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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  1. 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]
  2. 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 ).
  3. J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
    [CrossRef] [PubMed]
  4. J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
    [CrossRef] [PubMed]
  5. 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 ).
  6. S. Reinhorn , S. Gorodeisky , A. A. Friesem , and Y. Amitai , “ Fourier transformation with a planar holographic doublet ,” Opt. Lett.   20 , 495 – 497 ( 1995 ).
    [CrossRef] [PubMed]
  7. M. Testorf and J. Jahns , “ Paraxial theory of planar integrated systems ,” J. Opt. Soc. Am. A   14 , 1569 – 1575 ( 1997 ).
    [CrossRef]
  8. S. Sinzinger and J. Jahns , “ Integrated micro-optical imaging system with a high interconnection capacity fabricated in planar optics ,” Appl. Opt.   36 , 4729 – 4735 ( 1997 ).
    [CrossRef] [PubMed]
  9. M. C. Hutley , R. Hunt , R. F. Stevens , and P. Savander , “ The moiré magnifier ,” Pure Appl. Opt.   3 , 133 – 142 ( 1994 ).
    [CrossRef]
  10. R. F. Stevens , “ Optical inspection of periodic structures using lens arrays and moiré magnification ,” J. Imaging Sci.   47 , 173 – 179 ( 1999 ).
  11. H. Kamal , R. VÖlkel , and J. Alda , “ Properties of moiré magnifiers ,” Opt. Eng.   37 , 3007 – 3014 ( 1998 ).
    [CrossRef]
  12. Z. D. Popovich , R. A. Sprague , and G. A. N. Conell , “ Technique for monolithic fabrication of microlens arrays ,” Appl. Opt.   27 , 1281 – 1284 ( 1988 ).
    [CrossRef]
  13. 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]
  14. 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 ).
  15. L. Erdmann and D. Efferenn , “ Technique for monolithic fabrication of silicon microlenses with selectable rim angles ,” Opt. Eng.   36 , 1094 – 1098 ( 1997 ).
    [CrossRef]
  16. 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]
  17. 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]
  18. R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
    [CrossRef]
  19. 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 ).
  20. 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 ).
  21. 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 ).
  22. 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]
  23. C. Hofmann Die Optische Abbildung , 1st ed. ( Geest & Portig, Leipzig , 1980 ).
  24. A. Gullstrand , “ Beitrag zur Theorie des Astigmatismus ,” Skand. Arch. Physiol.   2 , 269 – 359 ( 1889 ).
  25. 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]
  26. J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
    [CrossRef]
  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 × 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/E-integration ,” in Proc. of Micromachining for Micro-Optics, S. H. Lee and E. G. Johnson , eds., SPIE   4179 , pp. 137 – 145 ( 2000 ).
    [CrossRef]

2005 (3)

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

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]

2004 (2)

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]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

2003 (1)

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

2000 (2)

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

1999 (2)

R. F. Stevens , “ Optical inspection of periodic structures using lens arrays and moiré magnification ,” J. Imaging Sci.   47 , 173 – 179 ( 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]

1998 (1)

H. Kamal , R. VÖlkel , and J. Alda , “ Properties of moiré magnifiers ,” Opt. Eng.   37 , 3007 – 3014 ( 1998 ).
[CrossRef]

1997 (6)

M. Testorf and J. Jahns , “ Paraxial theory of planar integrated systems ,” J. Opt. Soc. Am. A   14 , 1569 – 1575 ( 1997 ).
[CrossRef]

S. Sinzinger and J. Jahns , “ Integrated micro-optical imaging system with a high interconnection capacity fabricated in planar optics ,” Appl. Opt.   36 , 4729 – 4735 ( 1997 ).
[CrossRef] [PubMed]

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 ).

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 ).

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

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]

1996 (1)

R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
[CrossRef]

1995 (2)

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 ).

S. Reinhorn , S. Gorodeisky , A. A. Friesem , and Y. Amitai , “ Fourier transformation with a planar holographic doublet ,” Opt. Lett.   20 , 495 – 497 ( 1995 ).
[CrossRef] [PubMed]

1994 (1)

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

1993 (3)

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 ).

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]

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 ).

1990 (1)

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]

1988 (1)

1889 (1)

A. Gullstrand , “ Beitrag zur Theorie des Astigmatismus ,” Skand. Arch. Physiol.   2 , 269 – 359 ( 1889 ).

Alda, J.

H. Kamal , R. VÖlkel , and J. Alda , “ Properties of moiré magnifiers ,” Opt. Eng.   37 , 3007 – 3014 ( 1998 ).
[CrossRef]

Amitai, Y.

Bräuer, A.

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

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]

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

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 ).

Burgi, P.-Y.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Carey, C. D.

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 ).

Conell, G. A. N.

Crisci, R. J.

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 ).

Daly, D.

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 ).

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]

Daly, D. J.

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 ).

Dändliker, R.

R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
[CrossRef]

Dannberg, P.

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]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

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]

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

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 ).

Davies, N.

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]

Duparré, J.

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]

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

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]

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 ).

Efferenn, D.

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

Eisner, M.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

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. 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 ).

Erdmann, L.

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

Feldblum, A. Y.

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 ).

Friesem, A. A.

Gale, M. T.

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 ).

Godwin, D. P.

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 ).

Gorodeisky, S.

Grenet, E.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Gullstrand, A.

A. Gullstrand , “ Beitrag zur Theorie des Astigmatismus ,” Skand. Arch. Physiol.   2 , 269 – 359 ( 1889 ).

Gyger, S.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Haselbeck, S.

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]

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 ).

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]

Heim, P.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Heitger, F.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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. 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 ).

Herzig, H. P.

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]

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]

R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
[CrossRef]

Herzig, H.-P.

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]

Hessler, T.

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 ).

Hofmann, C.

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

Hunt, R.

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

Hutley, M. C.

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

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]

Jahns, J.

Kaess, F.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Kamal, H.

H. Kamal , R. VÖlkel , and J. Alda , “ Properties of moiré magnifiers ,” Opt. Eng.   37 , 3007 – 3014 ( 1998 ).
[CrossRef]

Kley, E. B.

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]

Lindlein, N.

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 ).

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 ).

Mann, G.

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

Matthes, A.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

Mersereau, K.

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 ).

Merz, R.

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]

Midwinter, J. E.

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 ).

Nijander, C. R.

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 ).

Nussbaum, P.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

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]

R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
[CrossRef]

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 ).

Ossmann, C.

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]

Pedersen, J.

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 ).

Pelli, P.

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]

Poon, P. C. H.

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 ).

Popovich, Z. D.

Pshenay-Severin, E.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

Reinhorn, S.

Rossi, M.

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 ).

Rüedi, P.-F.

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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]

Savander, P.

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

Scharf, T.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

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]

Schilling, A.

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]

Schreiber, H.

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]

Schreiber, P.

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]

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

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]

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 ).

Schwider, J.

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 ).

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 ).

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]

Selviah, D. R.

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 ).

Sinzinger, S.

Sprague, R. A.

Stevens, R. F.

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

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

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]

Streibl, N.

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]

Testorf, M.

Tiziani, H. J.

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 ).

Townsend, W. P.

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 ).

Tünnermann, A.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Thin compound eye camera ,” Appl. Opt.   44 , 2949 – 2956 ( 2005 ).
[CrossRef] [PubMed]

J. Duparré , P. Dannberg , P. Schreiber , A. Bräuer , and A. Tünnermann , “ Artificial apposition compound eye fabricated by micro-optics technology ,” Appl. Opt.   43 , 4303 – 4310 ( 2004 ).
[CrossRef] [PubMed]

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 ).

VÖlkel, R.

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

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]

H. Kamal , R. VÖlkel , and J. Alda , “ Properties of moiré magnifiers ,” Opt. Eng.   37 , 3007 – 3014 ( 1998 ).
[CrossRef]

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]

R. VÖlkel , H. P. Herzig , P. Nussbaum , and R. Dändliker , “ Microlens array imaging system for photolithography ,” Opt. Eng.   35 , 3323 – 3330 ( 1996 ).
[CrossRef]

Wagner, L.

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

Wegner, M.

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 ).

Wippermann, F.

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]

Wittig, L. C.

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]

Appl. Opt. (4)

EOS (5)

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 (1)

P.-F. Rüedi , P. Heim , F. Kaess , E. Grenet , F. Heitger , P.-Y. Burgi , S. Gyger , and P. Nussbaum , “ A 128 × 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. (1)

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. (1)

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 (1)

Opt. Eng. (5)

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. Exp. (1)

J. Duparré , P. Schreiber , A. Matthes , E. Pshenay-Severin , A. Bräuer , A. Tünnermann , R. VÖlkel , M. Eisner , and T. Scharf , “ Microoptical telescope compound eye ,” Opt. Exp.   13 , 889 – 903 ( 2005 ).
[CrossRef]

Opt. Lett. (1)

Pure Appl. Opt. (2)

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

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]

Skand. Arch. Physiol. (1)

A. Gullstrand , “ Beitrag zur Theorie des Astigmatismus ,” Skand. Arch. Physiol.   2 , 269 – 359 ( 1889 ).

SPIE (4)

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]

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]

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

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]

Other (2)

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 ).

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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