Abstract

The design of freeform lenses and reflectors allows to achieve non-radially symmetric irradiance distributions whilst keeping the optical system compact. In the case of a point-like source, such as an LED, it is often desired to capture a wide angle of source light in order to increase optical efficiency. This generally results in strongly curved optics, requiring both lens surfaces to contribute to the total ray refraction, and thereby minimising Fresnel losses. In this article, we report on a new design algorithm for multiple freeform optical surfaces based on the theory of optimal mass transport that adresses these requirements and give an example of its application to a problem in general lighting.

© 2012 OSA

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References

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  1. J. S. Schruben, “Formulation of a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. 62, 1498–1501 (1972).
    [CrossRef]
  2. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590–595 (2002).
    [CrossRef]
  3. W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
    [CrossRef]
  4. V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Rational Mech. Anal. 201, 1013–1045 (2011).
    [CrossRef]
  5. P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
    [CrossRef]
  6. A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
    [CrossRef]
  7. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
    [CrossRef]
  8. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18, 5295–5304 (2010).
    [CrossRef] [PubMed]
  9. L. V. Kantorovich, “On a problem of Monge,” Uspekhi Mat. Nauk. 3, 225–226 (1948).
  10. L.-C. Evans, “Partial differential equations and Monge-Kantorovich mass transfer,” tech. rep., Department of Mathematics, University of California, Berkeley (2001).
  11. “FRED Software - Optical Engineering,” http://www.photonengr.com .
  12. W. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics7th ed. (Cambridge University Press, 1999), pp. 41–42

2011 (2)

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Rational Mech. Anal. 201, 1013–1045 (2011).
[CrossRef]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

2010 (1)

2004 (2)

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

2002 (1)

1998 (1)

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[CrossRef]

1972 (1)

1948 (1)

L. V. Kantorovich, “On a problem of Monge,” Uspekhi Mat. Nauk. 3, 225–226 (1948).

Alvarez, J.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Angenent, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

Bäuerle, A.

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

Bentez, P.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Blen, J.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Born, W.

W. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics7th ed. (Cambridge University Press, 1999), pp. 41–42

Bruneton, A.

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

Cassarly, W. J.

Chaves, J.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Dross, O.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Evans, L.-C.

L.-C. Evans, “Partial differential equations and Monge-Kantorovich mass transfer,” tech. rep., Department of Mathematics, University of California, Berkeley (2001).

Falicoff, W.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Fournier, F. R.

Haker, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

Hernndez, M.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Kantorovich, L. V.

L. V. Kantorovich, “On a problem of Monge,” Uspekhi Mat. Nauk. 3, 225–226 (1948).

Loosen, P.

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

Miano, J.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Mohedano, R.

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

Muschaweck, J.

Oliker, V.

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Rational Mech. Anal. 201, 1013–1045 (2011).
[CrossRef]

Parkyn, W. A.

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[CrossRef]

Ries, H.

Rolland, J. P.

Schruben, J. S.

Tannenbaum, A.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

Wester, R.

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

Wolf, E.

W. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics7th ed. (Cambridge University Press, 1999), pp. 41–42

Zhu, L.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

Arch. Rational Mech. Anal. (1)

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Rational Mech. Anal. 201, 1013–1045 (2011).
[CrossRef]

Int. J. Comput. Vis. (1)

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis. 60, 225–240 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Proc. SPIE (3)

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[CrossRef]

P. Bentez, J. Miano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernndez, J. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: Examples and applications,” Proc. SPIE 5185 (2004).
[CrossRef]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).
[CrossRef]

Uspekhi Mat. Nauk. (1)

L. V. Kantorovich, “On a problem of Monge,” Uspekhi Mat. Nauk. 3, 225–226 (1948).

Other (3)

L.-C. Evans, “Partial differential equations and Monge-Kantorovich mass transfer,” tech. rep., Department of Mathematics, University of California, Berkeley (2001).

“FRED Software - Optical Engineering,” http://www.photonengr.com .

W. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics7th ed. (Cambridge University Press, 1999), pp. 41–42

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Figures (7)

Fig. 1
Fig. 1

Mapping computation configuration: the point light source is projected onto the plane Ω0 and the target illuminance is projected onto Ω1. The freeform surfaces are positioned between Ω0 and Ω1.

Fig. 2
Fig. 2

(a) geometry of the wallwashing application considered and definition of coordinate axes; (b) geometry of the simplified on-axis scenario.

Fig. 3
Fig. 3

Ray mapping (represented as a deformation of a regular grid) and corresponding curl z component of the mapping, both (a) before and (b) after optimization for the on-axis case. Note the curl reduction by a factor of about 200.

Fig. 4
Fig. 4

Wireframe representation and irradiance distribution resulting from Monte Carlo ray tracing for an on-axis wallwasher-type configuration (a.u.). (a) and (c) without mapping optimization; (b) and (d) after mapping optimization.

Fig. 5
Fig. 5

(a) Wireframe representation of the two final freeform optical surfaces; (b) Resulting irradiance distribution from Monte Carlo ray tracing of the final wallwasher-type configuration (a.u.).

Fig. 6
Fig. 6

Two dimensional representation of an optical system with (a) one active freeform surface deflecting the light rays; (b) two active freeform surfaces providing reduced Fresnel losses. Both systems achieve the same total ray deflection.

Fig. 7
Fig. 7

(a) Fresnel reflections as a function of angle of incidence on the optical surface. (Rin are the reflectivities for rays entering the lens, Rout those for rays leaving the lens; s means perpendicular polarization, p parallel polarization and without additional index refers to the average of both polarizations); (b) Fresnel reflection losses of a two active surface lens and a single active surface system respectively as a function of the capturing angle.

Equations (6)

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u : Ω 0 Ω 1 , ( x , y ) ( t x , t y )
μ 0 = | D u | μ 1 u ,
N curl ( N ) = 0
u t = 1 μ 0 D u ( Δ 1 div u )
r ( i ) = r 0 ( i ) + λ ( i ) s ( i )
F ( λ ) = i [ ( T x ( i ) t x ( i ) ) 2 + ( T y ( i ) t y ( i ) ) 2 ] ,

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