Abstract

The generation of wide-angle diffraction patterns can be done in different ways using either thin diffractive optical elements with small features sizes or arrays of microoptics with large optical paths that are thick diffractive optical elements. Our aim is to create as many high contrast diffraction-limited dots in the far-field as possible with a uniform intensity distribution. As a model system, we use a sinusoidal phase grating and as a peculiarity, we introduce non-uniform illumination using a Gaussian beam illumination. By making use of the self-imaging phenomenon, a large number of peaks with uniform distribution are generated for a defined range of the phase grating thicknesses due to the sinusoidal curvature. For very high structures, the pattern distribution is not uniform and it demonstrates that very thick sinusoidal phase gratings are not suitable pattern generators. For simulation, we compare thin element approximation, fast Fourier transform beam propagation method, and the rigorous finite difference time domain method. The large-angle diffraction is considered using a high numerical aperture propagator for far-field simulation. We demonstrate that the beam propagation and the Fraunhofer approximation are not accurate enough. Also, our rigorous near-field calculation versus phase grating thickness confirms the significant influence of reflection of thick structures on the far-field distribution, especially on pattern uniformity. Finally, experiments were carried out to confirm our findings and a good agreement between the simulation and experimental far-field distributions confirms our approach.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

2017 (1)

2016 (3)

A. Naqavi, H. P. Herzig, and M. Rossi, “High-contrast self-imaging with ordered optical elements,” J. Opt. Soc. Am. B 33(11), 2374–2382 (2016).
[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

2015 (1)

2013 (2)

2011 (1)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

2007 (1)

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

2004 (3)

2002 (1)

2000 (2)

1999 (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

1990 (1)

S. Som and A. Satpathi, “The generalised Lau effect,” J. Mod. Opt. 37(7), 1215–1225 (1990).
[Crossref]

1979 (1)

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28(3), 263–267 (1979).
[Crossref]

1978 (1)

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Arrizón, V.

Baretzky, C.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Bernabeu, E.

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

Bhargava, S.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Braun, P. V.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Bückmann, T.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Büttner, A.

Chen, H.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Chen, Q.-D.

Choi, H.

Cifci, O. S.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Eckstein, W.

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Eicke, D.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Engelberg, Y. M.

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Fainman, Y.

Fantini, S.

Feit, M.

Fiebelkorn, R.

R. Vandenhouten, A. Hermerschmidt, and R. Fiebelkorn, “Design and quality metrics of point patterns for coded structured light illumination with diffractive optical elements in optical 3D sensors,” in Digital Optical Technologies 2017, (International Society for Optics and Photonics, 2017), 1033518.

Fleck, J.

Fries, B.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Fusion, W. V.

W. V. Fusion, “LightTrans GmbH, Jena, Germany.”

Geng, J.

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Giessen, H.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Gillet, J.-N.

Gissibl, T.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Goodman, J. W.

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

Hallacoglu, B.

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Herkommer, A.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Hermerschmidt, A.

R. Vandenhouten, A. Hermerschmidt, and R. Fiebelkorn, “Design and quality metrics of point patterns for coded structured light illumination with diffractive optical elements in optical 3D sensors,” in Digital Optical Technologies 2017, (International Society for Optics and Photonics, 2017), 1033518.

Herzig, H. P.

A. Naqavi, H. P. Herzig, and M. Rossi, “High-contrast self-imaging with ordered optical elements,” J. Opt. Soc. Am. B 33(11), 2374–2382 (2016).
[Crossref]

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

Jahns, J.

V. Arrizón, M. Testorf, S. Sinzinger, and J. Jahns, “Iterative optimization of phase-only diffractive optical elements based on a lenslet array,” J. Opt. Soc. Am. A 17(12), 2157–2164 (2000).
[Crossref]

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28(3), 263–267 (1979).
[Crossref]

Jefimovs, K.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

Kettunen, V.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

Kim, H.-C.

Kley, E.-B.

Kress, B. C.

B. C. Kress, Field Guide to Digital Micro-Optics (SPIE Press, 2014).

B. C. Kress and P. Meyrueis, Applied Digital Optics: From Micro-optics to Nanophotonics (John Wiley & Sons, 2009).

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Kuittinen, M.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

Lee, I. Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Levy, U.

Lohmann, A. W.

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28(3), 263–267 (1979).
[Crossref]

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

McCord-Maughon, D.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Meyrueis, P.

B. C. Kress and P. Meyrueis, Applied Digital Optics: From Micro-optics to Nanophotonics (John Wiley & Sons, 2009).

Naqavi, A.

Niesler, F.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Perry, J. W.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Petrov, N. I.

Petrova, G. N.

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Radke, A.

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

Ripoll, O.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

Röckel, H.

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Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
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M. Yousefi, T. Scharf, and M. Rossi, “Dot pattern generation using thick sinusoidal phase grating under Gaussian beam illumination,” in Digital Optical Technologies 2019, (International Society for Optics and Photonics, 2019), 1106211.

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T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

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[Crossref]

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[Crossref]

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S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

Zhou, W.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

ACS Photonics (1)

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Adv. Opt. Photonics (1)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Appl. Opt. (3)

Biomed. Opt. Express (1)

J. Mod. Opt. (2)

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51(14), 2111–2123 (2004).
[Crossref]

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[Crossref]

J. Opt. Soc. Am. A (2)

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

Nat. Photonics (1)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Nature (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

Opt. Commun. (2)

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28(3), 263–267 (1979).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

Opt. Lett. (1)

Other (8)

R. Vandenhouten, A. Hermerschmidt, and R. Fiebelkorn, “Design and quality metrics of point patterns for coded structured light illumination with diffractive optical elements in optical 3D sensors,” in Digital Optical Technologies 2017, (International Society for Optics and Photonics, 2017), 1033518.

B. C. Kress, Field Guide to Digital Micro-Optics (SPIE Press, 2014).

M. Yousefi, T. Scharf, and M. Rossi, “Dot pattern generation using thick sinusoidal phase grating under Gaussian beam illumination,” in Digital Optical Technologies 2019, (International Society for Optics and Photonics, 2019), 1106211.

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

W. V. Fusion, “LightTrans GmbH, Jena, Germany.”

F. Solutions, “Lumerical solutions inc,” Vancouver, Canada (2003).

A. Radke, B. Fries, D. Eicke, F. Niesler, C. Baretzky, T. Bückmann, M. Wegener, and M. Thiel, “High-Speed 3D Direct Laser Writing of Micro-Optical Elements,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), ATu2N.4.

B. C. Kress and P. Meyrueis, Applied Digital Optics: From Micro-optics to Nanophotonics (John Wiley & Sons, 2009).

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Figures (16)

Fig. 1.
Fig. 1. (a) Dot pattern generation for a binary diffractive optical element. A series of well-defined dot positions are designed and dots are optimized for intensity. (b) Dot pattern generation for a periodic refractive-diffractive optical element. Dots appear by diffraction and the intensity distribution is designed by the surface profile of the micro-optical components. (c) Ray tracing for one period of a sinusoidal phase grating which shows two different focal points in one period
Fig. 2.
Fig. 2. Schematic of analytical calculation propagators for point source illumination.
Fig. 3.
Fig. 3. (a) Phase modulation generated by the sinusoidal phase grating using TEA, (b) The retrieved phase in the far-field according to Eq. (7).
Fig. 4.
Fig. 4. Far field light pattern generation for sinusoidal phase grating under the Gaussian beam illumination.
Fig. 5.
Fig. 5. Irradiance pattern using TEA for (a) plane wave illumination and (b) Gaussian beam with the beam waist of 2 um.
Fig. 6.
Fig. 6. Irradiance pattern using TEA for the Gaussian beam with the beam waist of (a) 3 um, (b) 2 um and (c) 1 um.
Fig. 7.
Fig. 7. (a) Moving one single period of the phase grating along the x-axis and (b) taking the Fourier transform from near field to obtain the pattern envelope for x = 0, -400 and -800 um.
Fig. 8.
Fig. 8. Normalized far-field irradiance using TEA and FFT-BPM under (a) plane wave and Gaussian beam with the beam waist of (b) 3 um, (c) 2 um and (d) 1 um.
Fig. 9.
Fig. 9. (a) moving one period of phase grating along the x-axis. (b)The calculated pattern envelope for x = 0,-400 and -800 um using FFT-BPM.
Fig. 10.
Fig. 10. Transmission versus source beam waist.
Fig. 11.
Fig. 11. Near-field simulation using FFT-BPM and FDTD for (a) h/P = 0.24, (b) 0.5 and (c) 1.
Fig. 12.
Fig. 12. Near field and far field for h = 12 um. (a) Near field distribution using FFT-BPM and FDTD and near field line plot of the amplitude and phase distribution. The corresponding far-field distributions and pattern envelopes using (b) Fraunhofer approximation and (c) high NA approximation.
Fig. 13.
Fig. 13. Near field and far field for h = 25 um. (a) Near field distribution using FFT-BPM and FDTD and near field line plot of the amplitude and phase distribution. The corresponding far-field distributions and pattern envelopes using (b) Fraunhofer approximation and (c) high NA approximation.
Fig. 14.
Fig. 14. Near field and far field for h = 50 um. (a) Near field distribution using FFT-BPM and FDTD and near field line plot of the amplitude and phase distribution. The corresponding far-field distributions and pattern envelopes using (b) Fraunhofer approximation and (c) high NA approximation.
Fig. 15.
Fig. 15. (a) Photograph from one of the fabricated samples. (b) Scanning electron microscopy (SEM) of the sample, showing a small gap between the stitched areas. (c) Zoom at a small area demonstrating the surface roughness.
Fig. 16.
Fig. 16. (a) the schematic of the optical setup. (b) and (c) Experimental versus simulation far-field pattern for h = 12 and 25um, respectively.

Tables (1)

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Table 1. Pattern standard deviation and numbers of points for 12 and 25 um thicknesses

Equations (12)

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Efarfield(x2,z=Z + D)=C1[E(x1,z=D + )exp(iπλzx12)],
E(x1,z=D+)=Esource(x,z=D).exp[ik(n - 1)H],
Esource(x1,z=D)=Esource(x1,z=0)exp(iπλDx12),
H=h2×(sin2πxP) + h2,
exp[ - 0.5ikh2sin(2πPx)]=q ={-} + Jq( - 0.5kh2)×exp(2πiqxP),
Efar-field(x2,z=Z + D)=C2exp(iπλzx22)q ={-} + Jq( - 0.5kh2)exp(i2πqDx2zP)(1)q2,
q ={-} + Jq( - 0.5kh2)exp(i2πqDx2zP)(1)q2=J0 - 2i[J1sin(2πDzPx) + J3sin(6πDzPx) + J5sin(10πDzPx)+] + 2[J2cos(4πDzPx) + J4cos(8πDzPx) + J6cos(12πDzPx)+],
Efarfield=FT[exp[0.5ik(h2×sin(2πxP) + h2)]],
Efarfield=q= + Jq( - 0.5kh2)×δ(xλz - qP)=+J1( - 0.5kh2)δ(x + λzP)+J0( - 0.5kh2)δ(x)+J1( - 0.5kh2)δ(x - λzP)+,
u(x,z)=w0w(z)exp[x2w(z)2].exp[ikzikx22R(z)],
E(x2,z=Z + D + h + )=exp(jkz)jλzFT[E(x1,z=D + h + )],
E(x2,z=Z + D + h + )=zexp(jkR2)jλR22FT[E(x1,z=D + h + )],