Abstract

More and more lighting applications require the design of dedicated optics to achieve a given radiant intensity or irradiance distribution. Freeform optics has the advantage of providing such a functionality with a compact design. It was previously demonstrated in [Bäuerle et al., Opt. Exp. 20, 14477–14485 (2012)] that the up-front computation of the light path through the optical system (ray mapping) provides a satisfactory approximation to the problem, and allows the design of multiple freeform surfaces in transmission or in reflection. This article presents one natural extension of this work by introducing an efficient optimization procedure based on the physics of the system. The procedure allows the design of multiple freeform surfaces and can render high resolution irradiance patterns, as demonstrated by several examples, in particular by a lens made of two freeform surfaces projecting a high resolution logo (530 × 160 pixels).

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References

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  1. A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
    [CrossRef] [PubMed]
  2. W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
    [CrossRef]
  3. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express18, 5295–5304 (2010).
    [CrossRef] [PubMed]
  4. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19, 590–595 (2002).
    [CrossRef]
  5. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
    [CrossRef]
  6. A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
    [CrossRef]
  7. A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
    [CrossRef]
  8. D. Bindel and J. Goodman, “Principles of scientific error computing,” tech. rep., New York University - Computer Science (2009).
  9. J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE6670, 66700A (2007).
    [CrossRef]

2012 (2)

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
[CrossRef] [PubMed]

2010 (2)

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express18, 5295–5304 (2010).
[CrossRef] [PubMed]

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

2007 (1)

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE6670, 66700A (2007).
[CrossRef]

2004 (1)

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

2002 (1)

1998 (1)

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
[CrossRef]

Angenent, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

Bäuerle, A.

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
[CrossRef] [PubMed]

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

Bindel, D.

D. Bindel and J. Goodman, “Principles of scientific error computing,” tech. rep., New York University - Computer Science (2009).

Bortz, J.

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE6670, 66700A (2007).
[CrossRef]

Bruneton, A.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
[CrossRef] [PubMed]

Cassarly, W. J.

Fournier, F. R.

Goodman, J.

D. Bindel and J. Goodman, “Principles of scientific error computing,” tech. rep., New York University - Computer Science (2009).

Haker, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

Loosen, P.

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
[CrossRef] [PubMed]

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

Muschaweck, J.

Parkyn, W. A.

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
[CrossRef]

Ries, H.

Rolland, J. P.

Schnitzler, C.

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

Shatz, N.

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE6670, 66700A (2007).
[CrossRef]

Stollenwerk, J.

Tannenbaum, A.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

Traub, M.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

Wester, R.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20, 14477–14485 (2012).
[CrossRef] [PubMed]

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

Zhu, L.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

Int. J. of Comput. Vision (1)

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. of Comput. Vision60, 225–240 (2004).
[CrossRef]

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

Opt. Express (2)

Proc. SPIE (4)

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
[CrossRef]

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE6670, 66700A (2007).
[CrossRef]

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, “Irradiance tailoring with two-sided, fresnel-type freeform optics,” Proc. SPIE8485, 84850H (2012).
[CrossRef]

A. Bäuerle, R. Wester, C. Schnitzler, and P. Loosen, “Design of efficient freeform lenses for mass-market illumination applications using hybrid algorithms,” Proc. SPIE7788, 778807 (2010).
[CrossRef]

Other (1)

D. Bindel and J. Goodman, “Principles of scientific error computing,” tech. rep., New York University - Computer Science (2009).

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Figures (5)

Fig. 1
Fig. 1

Point source case: the mapping u is computed between the projected source plane Ω0 and the target plane Ω1. The freeform surfaces are positioned between Ω0 and Ω1. They implement the mapping u which associates each point (x, y) ∈ Ω0 to its counterpart (tx, ty) ∈ Ω1. Here, two examples of such an association are represented by arrows.

Fig. 2
Fig. 2

Elementary light flux tube (prism-shaped) delimited by the rays passing through the vertices of a triangular surface element (blue). The vertex rays are represented in dark, the face ray in green. If the vertex ray directions (e.g. the red vector s) drawn from the source are held constant, the light flux within the triangular tube also remains constant.

Fig. 3
Fig. 3

Double sided freeform lens projecting the letter “B” (lengths in mm, irradiance in a.u.); (a) with mapping optimization only; (b) with mapping and flux optimization; (c) illustration of the geometry.

Fig. 4
Fig. 4

Ray-tracing of high-resolution logo generated with 16 million rays (lengths in mm, irradiance in a.u.); (a) prescribed irradiance distribution (passed to the algorithm in black and white); (b) one freeform surface with mapping optimization only; (c) one freeform surface with mapping and flux optimization; (d) two freeform surfaces with mapping and flux optimization.

Fig. 5
Fig. 5

Zoom on the lower right part of the logo for RMS analysis. Ray-tracing with 2 million rays on a grid of 66×39 points (lengths in mm, irradiance in a.u.). (a) one freeform surface with mapping optimization only; (b) one freeform surface with mapping and flux optimization; (c) two freeform surfaces with mapping and flux optimization.

Tables (1)

Tables Icon

Table 1 Fractional RMS for a sub-area of the logo projection. RMSavg (resp. RMSmax) denotes the RMS computed with Iref being the average irradiance (resp. with Iref being the peak irradiance)

Equations (10)

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u : Ω 0 Ω 1 , ( x , y ) ( t x , t y )
N ( × N ) = 0
u t = 1 μ 0 D u ( Δ 1 div u ) with u | t = 0 = u ˜
Φ S = d 2 Φ S = I ( θ , ϕ ) d 2 Ω
Φ S = d 2 Φ S = B S ( x , y ) d x d y
Φ T ( j ) = A j B T ( x , y ) d x d y
Φ T ( j ) = B T ( x j , y j ) A j
f ˜ ( x ) = f ( x ) ( 1 + ε m 2 f ( x ) h f ( x ) + f ( x ) 2 f ( x ) h )
n = ( u v + m ) / 2
R M S = ( I c I p I ref ) 2

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