Abstract

The fabrication of continuous-relief diffractive optical elements by direct laser beam writing in photoresist is analyzed. The main limitation and tolerances are identified, and their influence on optical performance is quantified. Fabricated structures show rounded profile steps resulting from the convolution of the desired profile with the writing beam. This leads to a reduction in diffraction efficiency. Optimization techniques are presented to minimize this effect. Scaling the profile depth by a factor of μ > 1 increases the first-order diffraction efficiency for blazed elements. This method is also applied to suppress the zeroth diffraction order in computer-generated holograms. A nonlinear compensation of the exposure data for the Gaussian beam convolution results in an 18% increase of the diffraction efficiency for a blazed grating with a 10-μm period to a value of 79%.

© 1998 Optical Society of America

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  1. M. T. Gale, “Direct writing of continuous-relief elements,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).
  2. C. G. Blough, M. Rossi, S. K. Mack, R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648–4654 (1997).
    [CrossRef] [PubMed]
  3. M. Ekberg, F. Nikolajeff, M. Larsson, S. Hard, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
    [CrossRef] [PubMed]
  4. F. Nikolajeff, J. Bengtson, M. Larrson, M. Ekberg, S. Hård, “Measuring and modeling the proximity effect in direct-write electron-beam lithography kinoforms,” Appl. Opt. 34, 897–903 (1994).
    [CrossRef]
  5. V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).
  6. M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  7. Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).
  8. M. Rossi, Th. Hessler, M. T. Gale, “Design and fabrication of micro-optical elements with deep relief structures,” in Vol. 12 of EOS Topical Meeting Digest Series (European Optical Society, Orsay, France, 1997), pp. 68–69.
  9. M. T. Gale, K. Knop, “The fabrication of fine lens arrays by laser beam writing,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. SPIE398, 347–353 (1983).
    [CrossRef]
  10. M. Rossi, R. E. Kunz, H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
    [CrossRef] [PubMed]
  11. Th. Hessler, R. E. Kunz, “Relaxed fabrication tolerances for low Fresnel number lenses,” J. Opt. Soc. Am. A 14, 1599–1606 (1997).
    [CrossRef]
  12. D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Crit. Rev. SPIECR49, 187–211 (1993).
  13. M. B. Fleming, M. C. Hutley, “Blazed diffractive optics,” Appl. Opt. 36, 4635–4643 (1997).
    [CrossRef] [PubMed]
  14. T. J. Suleski, D. C. O’Shea, “Gray-scale masks for diffractive-optics fabrication: I. Commercial slide imagers,” Appl. Opt. 34, 7507–7517 (1995).
    [CrossRef] [PubMed]
  15. D. C. O’Shea, W. S. Rockward, “Gray-scale masks for diffractive-optics fabrication: II. Spatially filtered halftone screens,” Appl. Opt. 34, 7518–7526 (1995).
    [CrossRef] [PubMed]
  16. H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).
  17. R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–9 (1993).
    [CrossRef]
  18. Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1998).
  19. E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]
  20. G. J. Swanson, “Binary optics technology: Theoretical limitations on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914 (MIT Lincoln Laboratory, Cambridge, Mass., 1991).
  21. M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.
  22. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), Chap. 10.2.
  23. The CSEM laser-beam-writing system was developed at the Paul Scherrer Institute Zurich, which was merged with CSEM in July 1997.
  24. M. T. Gale, “Replication,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).
  25. M. Kuittinen, H. P. Herzig, P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. 120, 230–234 (1995).
    [CrossRef]
  26. T. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
    [CrossRef] [PubMed]
  27. E. Carcolé, J. Campos, I. Juvells, S. Bosch, “Diffraction efficiency of low-resolution Fresnel encoded lenses,” Appl. Opt. 33, 6741–6746 (1994).
    [CrossRef] [PubMed]
  28. Matlab Optimization Toolbox 1.5, The MathWorks Inc., Natick, Mass. (1996).
  29. D. A. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
    [CrossRef] [PubMed]
  30. P. Ehbets, M. Rossi, H. P. Herzig, “Continuous-relief fan out elements with optimized fabrication tolerances,” Opt. Eng. 34, 3456–3464 (1995).
    [CrossRef]
  31. F. Nikolajeff, S. Hård, B. Curtis, “Diffractive microlenses replicated in fused silica for excimer laser-beam homogenizing,” Appl. Opt. 36, 8481–8489 (1997).
    [CrossRef]
  32. J. Bengtsson, “Direct inclusion of the proximity effect in the calculation of kinoforms,” Appl. Opt. 33, 4993–4996 (1994).
    [CrossRef] [PubMed]
  33. M. Larsson, M. Ekberg, F. Nikolajeff, S. Hård, “Successive development optimization of resist kinoforms manufactured with direct-writing, electron-beam lithography,” Appl. Opt. 33, 1176–1179 (1994).
    [CrossRef] [PubMed]

1997 (5)

1995 (5)

1994 (6)

1993 (2)

1992 (1)

1982 (1)

Bengtson, J.

Bengtsson, J.

Blough, C. G.

C. G. Blough, M. Rossi, S. K. Mack, R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648–4654 (1997).
[CrossRef] [PubMed]

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

Bosch, S.

Buralli, D. A.

Campos, J.

Carcolé, E.

Cherkashin, V. V.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Churin, E. G.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Curtis, B.

Ehbets, P.

P. Ehbets, M. Rossi, H. P. Herzig, “Continuous-relief fan out elements with optimized fabrication tolerances,” Opt. Eng. 34, 3456–3464 (1995).
[CrossRef]

M. Kuittinen, H. P. Herzig, P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. 120, 230–234 (1995).
[CrossRef]

Ekberg, M.

Fleming, M. B.

Fujita, T.

Gale, M. T.

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

M. Rossi, Th. Hessler, M. T. Gale, “Design and fabrication of micro-optical elements with deep relief structures,” in Vol. 12 of EOS Topical Meeting Digest Series (European Optical Society, Orsay, France, 1997), pp. 68–69.

M. T. Gale, K. Knop, “The fabrication of fine lens arrays by laser beam writing,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. SPIE398, 347–353 (1983).
[CrossRef]

M. T. Gale, “Direct writing of continuous-relief elements,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

M. T. Gale, “Replication,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), Chap. 10.2.

Hard, S.

Hård, S.

Herzig, H. P.

M. Kuittinen, H. P. Herzig, P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. 120, 230–234 (1995).
[CrossRef]

M. Rossi, R. E. Kunz, H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
[CrossRef] [PubMed]

P. Ehbets, M. Rossi, H. P. Herzig, “Continuous-relief fan out elements with optimized fabrication tolerances,” Opt. Eng. 34, 3456–3464 (1995).
[CrossRef]

H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

Hessler, Th.

Th. Hessler, R. E. Kunz, “Relaxed fabrication tolerances for low Fresnel number lenses,” J. Opt. Soc. Am. A 14, 1599–1606 (1997).
[CrossRef]

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

M. Rossi, Th. Hessler, M. T. Gale, “Design and fabrication of micro-optical elements with deep relief structures,” in Vol. 12 of EOS Topical Meeting Digest Series (European Optical Society, Orsay, France, 1997), pp. 68–69.

Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1998).

Hutley, M. C.

Juvells, I.

Kharissov, A. A.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Kiryanov, V. P.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Knop, K.

M. T. Gale, K. Knop, “The fabrication of fine lens arrays by laser beam writing,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. SPIE398, 347–353 (1983).
[CrossRef]

Korol’kov, V. P.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Koronkevich, V. P.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Koyama, J.

Kuittinen, M.

M. Kuittinen, H. P. Herzig, P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. 120, 230–234 (1995).
[CrossRef]

Kunz, R. E.

Larrson, M.

Larsson, M.

Mack, S. K.

Maystre, D.

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

Michaels, R. L.

Morris, G. M.

Nikolajeff, F.

Nishihara, H.

Noponen, E.

O’Shea, D. C.

Pedersen, J.

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Poleshchuk, A. G.

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Popov, E. K.

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

Raguin, D. H.

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

Ricks, D. W.

D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Crit. Rev. SPIECR49, 187–211 (1993).

Rockward, W. S.

Rossi, M.

C. G. Blough, M. Rossi, S. K. Mack, R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648–4654 (1997).
[CrossRef] [PubMed]

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

M. Rossi, R. E. Kunz, H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
[CrossRef] [PubMed]

P. Ehbets, M. Rossi, H. P. Herzig, “Continuous-relief fan out elements with optimized fabrication tolerances,” Opt. Eng. 34, 3456–3464 (1995).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–9 (1993).
[CrossRef]

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

M. Rossi, Th. Hessler, M. T. Gale, “Design and fabrication of micro-optical elements with deep relief structures,” in Vol. 12 of EOS Topical Meeting Digest Series (European Optical Society, Orsay, France, 1997), pp. 68–69.

Schütz, H.

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Steudle, D.

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

Suleski, T. J.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: Theoretical limitations on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914 (MIT Lincoln Laboratory, Cambridge, Mass., 1991).

Tiziani, H. J.

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

Turunen, J.

Vasara, A.

Wegner, M.

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

Appl. Opt. (12)

C. G. Blough, M. Rossi, S. K. Mack, R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648–4654 (1997).
[CrossRef] [PubMed]

M. Ekberg, F. Nikolajeff, M. Larsson, S. Hard, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
[CrossRef] [PubMed]

F. Nikolajeff, J. Bengtson, M. Larrson, M. Ekberg, S. Hård, “Measuring and modeling the proximity effect in direct-write electron-beam lithography kinoforms,” Appl. Opt. 34, 897–903 (1994).
[CrossRef]

M. B. Fleming, M. C. Hutley, “Blazed diffractive optics,” Appl. Opt. 36, 4635–4643 (1997).
[CrossRef] [PubMed]

T. J. Suleski, D. C. O’Shea, “Gray-scale masks for diffractive-optics fabrication: I. Commercial slide imagers,” Appl. Opt. 34, 7507–7517 (1995).
[CrossRef] [PubMed]

D. C. O’Shea, W. S. Rockward, “Gray-scale masks for diffractive-optics fabrication: II. Spatially filtered halftone screens,” Appl. Opt. 34, 7518–7526 (1995).
[CrossRef] [PubMed]

M. Rossi, R. E. Kunz, H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
[CrossRef] [PubMed]

E. Carcolé, J. Campos, I. Juvells, S. Bosch, “Diffraction efficiency of low-resolution Fresnel encoded lenses,” Appl. Opt. 33, 6741–6746 (1994).
[CrossRef] [PubMed]

D. A. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
[CrossRef] [PubMed]

F. Nikolajeff, S. Hård, B. Curtis, “Diffractive microlenses replicated in fused silica for excimer laser-beam homogenizing,” Appl. Opt. 36, 8481–8489 (1997).
[CrossRef]

J. Bengtsson, “Direct inclusion of the proximity effect in the calculation of kinoforms,” Appl. Opt. 33, 4993–4996 (1994).
[CrossRef] [PubMed]

M. Larsson, M. Ekberg, F. Nikolajeff, S. Hård, “Successive development optimization of resist kinoforms manufactured with direct-writing, electron-beam lithography,” Appl. Opt. 33, 1176–1179 (1994).
[CrossRef] [PubMed]

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

Th. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, D. Steudle, H. J. Tiziani, “Microlens arrays with spatial variation of the optical functions,” J. Eur. Opt. Soc. A 6, (6) 673–681 (1997).

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

Opt. Commun. (2)

M. Kuittinen, H. P. Herzig, P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. 120, 230–234 (1995).
[CrossRef]

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–9 (1993).
[CrossRef]

Opt. Eng. (2)

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

P. Ehbets, M. Rossi, H. P. Herzig, “Continuous-relief fan out elements with optimized fabrication tolerances,” Opt. Eng. 34, 3456–3464 (1995).
[CrossRef]

Opt. Lett. (1)

Other (13)

Matlab Optimization Toolbox 1.5, The MathWorks Inc., Natick, Mass. (1996).

G. J. Swanson, “Binary optics technology: Theoretical limitations on the diffraction efficiency of multilevel diffractive optical elements,” Tech. Rep. 914 (MIT Lincoln Laboratory, Cambridge, Mass., 1991).

M. Rossi, C. G. Blough, D. H. Raguin, E. K. Popov, D. Maystre, “Diffraction efficiency of high-NA continuous-relief diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 233–236.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), Chap. 10.2.

The CSEM laser-beam-writing system was developed at the Paul Scherrer Institute Zurich, which was merged with CSEM in July 1997.

M. T. Gale, “Replication,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

M. T. Gale, “Direct writing of continuous-relief elements,” in Micro-Optics—Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

M. Rossi, Th. Hessler, M. T. Gale, “Design and fabrication of micro-optical elements with deep relief structures,” in Vol. 12 of EOS Topical Meeting Digest Series (European Optical Society, Orsay, France, 1997), pp. 68–69.

M. T. Gale, K. Knop, “The fabrication of fine lens arrays by laser beam writing,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. SPIE398, 347–353 (1983).
[CrossRef]

V. P. Koronkevich, V. P. Kiryanov, V. P. Korol’kov, A. G. Poleshchuk, V. V. Cherkashin, E. G. Churin, A. A. Kharissov, “Fabrication of diffractive optical elements by direct laser-writing with circular scanning,” in Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 290–297 (1995).

Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1998).

D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Crit. Rev. SPIECR49, 187–211 (1993).

H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

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Figures (14)

Fig. 1
Fig. 1

Shadow effect for large deflecting angles θ.

Fig. 2
Fig. 2

(a) Desired and (b) convoluted profile. The finite size of the writing spot leads to rounded profile steps. Part of the grating is considered as dead blaze ε.

Fig. 3
Fig. 3

Effect of spot size convolution reduced by use of higher phase-matching orders. (a) Desired (solid lines) and convoluted (dashed curves) profiles for M = 1 and M = 3. (b) Calculated diffraction efficiency for the convoluted profiles dependent on the reduced grating period. The error bars indicate the efficiency decrease due to a 5% etching error.

Fig. 4
Fig. 4

Measured diffraction efficiencies for blazed gratings with different periods, working in the first, second, and third order. The diffraction efficiency has been normalized to the total transmission in the grating diffraction plane.

Fig. 5
Fig. 5

Effect of convolution on the diffraction pattern for a blazed grating with a period of Λ/M = 10 μm and M = 1, 2, and 3. Note the log scale for the efficiency axis.

Fig. 6
Fig. 6

Calculated efficiency in (a) the zeroth and (b) the first diffraction order for a blazed grating with depth scaling μ and grating period Λ/w. The scale ranges (a) from 0% to 40% with a line spacing of 0.8% and (b) from 30% to 100% with a line spacing of 2%.

Fig. 7
Fig. 7

(a) Exposure data obtained with linear distortion optimization (w = 1.4, μ = 1.15, bars) and original data (μ = 1.0, solid curve). (b) Resulting surface relief for μ = μ1 (solid curve) and for μ = 1.0 (dashed curve). The diffraction efficiency is increased from 63.7% to 66.3%.

Fig. 8
Fig. 8

(a) Exposure data obtained with difference optimization (bars) and (b) resulting surface relief for Λ = 10 μm, w = 1.4 μm (solid curve) and for comparison the nonoptimized relief (dashed curve).

Fig. 9
Fig. 9

Exposure data obtained with SQP optimization, Λ = 10 μm, w = 1.4 μm.

Fig. 10
Fig. 10

Diffraction efficiency of optimized (difference algorithm, solid curve; SQP algorithm, dashed curve) blazed gratings (Λ = 10 μm, w = 1.4 μm) (a) for linear etching tolerances and (b) for changes in writing spot size. For comparison, the tolerances for a nonoptimized grating are also shown (dotted curve).

Fig. 11
Fig. 11

Atomic force micrograph of a Λ = 10-μm first-order grating with individual exposure pixel optimization.

Fig. 12
Fig. 12

Effect of a phase offset φ0 on the Strehl ratio for a F/3 lens (M = 2) for depth tolerances, convolution, and depth tolerances combined with convolution. The inset shows the convoluted surface profile for φ0 = 2π.

Fig. 13
Fig. 13

Measured diffraction efficiency of the zero order for CGH’s having a different depth. For the parameters used here, we can suppress the zero order, using a depth-scaling factor of 1.65.

Fig. 14
Fig. 14

Reconstruction of CGH with (a) standard depth (μ = 1.0) and (b) optimized depth (μ = μ0 = 1.65). The zeroth order could be reduced to average signal level.

Tables (2)

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Table 1 Diffraction Efficiencies η in % (A) for Nonoptimized Convoluted Blazed Grating and (B) for Optimized Gratingsa

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Table 2 Measured Diffraction Efficiencies in Percent of Compensated Blazed Gratingsa

Equations (11)

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φ S x = Λ Λ 1 / 2 1 Λ comb x Λ     exp i 2 π   x Λ rect x Λ ,
η S = Λ Λ = 1 - δ Λ .
I x = I 0 exp - 2 x w 2 .
μ = d / d 0 ,
α = λ 0 n λ - 1 / λ n λ 0 - 1 .
η D = sinc 2 α μ M - N .
φ C x = 1 Λ comb x Λ     exp i 2 π x Λ rect x Λ ˜ .
η C = Λ ˜ Λ 2 = 1 - ε Λ 2 ,
φ CS x Λ ˜ Λ 1 / 2 1 Λ comb x Λ     exp i 2 π   x Λ rect x Λ ,
η CS = Λ ˜ Λ Λ 2 = 1 - ε Λ 2 1 - tan β tan θ = η C η S ,
N Z = a 2 2 λ f 1 2 M ,

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