Abstract

Picture-generating freeform surfaces are able to generate a picture in a defined plane by incoherent beam shaping comparable to illumination purposes. No classical imaging is performed. Therefore the classical Rayleigh criterion of the diffraction limit cannot be applied. In this paper, we investigate the physical light formation of picture-generating freeform surfaces using Fresnel-Huygens-based simulations. A criterion for the diffraction limit was found. The resolution of such surfaces is significantly inferior to the resolution of classical imaging systems. However, in many cases, such systems are limited by the geometrical resolution. The influence of those two limitations were examined and a maximum of resolution, being limited by diffraction and by geometrical parameters can be found.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic Press, 2005).
  7. J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
    [CrossRef]
  8. V. Oliker, “Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Kromker, R. Rannacher, and F. Tomi eds. (Springer, 2003), pp. 193–224.
  9. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces.” J. Opt. Soc. Am. A. 19, 590–595 (2002).
    [CrossRef]
  10. D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  13. M. Brennesholtz and E. Stupp, Projection Displays (Wiley SID, 2008).
  14. S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).
  15. A. V. Pogorelov and S. P. Novikov, Multidimensional Monge-Ampere equation (Harwood Academic Publishers, 1995).
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  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  19. D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE Tutorial Texts Vol. TT89) (SPIE Press, 2011).
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    [CrossRef]
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2011 (2)

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems.” Opt. Lett. 36, 918–920 (2011).
[CrossRef] [PubMed]

2010 (1)

J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
[CrossRef]

2009 (2)

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

2008 (3)

2002 (2)

D. L. Shealy, “Optical design of laser beam shaping systems,” Proc. SPIE 4832, 344–358 (2002).
[CrossRef]

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces.” J. Opt. Soc. Am. A. 19, 590–595 (2002).
[CrossRef]

1992 (1)

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 99–106 (1992).
[CrossRef]

1971 (1)

R. Shack and B. Platt, “Abstract: Production and Use of a Lenticular Hartmann Screen,” J. Opt. Soc. Am. 61, 656 (1971).

Adelson, E.

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 99–106 (1992).
[CrossRef]

Aikio, M.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Benitez, P.

Benítez, P.

J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
[CrossRef]

Blechinger, F.

H. Gross, H. Zügge, M. Peschka, and F. Blechinger, Handbook of Optical Systems, Vol. 3 (Wiley-VCH, 2007).

Blen, J.

Bräuer, A.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems.” Opt. Lett. 36, 918–920 (2011).
[CrossRef] [PubMed]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Brennesholtz, M.

M. Brennesholtz and E. Stupp, Projection Displays (Wiley SID, 2008).

Duval, G.

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

Fessler, R.

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Gebhardt, A.

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gross, H.

H. Gross, Handbook of Optical Systems, Vol. 1 (Wiley-VCH, 2005).

H. Gross, H. Zügge, M. Peschka, and F. Blechinger, Handbook of Optical Systems, Vol. 3 (Wiley-VCH, 2007).

Hanrahan, P.

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

Hicks, R. A.

Horowitz, M.

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

Jegorovs, J.

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Jin, G.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Kudaev, S.

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Kühmstedt, P.

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).

Kurz, M.

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Levoy, M.

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

Makinen, J.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Michaelis, D.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems.” Opt. Lett. 36, 918–920 (2011).
[CrossRef] [PubMed]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Minano, J. C.

Miñano, J. C.

J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
[CrossRef]

Muschaweck, J.

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces.” J. Opt. Soc. Am. A. 19, 590–595 (2002).
[CrossRef]

Ng, R.

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

Notni, G.

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).

Novikov, S. P.

A. V. Pogorelov and S. P. Novikov, Multidimensional Monge-Ampere equation (Harwood Academic Publishers, 1995).

Oberschmidt, D.

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Oliker, V.

V. Oliker, “Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Kromker, R. Rannacher, and F. Tomi eds. (Springer, 2003), pp. 193–224.

Peschka, M.

H. Gross, H. Zügge, M. Peschka, and F. Blechinger, Handbook of Optical Systems, Vol. 3 (Wiley-VCH, 2007).

Platt, B.

R. Shack and B. Platt, “Abstract: Production and Use of a Lenticular Hartmann Screen,” J. Opt. Soc. Am. 61, 656 (1971).

Pogorelov, A. V.

A. V. Pogorelov and S. P. Novikov, Multidimensional Monge-Ampere equation (Harwood Academic Publishers, 1995).

Ries, H.

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces.” J. Opt. Soc. Am. A. 19, 590–595 (2002).
[CrossRef]

Santamaria, A.

Santamaría, A.

J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
[CrossRef]

Schreiber, P.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems.” Opt. Lett. 36, 918–920 (2011).
[CrossRef] [PubMed]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Shack, R.

R. Shack and B. Platt, “Abstract: Production and Use of a Lenticular Hartmann Screen,” J. Opt. Soc. Am. 61, 656 (1971).

Shealy, D. L.

D. L. Shealy, “Optical design of laser beam shaping systems,” Proc. SPIE 4832, 344–358 (2002).
[CrossRef]

Siedow, N.

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Steinkopf, R.

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Stupp, E.

M. Brennesholtz and E. Stupp, Projection Displays (Wiley SID, 2008).

Voelz, D. G.

D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE Tutorial Texts Vol. TT89) (SPIE Press, 2011).

Wang, J.

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 99–106 (1992).
[CrossRef]

Wang, Y.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Winston, R.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic Press, 2005).

Yang, B.

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Zügge, H.

H. Gross, H. Zügge, M. Peschka, and F. Blechinger, Handbook of Optical Systems, Vol. 3 (Wiley-VCH, 2007).

Zwick, S.

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).

IEEE Transactions on Pattern Analysis and Machine Intelligence (1)

E. Adelson and J. Wang, “Single lens stereo with a plenoptic camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 99–106 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

R. Shack and B. Platt, “Abstract: Production and Use of a Lenticular Hartmann Screen,” J. Opt. Soc. Am. 61, 656 (1971).

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

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces.” J. Opt. Soc. Am. A. 19, 590–595 (2002).
[CrossRef]

Mikroproduktion (1)

M. Kurz, D. Oberschmidt, N. Siedow, R. Fessler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 03, 10–12 (2009).

Opt. Express (1)

Opt. Lett. (2)

Opt. Rev. (1)

J. C. Miñano, P. Benítez, and A. Santamaría, “Free-form optics for illumination,” Opt. Rev. 16, 99–102 (2010).
[CrossRef]

Optik (1)

B. Yang, J. Makinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik 120, 74–78 (2009).
[CrossRef]

Proc. SPIE (3)

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 816933 (2011).

D. L. Shealy, “Optical design of laser beam shaping systems,” Proc. SPIE 4832, 344–358 (2002).
[CrossRef]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Other (10)

M. Brennesholtz and E. Stupp, Projection Displays (Wiley SID, 2008).

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic Press, 2005).

V. Oliker, “Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Kromker, R. Rannacher, and F. Tomi eds. (Springer, 2003), pp. 193–224.

A. V. Pogorelov and S. P. Novikov, Multidimensional Monge-Ampere equation (Harwood Academic Publishers, 1995).

H. Gross, H. Zügge, M. Peschka, and F. Blechinger, Handbook of Optical Systems, Vol. 3 (Wiley-VCH, 2007).

H. Gross, Handbook of Optical Systems, Vol. 1 (Wiley-VCH, 2005).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE Tutorial Texts Vol. TT89) (SPIE Press, 2011).

R. Ng, M. Levoy, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Hand-held Plenoptic Camera,” Stanford Tech Report CTSR 2005-02 (2005).

F. M. Dickey and S. C. Holswade, eds., Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).

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