Abstract

We report on the microfabrication of continuous aspherical optical surfaces with a single-mask process, using anisotropic etching of silicon in a KOH water solution. Precise arbitrary aspherical surfaces with lateral scales on the order of several millimeters and a profile depth on the order of several micrometers were fabricated using this process. We discuss the factors defining the precision of the formed component and the resulting surface quality. We demonstrate 1 mm and 5 mm replicated aspherical phase plates, reproducing defocus, tilt, astigmatism and high-order aberrations. The technology has a potential for serial production of reflective and refractive arbitrary aspherical micro-optical components.

© 2003 Optical Society of America

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References

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  1. I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).
  2. C. Paterson and J. C. Dainty, “A hybrid curvature and gradient wavefront sensor,” Opt. Lett. 25 (23), 1687–1689 (2000).
    [Crossref]
  3. H.P. Herzig (ed), Micro-Optics: elements, systems and applications, (London, Taylor & Francis, 1998)
  4. D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
    [Crossref]
  5. G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
    [Crossref]
  6. D. Malacara and S. L. DeVore, “Optical interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, 2nd ed. (Wiley Interscience, New York, 1992).
  7. G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

2000 (2)

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

C. Paterson and J. C. Dainty, “A hybrid curvature and gradient wavefront sensor,” Opt. Lett. 25 (23), 1687–1689 (2000).
[Crossref]

1994 (1)

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Akhzar-Mehr, O.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Behringer, U.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Courtois, B.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Dainty, J. C.

de Lima Monteiro, D. W.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

DeVore, S. L.

D. Malacara and S. L. DeVore, “Optical interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, 2nd ed. (Wiley Interscience, New York, 1992).

Digges Jr., T. G.

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Eaton, W. P.

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Findler, G.

G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

Goto, K.

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Kavardjikov, V. I.

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Kendall, D. L.

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Khounsary, A. M.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Kim, Y. J.

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Koch, M.

G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

Loktev, M. Y.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Malacara, D.

D. Malacara and S. L. DeVore, “Optical interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, 2nd ed. (Wiley Interscience, New York, 1992).

Manginell, R.

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Mitsugi, S.

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Muchow, J.

G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

Munzel, H.

G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

Nikolov, I. D.

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Paterson, C.

Sarro, P. M.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Uttamchandani, D. G.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Vdovin, G.

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

Nanotechnology (1)

I. D. Nikolov, K. Goto, S. Mitsugi, Y. J. Kim, and V. I. Kavardjikov, “Nanofocusing recording probe for an optical disk memory,” Nanotechnology 13, 471477 (2000).

Opt. Eng. (1)

D. L. Kendall, W. P. Eaton, R. Manginell, and T. G. Digges Jr., “Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications,” Opt. Eng. 33 (11), 3578–3588 (1994).
[Crossref]

Opt. Lett. (1)

Other (4)

H.P. Herzig (ed), Micro-Optics: elements, systems and applications, (London, Taylor & Francis, 1998)

G. Vdovin, O. Akhzar-Mehr, P. M. Sarro, D. W. de Lima Monteiro, and M. Y. Loktev, “Arrays of spherical micromirrors and molded microlenses fabricated with bulk Si micromachining,” in MEMS/MOEMS: Advances in Photonic Communications, Sensing, Metrology, Packaging and Assembly, U. Behringer, B. Courtois, A. M. Khounsary, and D. G. Uttamchandani, Proc. SPIE4945, 107–111 (2003).
[Crossref]

D. Malacara and S. L. DeVore, “Optical interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, 2nd ed. (Wiley Interscience, New York, 1992).

G. Findler, J. Muchow, M. Koch, and H. Munzel, “Temporal evolution of silicon surface roughness during anisotropic etching processes,” in Micro Electro Mechanical Systems, pp.62–66 (New York, Institute of Electrical and Electronics Engineers, 1992)

Supplementary Material (1)

» Media 1: GIF (922 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Anisotropic etching of a<100>Si wafer through a circular mask.

Fig. 2.
Fig. 2.

Maskless etching of a pyramidal pit with KOH results in a rounded profile.

Fig. 3.
Fig. 3.

Interferometric pattern of a microlens array replicated from a fabricated Si template (top left); spots at the focal plane of the array (bottom left); calculated and measured 2D intensity profile of a single spot (top right); cross-section of the intensity profile (bottom right).

Fig. 4.
Fig. 4.

Combined profile obtained from the lateral overlap of three spherical sections (left) and an arbitrary function approximated by an array of spherical depressions (right). The initial pit size is indicated at the end of line that represents the center of the respective depression.

Fig. 5.
Fig. 5.

Interferometric pattern of a grid of pits for various etch depths. The interferogram at the bottom-right corner represents the aimed profile. [Media 1]

Fig. 6.
Fig. 6.

Method to approximate a 2D profile given by an arbitrary function S(x,y). The function amplitude determines the largest initial pit while the depression diameter at the deepest point dictates the etch depth.

Fig. 7.
Fig. 7.

Interferogram of 5×5mm aspherical phase plates corresponding to defocus, astigmatism and a high-order aberration (left to right). The samples were fabrictaed using 101×101 pit approximation. The relatively large pitch resulted in a higher surface roughness, compared to samples shown in Fig. 8.

Fig. 8.
Fig. 8.

Interferogram of a sample phase plate with several 1×1 mm aspherical structures fabricated using KOH anisotropic etching of Si (left) and micro-photograph of a 1×1 mm structure etched to a depth of 50 µm (right). All surfaces in the sample were fabricated using a 41×41 pit approximation, the initial pit structure of one surface is clearly visible in the micro photograph. Deeper etching will considerably improve the surface quality.

Tables (1)

Tables Icon

Table 1. Calculated rms error (in nm) of the best approximation of a plane (Ra =∞) by a regular grid with pitch p of pits with size d 0 etched to the depth h. To obtain the wavefront error for reflective and refractive surfaces, the table data should be multiplied by 2 and (n-1) respectively.

Equations (6)

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s = d 0 [ 1 2 + 1 m ( 1 2 sin θ 1 2 cos θ ) ]
D = 7.8 h 0.58 d 0 0.42 .
R d = D 2 8 s + s 2
( f d 0 ) ~ 7.6 β α ( h d 0 ) 1.16
F # ~ β α ( h d 0 ) 0.58
σ s = 10 60 · p 2 R ; R = R a R d R a R d

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