Abstract

Including free-form optical components in imaging systems provides numerous opportunities for enhanced performance and compact, lightweight packaging. This applies especially to the use of free-form optics in off-axis imaging applications. In case of on-axis imaging, rotationally symmetric lenses are typically used, as they greatly simplify the design and manufacturing process. However, for imaging applications with high aspect ratio, free-form optics can help to provide solutions with clearly better overall imaging performance. For such cases, the ray tracing simulations in this work demonstrate superior imaging performance of basic free-form lenses in comparison to conventional rotationally symmetric lenses, each consisting of two surfaces.

© 2013 Optical Society of America

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References

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  1. J. Rolland and K. Thompson, “Freeform optics: Evolution? no, revolution!” SPIE Newsroom (19July2012).
    [Crossref]
  2. W. T. Plummer, “Unusual optics of the Polaroid SX-70 land camera,” Appl. Opt. 21, 196–208 (1982).
    [Crossref] [PubMed]
  3. W. T. Plummer, J. G. Baker, and J. Van Tassell, “Photographic optical systems with nonrotational aspheric surfaces,” Appl. Opt. 38, 3572–3592 (1999).
    [Crossref]
  4. O. Cakmakci and J. Rolland, “Design and fabrication of a dual-element off-axis near-eye optical magnifier,” Opt. Lett. 32, 1363–1365 (2007).
    [Crossref] [PubMed]
  5. O. Cakmakci, B. Moore, H. Foroosh, and J. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16, 1583–1589 (2008).
    [Crossref] [PubMed]
  6. T. Nakano and Y. Tamagawa, “Configuration of an off-axis three-mirror system focused on compactness and brightness,” Appl. Opt. 44, 776–783 (2005).
    [Crossref] [PubMed]
  7. J. M. Rodgers, “Catoptric optical system including concave and convex reflectors,” (1994). US Patent 5,309, 276.
  8. K. Fuerschbach, J. Rolland, and K. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19, 21919–21928 (2011).
    [Crossref] [PubMed]
  9. R. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
  10. K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
    [Crossref] [PubMed]
  11. T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18, 17433–17447 (2010).
    [Crossref] [PubMed]
  12. P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
    [Crossref]
  13. J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
    [Crossref]
  14. J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).
  15. W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).
  16. W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
    [Crossref] [PubMed]
  17. F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
    [Crossref] [PubMed]
  18. F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces,” Opt. Express 20, 10839–10846 (2012).
    [Crossref] [PubMed]
  19. CODE V Reference Manual (Synopsis, 2011), chap. 18: Automatic Design in CODE V, pp. 18.1–18.50.
  20. O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).
  21. J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

2012 (4)

2011 (2)

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

K. Fuerschbach, J. Rolland, and K. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19, 21919–21928 (2011).
[Crossref] [PubMed]

2010 (2)

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18, 17433–17447 (2010).
[Crossref] [PubMed]

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

2009 (2)

J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
[Crossref]

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (1)

2005 (1)

1999 (1)

1997 (1)

1982 (1)

1980 (1)

R. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

Baker, J. G.

Benítez, P.

J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
[Crossref] [PubMed]

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
[Crossref] [PubMed]

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces,” Opt. Express 20, 10839–10846 (2012).
[Crossref] [PubMed]

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
[Crossref]

P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
[Crossref]

Biot, G.

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
[Crossref] [PubMed]

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

Cakmakci, O.

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).

O. Cakmakci, B. Moore, H. Foroosh, and J. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16, 1583–1589 (2008).
[Crossref] [PubMed]

O. Cakmakci and J. Rolland, “Design and fabrication of a dual-element off-axis near-eye optical magnifier,” Opt. Lett. 32, 1363–1365 (2007).
[Crossref] [PubMed]

de la Fuente, M.

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
[Crossref] [PubMed]

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

Duerr, F.

Foroosh, H.

Fuerschbach, K.

Infante, J. M.

Infante Herrero, J. M.

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

Lin, W.

J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
[Crossref] [PubMed]

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
[Crossref]

Liu, J.

J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

Meuret, Y.

Miñano, J. C.

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
[Crossref] [PubMed]

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, G. Biot, and M. de la Fuente, “SMS-based optimization strategy for ultra-compact SWIR telephoto lens design,” Opt. Express 20, 9726–9735 (2012).
[Crossref] [PubMed]

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces,” Opt. Express 20, 10839–10846 (2012).
[Crossref] [PubMed]

J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
[Crossref]

P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
[Crossref]

Moore, B.

Muñoz, F.

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

J. C. Miñano, P. Benítez, W. Lin, J. M. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
[Crossref]

Nakano, T.

Plummer, W. T.

Rakich, A.

Rodgers, J. M.

J. M. Rodgers, “Catoptric optical system including concave and convex reflectors,” (1994). US Patent 5,309, 276.

Rogers, J.

O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).

Rolland, J.

K. Fuerschbach, J. Rolland, and K. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19, 21919–21928 (2011).
[Crossref] [PubMed]

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).

O. Cakmakci, B. Moore, H. Foroosh, and J. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16, 1583–1589 (2008).
[Crossref] [PubMed]

O. Cakmakci and J. Rolland, “Design and fabrication of a dual-element off-axis near-eye optical magnifier,” Opt. Lett. 32, 1363–1365 (2007).
[Crossref] [PubMed]

J. Rolland and K. Thompson, “Freeform optics: Evolution? no, revolution!” SPIE Newsroom (19July2012).
[Crossref]

Rolland, J. P.

Santamaría, A.

Schmid, T.

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18, 17433–17447 (2010).
[Crossref] [PubMed]

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

Shack, R.

R. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

Tamagawa, Y.

Thienpont, H.

Thompson, K.

K. Fuerschbach, J. Rolland, and K. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19, 21919–21928 (2011).
[Crossref] [PubMed]

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).

R. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

J. Rolland and K. Thompson, “Freeform optics: Evolution? no, revolution!” SPIE Newsroom (19July2012).
[Crossref]

Thompson, K. P.

Van Tassell, J.

Vilaplana, J.

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

Wang, L.

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

Appl. Opt. (3)

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

JOSA A (1)

K. Thompson, T. Schmid, O. Cakmakci, and J. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” JOSA A 26, 1503–1517 (2009).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (1)

Proc. SPIE (5)

R. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

J. M. Infante Herrero, F. Muñoz, P. Benítez, J. C. Miñano, L. Wang, J. Vilaplana, G. Biot, and M. de La Fuente, “Novel fast catadioptric objective with wide field of view,” Proc. SPIE 7787, 778704 (2010).

W. Lin, P. Benítez, J. C. Miñano, J. M. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE 8167, 81670M (2011).

O. Cakmakci, J. Rolland, K. Thompson, and J. Rogers, “Design efficiency of 3188 optical designs,” Proc. SPIE 7060, 70600S (2008).

J. Liu, J. C. Miñano, P. Benítez, and W. Lin, “Single optical surface imaging designs with unconstrained object to image mapping,” Proc. SPIE 8550, 855011 (2012).

Other (3)

CODE V Reference Manual (Synopsis, 2011), chap. 18: Automatic Design in CODE V, pp. 18.1–18.50.

J. M. Rodgers, “Catoptric optical system including concave and convex reflectors,” (1994). US Patent 5,309, 276.

J. Rolland and K. Thompson, “Freeform optics: Evolution? no, revolution!” SPIE Newsroom (19July2012).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

(Left) Layout of U.S. Patent 5,309,276 consisting of three off-axis sections of rotationally symmetric mirrors and a fourth fold mirror [7]. (Right) A new free-form optical design based on tilted ϕ-polynomial surfaces (images source: Fuerschbach et al. [8]).

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Fig. 2
Fig. 2

(Left) The rotationally symmetric field for which the system is designed, is oversized for image sensors with rectangular aspect ratio. (Right) Any rotationally symmetric optical system for a rectangular field could be improved by making the surfaces free-form.

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Fig. 3
Fig. 3

(Left) A rotationally symmetric field is clearly mismatching a rectangular receiver with high aspect ratio. (Right) The free-form lens seems as a very promising solution to better suit the desired aspect ratio than a classic rotationally symmetric lens.

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Fig. 4
Fig. 4

3D viewing of ray tracing for the circular rotationally symmetric lens on the left, and the rectangular free-form lens on the right, after conversion to Code V surfaces.

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Fig. 5
Fig. 5

Comparison of the in-plane cross-section profiles of the two lenses: the profiles of the aspherical lens and the free-form lens in x-z-plane coincide, whereas the (dashed) profiles of the free-form lens in y-z-plane clearly deviate from the aspherical profiles.

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Fig. 6
Fig. 6

Spot diagrams for the circular rotationally symmetric lens (left), and for the rectangular free-form lens (right). As expected from the design characteristics, the RMS spot diameters are minimal at the design angles ±11° and 0° for the 3D free-form design, and at 0° for the rotationally symmetric lens, highlighted in red.

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Fig. 7
Fig. 7

The comparison of the RMS spot diameter contour plots for the circular rotationally symmetric lens (top) and for the rectangular free-form lens (bottom) illustrate the very different allocation of the designed fields.

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Fig. 8
Fig. 8

RMS spot diameter contour plots for the circular rotationally symmetric lens (top) and the rectangular free-form lens (bottom) after optimization for the indicated 10:1 FOV. The figures clearly show the superior imaging performance of the free-form lens in terms of RMS spot diameter, compared with the rotationally symmetric lens.

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Fig. 9
Fig. 9

Surface contour plots of the first (left) and second (right) lens surface where the optimized rotationally symmetric surfaces are subtracted from the free-form lens surfaces.

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