Abstract

The Simultaneous Multiple Surface (SMS) method in planar geometry (2D) is applied to imaging designs, generating lenses that compare well with aplanatic designs. When the merit function utilizes image quality over the entire field (not just paraxial), the SMS strategy is superior. In fact, the traditional aplanatic approach is actually a particular case of the SMS strategy.

© 2009 OSA

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References

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  1. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).
  2. W. J. Smith, Modern Optical Engineering, 3rd ed., (McGraw-Hill, 2000).
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  4. A. E. Conrady, Applied Optics and Optical Design, Part 1, New edition 1992 (Oxford University Press and Dover Publications, 1929).
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  6. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-5218 .
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    [CrossRef]
  8. J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
    [CrossRef]
  9. R. Winston and W. Zhang, “Novel aplanatic designs,” Opt. Lett. 34(19), 3018–3019 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-19-3018 .
    [CrossRef] [PubMed]
  10. J. C. Miñano, J. C. González, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. 34(34), 7850–7856 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-34-7850 .
    [CrossRef] [PubMed]
  11. K. Schwarzschild, “Astronomische Mitteilungen der Königlichen Sternwarte zu Göttingen 10, 3 (1905), Reprinted: Selected Papers on Astronomical Optics,” SPIE Milestone Ser. 73, 3 (1993).
  12. G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. R. V. Willstrop and D. Lynden-Bell, “Exact Optics — II. Exploration of Designs On- and Off-Axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
    [CrossRef]
  18. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic Press, New York, 2005)
  19. M. Mansuripur, Classical Optics and its Applications (Cambridge University Press, Cambridge, 2002) p. 16.
  20. G. Schulz, “Higher order aplanatism,” Opt. Commun. 41(5), 315–319 (1982).
    [CrossRef]
  21. G. Schulz, Aspheric surfaces, E. Wolf, (Ed.), Progress in Optics, 25, 1988, pp. 349–415.
  22. J. C. Miñano and J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. 31(16), 3051–3060 (1992), http://www.opticsinfobase.org/abstract.cfm?URI=ao-31-16-3051 .
    [CrossRef] [PubMed]
  23. J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34(13), 2226–2235 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-13-2226 .
    [CrossRef] [PubMed]
  24. J. C. Miñano, J. C. González, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. 34(34), 7850–7856 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-34-7850 .
    [CrossRef] [PubMed]
  25. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
    [CrossRef]
  26. J. Chaves, Introduction to Nonimaging Optics, (CRC Press, Boca Ratón, 2008).
  27. F. Muñoz, Doctoral Thesis “Sistemas ópticos avanzados de gran compactibilidad con aplicaciones en formación de imagen y en iluminación” 2004 http://www-app.etsit.upm.es/tesis_etsit/documentos_biblioteca/masinformacion.php?sgt=TESIS-04-030
  28. N. Shatz and J. Bortz, “Optimized image-forming cemented-doublet concentrator,” Proc. SPIE 5942, 59420G (2005).
    [CrossRef]

2009

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

R. Winston and W. Zhang, “Novel aplanatic designs,” Opt. Lett. 34(19), 3018–3019 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-19-3018 .
[CrossRef] [PubMed]

2007

2005

N. Shatz and J. Bortz, “Optimized image-forming cemented-doublet concentrator,” Proc. SPIE 5942, 59420G (2005).
[CrossRef]

2003

R. V. Willstrop and D. Lynden-Bell, “Exact Optics — II. Exploration of Designs On- and Off-Axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

2002

D. Lynden-Bell, “Exact Optics: A Unification of Optical Telescope Design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[CrossRef]

1997

1995

1993

K. Schwarzschild, “Astronomische Mitteilungen der Königlichen Sternwarte zu Göttingen 10, 3 (1905), Reprinted: Selected Papers on Astronomical Optics,” SPIE Milestone Ser. 73, 3 (1993).

1992

1982

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41(5), 315–319 (1982).
[CrossRef]

1981

1979

1976

W. T. Welford, “Aplanatism and Isoplanatism,” Progress in Optics 13, 267–293 (1976).
[CrossRef]

1949

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Alvarez, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Benítez, P.

Blen, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Bortz, J.

N. Shatz and J. Bortz, “Optimized image-forming cemented-doublet concentrator,” Proc. SPIE 5942, 59420G (2005).
[CrossRef]

Chaves, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Dross, O.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Falicoff, W.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Forbes, G. W.

González, J. C.

Hernández, M.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Infante, J.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

Lin, W.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

Lynden-Bell, D.

R. V. Willstrop and D. Lynden-Bell, “Exact Optics — II. Exploration of Designs On- and Off-Axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[CrossRef]

D. Lynden-Bell, “Exact Optics: A Unification of Optical Telescope Design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[CrossRef]

Mertz, L.

Miñano, J. C.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

P. Benítez and J. C. Miñano, “Ultra high-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14(8), 1988–1997 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-14-8-1988 .
[CrossRef]

J. C. Miñano, J. C. González, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. 34(34), 7850–7856 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-34-7850 .
[CrossRef] [PubMed]

J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34(13), 2226–2235 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-13-2226 .
[CrossRef] [PubMed]

J. C. Miñano, J. C. González, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. 34(34), 7850–7856 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-34-7850 .
[CrossRef] [PubMed]

J. C. Miñano and J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. 31(16), 3051–3060 (1992), http://www.opticsinfobase.org/abstract.cfm?URI=ao-31-16-3051 .
[CrossRef] [PubMed]

Mohedano, R.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Muñoz, F.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

Santamaría, A.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

Schulz, G.

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41(5), 315–319 (1982).
[CrossRef]

Schwarzschild, K.

K. Schwarzschild, “Astronomische Mitteilungen der Königlichen Sternwarte zu Göttingen 10, 3 (1905), Reprinted: Selected Papers on Astronomical Optics,” SPIE Milestone Ser. 73, 3 (1993).

Shatz, N.

N. Shatz and J. Bortz, “Optimized image-forming cemented-doublet concentrator,” Proc. SPIE 5942, 59420G (2005).
[CrossRef]

Wassermann, G. D.

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Welford, W. T.

W. T. Welford, “Aplanatism and Isoplanatism,” Progress in Optics 13, 267–293 (1976).
[CrossRef]

Willstrop, R. V.

R. V. Willstrop and D. Lynden-Bell, “Exact Optics — II. Exploration of Designs On- and Off-Axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[CrossRef]

Winston, R.

Wolf, E.

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Zhang, W.

Appl. Opt.

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

D. Lynden-Bell, “Exact Optics: A Unification of Optical Telescope Design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[CrossRef]

R. V. Willstrop and D. Lynden-Bell, “Exact Optics — II. Exploration of Designs On- and Off-Axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[CrossRef]

Opt. Commun.

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41(5), 315–319 (1982).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Phys. Soc. B

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Proc. SPIE

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[CrossRef]

N. Shatz and J. Bortz, “Optimized image-forming cemented-doublet concentrator,” Proc. SPIE 5942, 59420G (2005).
[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff, “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE 5185, 18–29 (2003).
[CrossRef]

Progress in Optics

W. T. Welford, “Aplanatism and Isoplanatism,” Progress in Optics 13, 267–293 (1976).
[CrossRef]

SPIE Milestone Ser.

K. Schwarzschild, “Astronomische Mitteilungen der Königlichen Sternwarte zu Göttingen 10, 3 (1905), Reprinted: Selected Papers on Astronomical Optics,” SPIE Milestone Ser. 73, 3 (1993).

Other

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic Press, New York, 2005)

M. Mansuripur, Classical Optics and its Applications (Cambridge University Press, Cambridge, 2002) p. 16.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

W. J. Smith, Modern Optical Engineering, 3rd ed., (McGraw-Hill, 2000).

R. E. Fisher, and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

A. E. Conrady, Applied Optics and Optical Design, Part 1, New edition 1992 (Oxford University Press and Dover Publications, 1929).

G. G. Slyusarev, in Aberration and Optical Design Theory, pp. 499–502, Adam Hilger, (Techno House, Bristol, 1984).

J. Chaves, Introduction to Nonimaging Optics, (CRC Press, Boca Ratón, 2008).

F. Muñoz, Doctoral Thesis “Sistemas ópticos avanzados de gran compactibilidad con aplicaciones en formación de imagen y en iluminación” 2004 http://www-app.etsit.upm.es/tesis_etsit/documentos_biblioteca/masinformacion.php?sgt=TESIS-04-030

G. Schulz, Aspheric surfaces, E. Wolf, (Ed.), Progress in Optics, 25, 1988, pp. 349–415.

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Figures (9)

Fig. 1
Fig. 1

Two-surface SMS design for bundles incoming at ± 2°. Focal length 14.32 mm.(f/1.576) refractive index = 1.5

Fig. 2
Fig. 2

Initial calculations for the four-surface SMS design method.

Fig. 3
Fig. 3

SMS calculation of the remaining parts of the surfaces A, B, C and D.

Fig. 4
Fig. 4

Four-surface SMS design for bundles at both ± 2° and ± 6°. Focal length 8.59 mm. (f/2.2413), refractive index = 1.5

Fig. 5
Fig. 5

Continuous lines are results for tangential rays, while dotted lines are for all rays. All the lenses have focal length 14.32mm and f/1.576. Left: RMS spot radius in microns. Two of the lenses are two-surface SMS designs for perfect tangential-ray imaging of rays incoming at ± 1° and ± 2° respectively. The third lens is an aplanatic design. Right: Maximum spot radius vs. the FOV diameter for aplanatic and SMS lenses of different design directions θ i.

Fig. 6
Fig. 6

Spot diagrams for different incidence angle in the aplanatic design ( = 0° two-surface SMS design).

Fig. 7
Fig. 7

Spot diagrams for different incidence angle in the ± 1° two-surface SMS design (top), and close up of the spots 0.5°, 1° and 1.5° (bottom).

Fig. 8
Fig. 8

Spot diagrams for different incidence angle in the ± 2° two-surface SMS design (top), and close up of the spots 1.5°, 2° and 2.5° (bottom).

Fig. 9
Fig. 9

RMS spot radius of the four-surface SMS designs with focal length 8.59 mm and f/2.2413 shown in Fig. 4. This design has been done for perfect imaging of incoming tangential rays in directions ± 2° and ± 6° respectively. The continuous line shows the spot radius calculated only with tangential rays. The dotted line shows the spot radius for all the rays (not only tangential).

Equations (2)

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z = c ρ 2 1 + 1 c 2 ρ 2 ( 1 + k ) + a 4 ρ 4 + a 6 ρ 6 + a 8 ρ 8 +
σ 2 D ( θ ) = | A ( θ ) i = 1 N ( θ θ i ) |

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