to achieve an elongated focus along the axial direction. The shift of the two foci towards the focal plane can be handled by superimposing the defocus term in the continuous pupil function. We demonstrate our proposed design approach for two representative axisymmetric aberration functions, i.e., defocused phase axicon and spherical aberration. The manipulation of topological parameters in the phase axicon and spherical aberration, along with the defocus strength, enables the multiple binary phase-filter designs of DoF extension of 3.2–7.1 fold with a phase axicon and 2.8–14.8 fold with a spherical aberration, compared to the case with a clear aperture.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

2016 (6)

J. Xing, J. Kim, and H. Yoo, “Design and fabrication of an optical probe with a phase filter for extended depth of focus,” Opt. Express 24(2), 1037–1044 (2016).
[PubMed]

D. Wilding, P. Pozzi, O. Soloviev, G. Vdovin, C. J. R. Sheppard, and M. Verhaegen, “Pupil filters for extending the field-of-view in light-sheet microscopy,” Opt. Lett. 41(6), 1205–1208 (2016).
[PubMed]

J. Lin, H. Zhao, Y. Ma, J. Tan, and P. Jin, “New hybrid genetic particle swarm optimization algorithm to design multi-zone binary filter,” Opt. Express 24(10), 10748–10758 (2016).
[PubMed]

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Z. Huang, Z. Hao, and L. Zhu, “Axial multifocal binary-phase zone plate for high numerical aperture focusing,” Opt. Eng. 55, 123101 (2016).

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

2015 (4)

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

S. Mori, “Side lobe suppression of a Bessel beam for high aspect ratio laser processing,” Precis. Eng. 39, 79–85 (2015).

O. E. Olarte, J. Andilla, D. Artigas, and P. Loza-Alvarez, “Decoupled illumination detection in light sheet microscopy for fast volumetric imaging,” Optica 2, 702–705 (2015).

2014 (8)

P. Zhang, P. M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22(10), 12398–12409 (2014).
[PubMed]

O. Palillero-Sandoval, J. Félix Aguilar, and L. R. Berriel-Valdos, “Phase mask coded with the superposition of four Zernike polynomials for extending the depth of field in an imaging system,” Appl. Opt. 53(18), 4033–4038 (2014).
[PubMed]

A. Bencheikh, M. Fromager, and K. A. Ameur, “Generation of Laguerre-Gaussian LGp0 beams using binary phase diffractive optical elements,” Appl. Opt. 53(21), 4761–4767 (2014).
[PubMed]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[PubMed]

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
[PubMed]

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

2013 (4)

S. Khonina, A. Ustinov, and S. Volotovsky, “Fractional axicon as a new type of diffractive optical element with conical focal region,” Precis. Instrum. Mechanol. 2, 132–143 (2013).

Y. Zha, J. Wei, and F. Gan, “Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films,” Opt. Commun. 293, 139–148 (2013).

C. J. R. Sheppard, “Pupil filters for generation of light sheets,” Opt. Express 21(5), 6339–6345 (2013).
[PubMed]

S. Quirin, D. S. Peterka, and R. Yuste, “Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging,” Opt. Express 21(13), 16007–16021 (2013).
[PubMed]

2012 (3)

2011 (2)

2010 (1)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).

2009 (6)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[PubMed]

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

F. Zhou, R. Ye, G. Li, H. Zhang, and D. Wang, “Optimized circularly symmetric phase mask to extend the depth of focus,” J. Opt. Soc. Am. A 26(8), 1889–1895 (2009).
[PubMed]

T. Cizmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
[PubMed]

A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. 34(19), 3041–3043 (2009).
[PubMed]

2008 (3)

2007 (3)

M. J. Booth, “Adaptive optics in microscopy,” Philos. Trans. R. Soc. A 365, 2829–2843 (2007).

M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett. 32(1), 5–7 (2007).
[PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[PubMed]

2006 (2)

Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express 14(7), 2631–2643 (2006).
[PubMed]

E. Botcherby, R. Juškaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268, 253–260 (2006).

2005 (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).

2003 (1)

D. Gil, R. Menon, and H. I. Smith, “Fabrication of high-numerical-aperture phase zone plates with a single lithography exposure and no etching,” J. Vac. Sci. Technol. B 21, 2956–2960 (2003).

2002 (1)

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[PubMed]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).

1997 (1)

1995 (1)

1990 (1)

1988 (2)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[PubMed]

Adamec, F.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Ameur, K. A.

Andalman, A.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Andilla, J.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).

Artigas, D.

Bembenek, J. N.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Bencheikh, A.

Ben-Eliezer, E.

Ben-Yaish, S.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Berriel-Valdos, L. R.

Betzig, E.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
[PubMed]

Böhme, R.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Booth, M. J.

M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett. 32(1), 5–7 (2007).
[PubMed]

M. J. Booth, “Adaptive optics in microscopy,” Philos. Trans. R. Soc. A 365, 2829–2843 (2007).

Botcherby, E.

E. Botcherby, R. Juškaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268, 253–260 (2006).

Bourgenot, C.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[PubMed]

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R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Burns, V. M.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
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G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
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Chang, H.

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
[PubMed]

Chen, G.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Chen, N.

Chen, P.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Chen, S.

Chigrinov, V.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[PubMed]

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Cižmár, T.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
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T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).

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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

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G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

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A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Dalgarno, H. I.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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De Koninck, Y.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
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R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
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Dholakia, K.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
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T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).

T. Cizmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
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D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).

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Díaz, A.

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Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Dowski, E. R.

Dyba, M.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
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English, B. P.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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Félix Aguilar, J.

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T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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Y. Zha, J. Wei, and F. Gan, “Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films,” Opt. Commun. 293, 139–148 (2013).

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L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
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J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).

Ge, S.-J.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
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S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
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D. Gil, R. Menon, and H. I. Smith, “Fabrication of high-numerical-aperture phase zone plates with a single lithography exposure and no etching,” J. Vac. Sci. Technol. B 21, 2956–2960 (2003).

Girkin, J. M.

Gong, Q.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

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Grill, S. W.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
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Z. Huang, Z. Hao, and L. Zhu, “Axial multifocal binary-phase zone plate for high numerical aperture focusing,” Opt. Eng. 55, 123101 (2016).

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Hell, S. W.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[PubMed]

Hu, W.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
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Z. Huang, Z. Hao, and L. Zhu, “Axial multifocal binary-phase zone plate for high numerical aperture focusing,” Opt. Eng. 55, 123101 (2016).

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Janetopoulos, C.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Ji, W.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Ji, Z.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
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A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
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R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
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Kiehart, D. P.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Kim, J.

Kim, J. W.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[PubMed]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[PubMed]

Konforti, N.

Legant, W. R.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Li, G.

Li, Y. Y.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Liang, J.

Lin, J.

Lippincott-Schwartz, J.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Liu, L.

Liu, Z.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

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Love, G. D.

Lovett-Barron, M.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Loza-Alvarez, P.

Lu, Y. Q.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).

Luo, X. G.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

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Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

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Marom, E.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).

McCarthy, N.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).

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Menon, R.

D. Gil, R. Menon, and H. I. Smith, “Fabrication of high-numerical-aperture phase zone plates with a single lithography exposure and no etching,” J. Vac. Sci. Technol. B 21, 2956–2960 (2003).

Milgrom, B.

Milkie, D. E.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Miller, D. T.

Mimori-Kiyosue, Y.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Ming, Y.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Mitchell, D. M.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[PubMed]

Mori, S.

S. Mori, “Side lobe suppression of a Bessel beam for high aspect ratio laser processing,” Precis. Eng. 39, 79–85 (2015).

Mullins, R. D.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Nam, H. S.

Nylk, J.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

Ojeda-Castaneda, J.

Ojeda-Castañneda, J.

Olarte, O. E.

Palillero-Sandoval, O.

Peterka, D. S.

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[PubMed]

Pozzi, P.

Quirin, S.

Reymann, A. C.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Ritter, A. T.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Rohrbach, A.

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[PubMed]

A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. 34(19), 3041–3043 (2009).
[PubMed]

Romero, D. P.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Sankaran, S.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Saunter, C. D.

Seydoux, G.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Shao, L.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
[PubMed]

Shemer, A.

Sheppard, C. J. R.

Shi, K.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[PubMed]

Smith, H. I.

D. Gil, R. Menon, and H. I. Smith, “Fabrication of high-numerical-aperture phase zone plates with a single lithography exposure and no etching,” J. Vac. Sci. Technol. B 21, 2956–2960 (2003).

Soloviev, O.

Song, J. W.

Tan, J.

Taylor, J. M.

Thériault, G.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

Tomer, R.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Tulu, U. S.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Ustinov, A.

S. Khonina, A. Ustinov, and S. Volotovsky, “Fractional axicon as a new type of diffractive optical element with conical focal region,” Precis. Instrum. Mechanol. 2, 132–143 (2013).

Vacha, F.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[PubMed]

Vdovin, G.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[PubMed]

Verhaegen, M.

Vettenburg, T.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

Volotovsky, S.

S. Khonina, A. Ustinov, and S. Volotovsky, “Fractional axicon as a new type of diffractive optical element with conical focal region,” Precis. Instrum. Mechanol. 2, 132–143 (2013).

Wang, C. T.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Wang, D.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).

Wang, J. T.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Wang, K.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Wang, L.

Wang, X.

Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

Wei, B. Y.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Wei, J.

Y. Zha, J. Wei, and F. Gan, “Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films,” Opt. Commun. 293, 139–148 (2013).

Wen, Z. Q.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Werner, J. H.

Wilding, D.

Williams, D. R.

Wilson, T.

E. Botcherby, R. Juškaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268, 253–260 (2006).

Wu, X. S.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[PubMed]

Wu, Z. X.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Xi, P.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Xiao, Y.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Xing, J.

Xu, Z.

Yang, S.

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Yang, X.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Ye, R.

Yoo, H.

Yu, A. P.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Yu, W.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Yuste, R.

Zalevsky, Z.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express 14(7), 2631–2643 (2006).
[PubMed]

Zha, Y.

Y. Zha, J. Wei, and F. Gan, “Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films,” Opt. Commun. 293, 139–148 (2013).

Zhai, Z.

Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

Zhang, H.

Zhang, K.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Zhang, P.

Zhang, Z. H.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[PubMed]

Zhao, H.

Zheng, L. Y.

B. Y. Wei, P. Chen, W. Hu, W. Ji, L. Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y. Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Rep. 5, 17484 (2015).
[PubMed]

Zhong, Y.

Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

Zhou, F.

Zhu, L.

Z. Huang, Z. Hao, and L. Zhu, “Axial multifocal binary-phase zone plate for high numerical aperture focusing,” Opt. Eng. 55, 123101 (2016).

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[PubMed]

Zlotnik, A.

Appl. Opt. (6)

Cell (1)

R. Tomer, M. Lovett-Barron, I. Kauvar, A. Andalman, V. M. Burns, S. Sankaran, L. Grosenick, M. Broxton, S. Yang, and K. Deisseroth, “SPED light sheet microscopy: fast mapping of biological system structure and function,” Cell 163(7), 1796–1806 (2015).
[PubMed]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).

Front. Cell. Neurosci. (1)

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell. Neurosci. 8, 139 (2014).
[PubMed]

J. Mod. Opt. (1)

Z. Zhai, S. Ding, Q. Lv, X. Wang, and Y. Zhong, “Extended depth of field through an axicon,” J. Mod. Opt. 56, 1304–1308 (2009).

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (1)

D. Gil, R. Menon, and H. I. Smith, “Fabrication of high-numerical-aperture phase zone plates with a single lithography exposure and no etching,” J. Vac. Sci. Technol. B 21, 2956–2960 (2003).

Laser Photonics Rev. (1)

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super‐resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10, 147–152 (2016).

Nat. Commun. (1)

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[PubMed]

Nat. Methods (1)

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[PubMed]

Nat. Photonics (3)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[PubMed]

H. Wang, L. Shi, B. Lukyanchuk, C. J. R. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).

Nat. Protoc. (1)

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9(5), 1083–1101 (2014).
[PubMed]

Opt. Commun. (4)

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501 (2009).

Y. Zha, J. Wei, and F. Gan, “Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films,” Opt. Commun. 293, 139–148 (2013).

E. Botcherby, R. Juškaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268, 253–260 (2006).

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).

Opt. Eng. (1)

Z. Huang, Z. Hao, and L. Zhu, “Axial multifocal binary-phase zone plate for high numerical aperture focusing,” Opt. Eng. 55, 123101 (2016).

Opt. Express (10)

Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, “All-optical axial super resolving imaging using a low-frequency binary-phase mask,” Opt. Express 14(7), 2631–2643 (2006).
[PubMed]

T. Cizmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
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Supplementary Material (2)

NameDescription
» Visualization 1       Video of numerically calculated 3D PSF of BPM-DF-AXI varying defocus parameter with a fixed axicon value of 2.
» Visualization 2       Video of numerically calculated 3D PSF of BPM-DF-SA varying defocus parameter with a fixed SA value of 4.

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Figures (10)

Fig. 1
Fig. 1

(a-c) Computer-generated pupil phase maps of axicon, defocus, and spherical aberration, along with the corresponding three-dimensional (3D) focal responses. (d-f) Binarized version of the pupil functions (a1, b1, c1), and their 3D focal responses. The pupil coordinates k ¯ x and k ¯ y are the spatial frequencies normalized with NA/λ. The u and v represent the dimensionless optical coordinates in the axial and lateral directions, respectively, as defined in [39]. Note that the binary phase filter generates two foci symmetric to the focal plane (u = 0 plane) in the optical axis.

Fig. 2
Fig. 2

BPMs through binarization of defocused phase axicon. (a-e) computer-generated BPM phase maps with optimal defocus parameters for given α’s. (f-j) Focal intensity profiles in a meridional plane generated by the corresponding pupil functions (a-e).

Fig. 3
Fig. 3

Normalized (a) axial and (b) lateral intensity profiles for the BPM-DF-AXIs. The inset in (b) shows the magnified version of (b). In (a) and (b), the black line denoted by “Clear” represents the focal responses with a clear aperture.

Fig. 4
Fig. 4

Strehl ratio (S) vs. DoF gain ( G DoF ). It can be noted that S decreases as G DoF increases. The BPM designs in the insets correspond to the ones in Fig. 2.

Fig. 5
Fig. 5

BPMs through binarization of DF and spherical aberration. (a-e) computer-generated BPM phase maps with optimal defocus parameters for a given γ. (f-j) Intensity in a meridional plane generated by the corresponding pupil functions (a-e).

Fig. 6
Fig. 6

Normalized axial (a) and lateral (b) intensity profiles for the BPM-DF-SAs. The inset in (b) shows the magnified version of (b). In (a) and (b), the black line denoted by “Clear” represents the focal responses with a clear aperture.

Fig. 7
Fig. 7

Strehl ratio (S) vs. DoF gain ( G DoF ). It is observed that S decreases as G DoF increases. The BPM designs in the insets correspond to the ones in Fig. 5.

Fig. 8
Fig. 8

Axial and lateral focal responses of BPM-DF-AXI (a, b) and BPM-DF-SA (c, d) for the DoF gain of 5 obtained with the proposed design strategy. The BPM parameters were found via direct searching, and specified in the insets of (b) and (d). The insets in (a) and (c) are the phase maps of the BPM-DF-AXI and BPM-DF-SA designs.

Fig. 9
Fig. 9

Axial and lateral focal responses of representative BPM-DF-AXI ( α=10,ψ=4.808) (a-b) and BPM-DF-SA ( γ=10,ψ=1.488) (c-d), under the monochromatic ( λ=0.47μm) and broadband light ( λ=0.47μm,Δλ=100nm) illuminations. No significant deteriorations in the focal responses of the BPMs to the broadband light were observed as compared to the monochromatic cases. The insets in (a) and (b) are the BPM designs employed in the simulation.

Fig. 10
Fig. 10

Beam-propagation simulations of axicon-lens systems. Positive (a), negative (b) and binary phase axicons (c) are placed in the back focal plane of the lens. Shown in the Insets are the x-y intensity profiles for each axial position. The intensities of the insets are normalized for better visualization.

Equations (6)

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Bin[P(ρ)]={ 1(Re[P(ρ)]0) 1(Re[P(ρ)]<0) ,
P Axi (ρ)=exp(2πiαρ), P DF (ρ)=exp(2πiψ ρ 2 ), (0ρ1) P SA (ρ)=exp(2πiγ ρ 4 )
ψ= Δz λ N A 2 2n ,
P BPM-DF-AXI (ρ)=Bin[ P DF P Axi ]=Bin[exp(2πi(ψ ρ 2 +αρ))].
P BPM-DF-SA (ρ)=Bin[ P DF P SA ]=Bin[exp(2πi(ψ ρ 2 +γ ρ 4 ))].
min p | G DoF (p) G DoF.d | subject to: I p (uDoF)>0.9×max[ I p (u)].