Abstract

Thin-film microlens arrays with high fill factors have been fabricated in a one-step process by shading a vapor beam in a vacuum-deposition apparatus with metallic meshes placed at defined distances to the substrate surface. To generate three-dimensional mask structures with the necessary depth profiles, microgalvanic technology has been applied. Profiles and optical properties of the microlenses have been studied theoretically and experimentally.

© 1999 Optical Society of America

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References

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  1. H.-P. Herzig, ed., Micro-Optics—Elements, Systems and Applications (Taylor & Francis, London, 1997), pp. 199–221, 223–257.
  2. S. K. Yao, D. B. Anderson, “Shadow sputtered diffraction-limited waveguide Luneburg lenses,” Appl. Phys. Lett. 33, 307–309 (1978).
    [CrossRef]
  3. R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.
  4. R. Grunwald, S. Woggon, R. Ehlert, “Fabrication of thin-film microlens arrays by mask-shaded vacuum deposition,” in Diffractive Optics and Optical Microsystems, S. Martellucci, A. N. Chester, eds. (Plenum, New York, 1997), pp. 169–177.
    [CrossRef]
  5. R. Grunwald, U. Griebner, D. Schäfer, “Graded reflectivity micro-mirror arrays,” in Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 49–50 (1993).
  6. R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.
  7. U. Griebner, H. Schönnagel, R. Grunwald, “Diode-pumping of fiber array lasers via microlens arrays,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds. Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 253–256.
  8. R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
    [CrossRef]
  9. R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
    [CrossRef]
  10. R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).
  11. S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).
  12. J. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), p. 44.
  13. W. Singer, “Development and experimental verification of non-paraxial wave propagation methods for the analysis of microoptical components,” M.S. thesis (Friedrich-Alexander-University, Erlangen-Nürnberg, Germany, 1995).
  14. J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
    [CrossRef]
  15. R. Grunwald, U. Griebner, “Segmented solid-state laser resonators with graded reflectance micro-mirror arrays,” Pure Appl. Opt. 3, 435–440 (1994).
    [CrossRef]
  16. R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

1998 (1)

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

1997 (1)

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

1994 (1)

R. Grunwald, U. Griebner, “Segmented solid-state laser resonators with graded reflectance micro-mirror arrays,” Pure Appl. Opt. 3, 435–440 (1994).
[CrossRef]

1989 (1)

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

1978 (1)

S. K. Yao, D. B. Anderson, “Shadow sputtered diffraction-limited waveguide Luneburg lenses,” Appl. Phys. Lett. 33, 307–309 (1978).
[CrossRef]

Anderson, D. B.

S. K. Yao, D. B. Anderson, “Shadow sputtered diffraction-limited waveguide Luneburg lenses,” Appl. Phys. Lett. 33, 307–309 (1978).
[CrossRef]

Bennett, J.

J. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), p. 44.

Ehlert, R.

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

R. Grunwald, S. Woggon, R. Ehlert, “Fabrication of thin-film microlens arrays by mask-shaded vacuum deposition,” in Diffractive Optics and Optical Microsystems, S. Martellucci, A. N. Chester, eds. (Plenum, New York, 1997), pp. 169–177.
[CrossRef]

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

Griebner, U.

R. Grunwald, U. Griebner, “Segmented solid-state laser resonators with graded reflectance micro-mirror arrays,” Pure Appl. Opt. 3, 435–440 (1994).
[CrossRef]

R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

R. Grunwald, U. Griebner, D. Schäfer, “Graded reflectivity micro-mirror arrays,” in Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 49–50 (1993).

U. Griebner, H. Schönnagel, R. Grunwald, “Diode-pumping of fiber array lasers via microlens arrays,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds. Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 253–256.

Grunwald, R.

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

R. Grunwald, U. Griebner, “Segmented solid-state laser resonators with graded reflectance micro-mirror arrays,” Pure Appl. Opt. 3, 435–440 (1994).
[CrossRef]

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).

R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

U. Griebner, H. Schönnagel, R. Grunwald, “Diode-pumping of fiber array lasers via microlens arrays,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds. Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 253–256.

R. Grunwald, U. Griebner, D. Schäfer, “Graded reflectivity micro-mirror arrays,” in Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 49–50 (1993).

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

R. Grunwald, S. Woggon, R. Ehlert, “Fabrication of thin-film microlens arrays by mask-shaded vacuum deposition,” in Diffractive Optics and Optical Microsystems, S. Martellucci, A. N. Chester, eds. (Plenum, New York, 1997), pp. 169–177.
[CrossRef]

Huschke, J.

R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

Leger, J. R.

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

Mattson, L.

J. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), p. 44.

Pätzold, H.-J.

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

Reinecke, W.

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

Schäfer, D.

R. Grunwald, U. Griebner, D. Schäfer, “Graded reflectivity micro-mirror arrays,” in Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 49–50 (1993).

Schönnagel, H.

U. Griebner, H. Schönnagel, R. Grunwald, “Diode-pumping of fiber array lasers via microlens arrays,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds. Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 253–256.

R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

Singer, W.

W. Singer, “Development and experimental verification of non-paraxial wave propagation methods for the analysis of microoptical components,” M.S. thesis (Friedrich-Alexander-University, Erlangen-Nürnberg, Germany, 1995).

Witzmann, H.-H.

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

Woggon, S.

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).

R. Grunwald, S. Woggon, R. Ehlert, “Fabrication of thin-film microlens arrays by mask-shaded vacuum deposition,” in Diffractive Optics and Optical Microsystems, S. Martellucci, A. N. Chester, eds. (Plenum, New York, 1997), pp. 169–177.
[CrossRef]

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.

Yao, S. K.

S. K. Yao, D. B. Anderson, “Shadow sputtered diffraction-limited waveguide Luneburg lenses,” Appl. Phys. Lett. 33, 307–309 (1978).
[CrossRef]

Appl. Phys. Lett. (2)

S. K. Yao, D. B. Anderson, “Shadow sputtered diffraction-limited waveguide Luneburg lenses,” Appl. Phys. Lett. 33, 307–309 (1978).
[CrossRef]

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

Jpn. J. Appl. Phys. (1)

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Axial beam shaping with non-spherical microlenses,” Jpn. J. Appl. Phys. 37, 3701–3707 (1998).
[CrossRef]

Pure Appl. Opt. (2)

R. Grunwald, U. Griebner, “Segmented solid-state laser resonators with graded reflectance micro-mirror arrays,” Pure Appl. Opt. 3, 435–440 (1994).
[CrossRef]

R. Grunwald, S. Woggon, R. Ehlert, W. Reinecke, “Thin-film microlens arrays with nonspherical elements,” Pure Appl. Opt. 6, 663–671 (1997).
[CrossRef]

Other (11)

H.-P. Herzig, ed., Micro-Optics—Elements, Systems and Applications (Taylor & Francis, London, 1997), pp. 199–221, 223–257.

R. Grunwald, U. Griebner, J. Huschke, H. Schönnagel, “Compact diode-pumped microlaser with mode-selective thin film micro-mirrors,” in Advanced Solid State Lasers, W. R. Bosenberg, M. M. Fejer, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999).

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Microlens arrays for technical viewing systems,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1998).

S. Woggon, H.-J. Pätzold, R. Ehlert, R. Grunwald, J. Huschke, “Beam shaping of UV and IR pulse lasers with new thin film components,” (Gesellschaft zur Förderung angewandter Optik, Optoelektronik, Quantenelektronik und Spektroskopie e.V., Berlin, 1997).

J. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), p. 44.

W. Singer, “Development and experimental verification of non-paraxial wave propagation methods for the analysis of microoptical components,” M.S. thesis (Friedrich-Alexander-University, Erlangen-Nürnberg, Germany, 1995).

R. Grunwald, R. Ehlert, S. Woggon, H.-J. Pätzold, H.-H. Witzmann, “Microlens arrays formed by crossed thin-film deposition of cylindrical microlenses,” in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 27–30.

R. Grunwald, S. Woggon, R. Ehlert, “Fabrication of thin-film microlens arrays by mask-shaded vacuum deposition,” in Diffractive Optics and Optical Microsystems, S. Martellucci, A. N. Chester, eds. (Plenum, New York, 1997), pp. 169–177.
[CrossRef]

R. Grunwald, U. Griebner, D. Schäfer, “Graded reflectivity micro-mirror arrays,” in Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 49–50 (1993).

R. Grunwald, R. Ehlert, S. Woggon, H.-H. Witzmann, “Thin-film microlens arrays on flexible polymer substrates,” in Micro System Technologies 96, H. Reichl, A. Heuberger, eds. (VDE-Verlag GmbH, Berlin, 1996), pp. 793–795.

U. Griebner, H. Schönnagel, R. Grunwald, “Diode-pumping of fiber array lasers via microlens arrays,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds. Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 253–256.

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Figures (21)

Fig. 1
Fig. 1

Hypotrochoidal orbit of a point on a circular substrate during a simple planetary rotation (schematically).

Fig. 2
Fig. 2

Schematic of deposition of thin-film micro-optics in a system with planetary rotation and shading with a distant (a) circular-hole and (b) a square-shaped-hole mask: M’s, masks; V’s, vapor beam of a pointlike source; R 1, rotation 1 with the larger radius; R 2, rotation 2 with a smaller radius; dashed curves, partial trajectories of a point on the rotating substrate; +, region with deposition; -, region without deposition.

Fig. 3
Fig. 3

Shading of the vapor beam with distant hole-array masks in a rotating deposition system: (a) with a mask of low aspect ratio, resulting in a lower fill factor; (b) with a mask of high aspect ratio, resulting in a higher fill factor (schematically).

Fig. 4
Fig. 4

Part of a mesh-shaped orthogonal shading Ni mask for deposition of microlenses (inspected with a REM).

Fig. 5
Fig. 5

Cut through a mesh-shaped orthogonal Ni mask with mushroomlike depth profile of the bridges (inspected with a REM, 120 × 120 elements, 300-µm pitch).

Fig. 6
Fig. 6

Measured profile of an integrated spacer as a part of a mesh-shaped deposition mask (measured with a Zygo white-light interferometer of Mirau type; the top of the shown profile is oriented to the substrate).

Fig. 7
Fig. 7

Interferometrically measured phase profile of part of a microlens array (SiO2 on quartz, 120 × 120 elements, deposited with a shaded vapor beam by a mesh-shaped Ni mask with integrated spacers).

Fig. 8
Fig. 8

Central cut through the measured phase profile of a single SiO2 microlens (h, thickness; data according to Fig. 7; cut parallel to the structure grating. Solid curve, measured curve; dashed curve, parabolic fit).

Fig. 9
Fig. 9

Interference fringes for part of the same microlens array as that of Fig. 7 (measured at λ = 616 nm, data according to Fig. 7).

Fig. 10
Fig. 10

Amplitude spectrum of the spatial frequencies of part of a microlens array (data according to Fig. 7).

Fig. 11
Fig. 11

Autocovariance function G(τ)/G(0) for the spatial frequencies of a part of a microlens array with G(0) = 900 Å2 c , correlation length; data according to Fig. 7).

Fig. 12
Fig. 12

Fourier spectrum of surface spatial frequencies for a part of a microlens array (data according to Fig. 7).

Fig. 13
Fig. 13

BPM simulation of coherent beam propagation (intensity) on the basis of interferometric data (profile according to Fig. 7, five elements, 300-µm pitch, 10-mm z interval, λ = 635 nm): (a) linear plot, (b) logarithmic plot, (c) normalized on maxima for each axial position z.

Fig. 14
Fig. 14

Axial intensity distribution in the focus of a single microlens calculated with the BPM (linear cut along the optical axis, thickness profile according to Fig. 7, λ = 635 nm).

Fig. 15
Fig. 15

Transversal intensity distribution in the focus of a single microlens calculated with the BPM (linear cut, thickness profile according to Fig. 7, λ = 635 nm).

Fig. 16
Fig. 16

Measured transversal intensity distribution in the focus of a single microlens (linear cut, thickness profile according to Fig. 7, λ = 635 nm).

Fig. 17
Fig. 17

Modulation transfer function for circular, concentric parts of different radii of a single lens (qualitatively; phase profile according to Fig. 7; λ = 648 nm; abscissa; wave number/radius). Diameter of the software mask: (a) 50 µm, (b) 100 µm, (c) 150 µm, (d) 200 µm, (e) 250 µm.

Fig. 18
Fig. 18

2D point-spread function for circular, concentric parts of different radii of a single lens as a density plot (phase profile according to Fig. 7; λ = 648 nm; abscissa, wave number/radius). Diameter of the software mask: (a) 50 µm, (b) 100 µm, (c) 150 µm, (d) 200 µm, (e) 250 µm.

Fig. 19
Fig. 19

Encircled energy for circular, concentric parts of different radii of a single lens (phase profile according to Fig. 7; λ = 648 nm; abscissa, wave number/radius). Diameter of the software mask: (a) 50 µm, (b) 100 µm, (c) 150 µm, (d) 200 µm, (e) 250 µm.

Fig. 20
Fig. 20

Self-imaging by constructive interference in reflection: intensity pattern on a CCD matrix camera at the first Talbot distance for the illumination of an orthogonal array of square-shaped curved micromirrors (Au layer on SiO2) with a He–Ne-laser (λ = 633 nm; distance between micromirror array and CCD matrix, 284 mm; periods of generating array and light pattern, 300 µm, tilted).

Fig. 21
Fig. 21

Characterization of the uniformity of a thin-film microlens array by the measured sag heights as a function of the position of the elements in the array (part of a single row of an orthogonal array structure of 120 × 120 elements, square-shaped parabolic SiO2 microlenses on a quartz substrate, 300-µm pitch, mask with magnetic holder).

Equations (4)

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Gl=1/N×i=1n-l zizi+l  l=0, 1, 2, , N-1.
τc=G0/e,
F=d2/4λf,
dT=2mp2/λ,

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