Abstract

Improvements of the resolution homogeneity of an ultra-thin artificial apposition compound eye objective are accomplished by the use of a chirped array of ellipsoidal micro-lenses. The array contains 130×130 individually shaped ellipsoidal lenses for channel-wise correction of astigmastism and field curvature occurring under oblique incidence. We present an analytical approach for designing anamorphic micro-lenses for such purpose based on Gullstrand’s equations and experimentally validate the improvement. Considerations for the design of the photolithographical masks for the micro-lens array fabrication by melting of photoresist cylinders with ellipsoidal basis are presented. Measurements of the optically performance are proceed on first realized artificial compound eye prototypes showing a significant improvement of angular resolution homogeneity over the complete field of view of 64.3°.

© 2005 Optical Society of America

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    [CrossRef]
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  27. F. Wippermann, J. Duparré, P. Schreiber, and P. Dannberg, "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective," in Proc. of Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., SPIE 5962, (2005).
    [CrossRef]
  28. P.-F. Rüedi, P. Heim, F. Kaess, E. Grenet, F. Heitger, P.-Y. Burgi, S. Gyger, and P. Nussbaum, "A 128 x 128 Pixel 120-dB Dynamic-Range Vision-Sensor Chip for Image Contrast and Orientation Extraction," IEEE J. Solid-State Circuits 38, 2325-2333 (2003).
    [CrossRef]
  29. P. Dannberg, G. Mann, L. Wagner, and A. Bräuer, "Polymer UV-molding for micro-optical systems and O/Eintegration," in Proc. of Micromachining for Micro-Optics, S. H. Lee and E. G. Johnson, eds., SPIE 4179, pp. 137-145 (2000).
    [CrossRef]

Appl. Opt.

Dgst of Top Mtg:Microlens Arrays at NPL

K. Mersereau, C. R. Nijander, W. P. Townsend, R. J. Crisci, A. Y. Feldblum, and D. Daly, "Design, fabrication and testing of refractive microlens arrays," in Digest of Top. Meet. on Microlens Arrays at NPL, Teddington, M. C. Hutley, ed., EOS 2, pp. 60-64 (1993).

T. Hessler, M. Rossi, J. Pedersen, M. T. Gale, M. Wegner, and H. J. Tiziani, "Microlens arrays with spatial variation of the optical functions," in Digest of Top. Meet. on Microlens Arrays at NPL, Teddington, M. C. Hutley, ed., EOS 13, pp. 42-47 (1997).

N. Lindlein, S. Haselbeck, and J. Schwider, "Simplified Theory for Ellipsoidal Melted Microlenses," in Digest of Top. Meet. on Microlens Arrays at NPL, Teddington, M. C. Hutley, ed., EOS 5, pp. 7-10 (1995).

M. Eisner, N. Lindlein, and J. Schwider, "Making diffraction limited refractive microlenses of spherical and elliptical form," in Digest of Top. Meet. on Microlens Arrays at NPL, Teddington, M. C. Hutley, ed., EOS 13, pp. 39-41 (1997).

C. D. Carey, D. P. Godwin, P. C. H. Poon, D. J. Daly, D. R. Selviah, and J. E. Midwinter, "Astigmatism in ellipsoidal and spherical photoresist microlenses used at oblique incidence," in Digest of Top. Meet. on Microlens Arrays at NPL, Teddington, M. C. Hutley, ed., EOS 2, pp. 65-68 (1993).

IEEE J. Solid-State Circuits

P.-F. Rüedi, P. Heim, F. Kaess, E. Grenet, F. Heitger, P.-Y. Burgi, S. Gyger, and P. Nussbaum, "A 128 x 128 Pixel 120-dB Dynamic-Range Vision-Sensor Chip for Image Contrast and Orientation Extraction," IEEE J. Solid-State Circuits 38, 2325-2333 (2003).
[CrossRef]

J. Imaging Sci.

R. F. Stevens, "Optical inspection of periodic structures using lens arrays and moiré magnification," J. Imaging Sci. 47, 173-179 (1999).

J. Meas. Sci. Technol.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photoresist," J. Meas. Sci. Technol. 1, 759-766 (1990).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

H. Kamal, R. Völkel, and J. Alda, "Properties of moiré magnifiers," Opt. Eng. 37, 3007-3014 (1998).
[CrossRef]

L. Erdmann and D. Efferenn, "Technique for monolithic fabrication of silicon microlenses with selectable rim angles," Opt. Eng. 36, 1094-1098 (1997).
[CrossRef]

A. Schilling, R. Merz, C. Ossmann, and H. P. Herzig, "Surface profiles of reflow microlenses under the influence of surface tension and gravity," Opt. Eng. 39, 2171-2176 (2000).
[CrossRef]

S. Haselbeck, H. Schreiber, J. Schwider, and N. Streibl, "Microlenses fabricated by melting a photoresist on a base layer," Opt. Eng. 32, 1322-1324 (1993).
[CrossRef]

R. Völkel, H. P. Herzig, P. Nussbaum, and R. Dändliker, "Microlens array imaging system for photolithography," Opt. Eng. 35, 3323-3330 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. of 10th Microopt. Conf., 2004

J. Duparré, P. Dannberg, P. Schreiber, A. Bräuer, P. Nussbaum, F. Heitger, and A. Tünnermann, "Ultra-Thin Camera Based on Artificial Apposition Compound Eyes," in Proc. of 10th Microopt. Conf., W. Karthe, G. D. Khoe, and Y. Kokubun, eds., ISBN: 3-8274-1603-5, p. E-2 (Elsevier, 2004).

Proc. of Micromachining for Micro-Optics

P. Dannberg, G. Mann, L. Wagner, and A. Bräuer, "Polymer UV-molding for micro-optical systems and O/Eintegration," in Proc. of Micromachining for Micro-Optics, S. H. Lee and E. G. Johnson, eds., SPIE 4179, pp. 137-145 (2000).
[CrossRef]

Proc. of MOEMS & Miniaturized Syst. 2004

J. Duparré, P. Schreiber, P. Dannberg, T. Scharf, P. Pelli, R. Völkel, H.-P. Herzig, and A. Bräuer, "Artificial compound eyes-different concepts and their application to ultra flat image acquisition sensors," in Proc. of MOEMS and Miniaturized Systems IV, A. El-Fatatry, ed., SPIE 5346, pp. 89-100 (2004).
[CrossRef]

Proc. of Optical Design & Engineering II

F. Wippermann, J. Duparré, P. Schreiber, and P. Dannberg, "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective," in Proc. of Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., SPIE 5962, (2005).
[CrossRef]

Pure Appl. Opt.

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, "Design, fabrication and testing of microlens arrays for sensors and microsystems," Pure Appl. Opt. 6, 617-636 (1997).
[CrossRef]

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, "The moiré magnifier," Pure Appl. Opt. 3, 133-142 (1994).
[CrossRef]

Skand. Arch. Physiol.

A. Gullstrand, "Beitrag zur Theorie des Astigmatismus," Skand. Arch. Physiol. 2, 269-359 (1889).

SPIE Proc. 3879 (1999)

L. C. Wittig and E. B. Kley, "Approximation of refractive micro optical profiles by minimal surfaces," in Proc. of Micromachine Technology for Diffractive and Holographic Optics, S. H. Lee and J. A. Cox, eds., SPIE 3879, pp. 32-38 (1999).
[CrossRef]

Other

C. Hofmann, Die Optische Abbildung, 1st ed. (Geest & Portig, Leipzig, 1980).

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Figures (11)

Fig. 1.
Fig. 1.

Circular lens and ellipsoidal lens under perpendicular and oblique incidence and related spot diagrams (Arrows indicate the position of the corresponding spot.). A circular lens with radius of curvature R=339μm and diameter D=242.8μm in fused silica (n=1.46 at 550nm wavelength) under perpendicular incidence produces a diffraction limited focus (geometrical spot size smaller than Airy-disk diameter indicated by black circle). However, if illuminated under oblique incidence astigmatism and especially field curvature lead to very large spots in the Gaussian image plane. The tangential and sagittal image planes are separated from the Gaussian image plane (here -165μm and -262μm, respectively) and the foci are blurred to lines. Using an anamorphic lens with adapted tangential and sagittal radii of curvature (Rt =579μm, Rs =451μm) for this special angle of incidence a diffraction limited spot size is achieved.

Fig. 2.
Fig. 2.

Geometrical parameters of an ellipsoidal lens for explanation of the notation in Gullstrands equations. n, n′: index of refraction in object and image space, respectively; σ, σ′: chief ray angle in object and image space, respectively; s′ 0: paraxial back focal length; Rt : radius of curvature in tangential plane; Rs : radius of curvature in sagittal plane; at : axis of ellipsoidal at rim of lens laying in the tangential plane; as : axis of ellipsoidal at rim of lens laying in the sagittal plane.

Fig. 3.
Fig. 3.

Optimum tangential and sagittal radii of curvature under oblique incidence calculated by Gullstrand’s equations (lines) and using ray-tracing optimization (crosses); parax-ial focal length is 145μm, NA is 0.23.

Fig. 4.
Fig. 4.

Surface deviation between torus segment and ellipsoidal lens with identical paraxial radii of curvature Rt = 485.7μm and Rs = 609.6μm, lens height 20.2μm and conical constants for representation of the ellipsoidal lens kt = -0.096 and ks = 0.134. For the representation of the torus segment kx = ky = 0 is set.

Fig. 5.
Fig. 5.

(a) Resist cylinder on an ellipsoidal basis to be melted, height: 10.18μm, lens bases: at = 138.9μm, as = 155.6μm; (b) Computer simulated surface by iterative melting of the elliptical resist cylinder, lens height: 20.3μm; (c) Surface deviation (PV) of ideal ellipsoidal lens and iterated surface is maximum λ/7 and thus diffraction limited.

Fig. 6.
Fig. 6.

Experimental setup for focus evaluation under oblique incidence. Rotation axis is aligned with vertex/center of microlens under test. Resolution of the measurement was determined imaging Ronchi rulings to 0.18μm/Pixel on CCD.

Fig. 7.
Fig. 7.

Experimentally obtained spots. (a) Circular lens under 0° (design angle), window width is 18μm, 1/e 2-width is 4.3μm, Strehl ratio is 0.98. (b) Circular lens under 35°, window width is 92μm, image plane is the same as in (a). (c) Ellipsoidal lens under 35° (design angle), window width is 18μm, Strehl ratio is 0.52, image plane is the same as in (a). (d) Ellipsoidal lens under 32° (best angle), window width is 18μm, Strehl ratio is 0.94, image plane is moved 80μm away from lens compared to (a). Elliptical lens was optimized for 35° angle of incidence. Design radii of curvature: Rt = 485.7μm, Rs = 609.6μm; resulting minor and major axes: at = 138.9μm, as = 155.6μm; measured radii of curvature of resist lenses transferred into quartz: Rt = 451μm, Rs = 579μm; circular lens parameters: design radius of curvature: R = 375.2μm; diameter: d = 242.8μm; measured radius of curvature: R = 339μm.

Fig. 8.
Fig. 8.

Experimentally obtained spots. Window width is 92μm for all images: (a) Circular lens under 35°, 170μm axial distance from paraxial focus towards the lens = tangential image plane. (b) Circular lens under 35°, 240μm axial distance from paraxial focus towards the lens = circle of least confusion. (c) Circular lens under 35°, 300μm axial distance from paraxial focus towards the lens = sagittal image plane. (d) Ellipsoidal lens under 0°, 380μm axial distance from paraxial focus off the lens = circle of least confusion.

Fig. 9.
Fig. 9.

Schematic drawing of a camera chip capturing a quadrant of the full FOV. The left and bottom margins serve as docking areas for the gripping tool during assembly. The channel in the lower left corner has a perpendicular viewing direction with respect to the objective-plane and consequently applies a circular lens. With increasing viewing angle of the channel the ellipticity of the corresponding lens is increased up to an angle of σ max =32° on the diagonal.

Fig. 10.
Fig. 10.

Circular symmetric test patterns of different spatial frequency (LP stands for line-pairs over the FOV) centered on the center of FOV and captured images of those by using a chirped lens array for channelwise aberration correction for the oblique incidence and by using a regular lens array for comparison.

Fig. 11.
Fig. 11.

Bar targets of different spatial frequency and captured images of those by using a chirped lens array for channel-wise aberration correction for the oblique incidence and by using a regular lens array for comparison. Additionally, a specially adopted 4×1/4 radial star test pattern demonstrates the obtainable resolution in the four image corners as a function of the angle of incidence by the different radii of vanishing contrast of the radial star patterns.

Tables (1)

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Table 1. Parameters of fabricated artificial apposition eye objectives.

Equations (8)

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Δ ( n sin σ ) = 0 ,
Δ ( n s t cos 2 σ ) = 1 R Δ ( n cos σ )
Δ ( n s s ) = 1 R Δ ( n cos σ )
s t i , j = s s i , j = s 0 cos σ i , j
R t i , j = s 0 ( n′ cos σ i , j n cos σ i , j n′ cos 3 σ i , j ) and
R s i , j = s 0 ( 1 n cos σ i , j n′ cos σ i , j ) .
R = h L 2 + r 2 2 h L
R t R s = ( a t a s ) 2

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