Abstract

We show how to correct an optical surface to transform an arbitrary incident light field into a desired irradiance pattern on a projection surface. Beam dilation errors and optical surface corrections are derived from the pullbacks of the actual and desired irradiances. Étendue effects — the principal obstacle to extended-source tailoring — are factored out by solving a sparse linear system. The method accommodates nontrivial projection surfaces, transport phenomena, and incident wavefronts, including those from multiple extended light sources. Numerical experiments achieve high fidelity and contrast ratios in as little as O(Nlog N)-time for a surface represented by N height values.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590–595 (2002).
    [Crossref]
  2. V. Oliker, Trends in nonlinear analysis(Springer, 2003), chap. 3.
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    [Crossref] [PubMed]
  4. C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).
  5. Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
    [Crossref]
  6. G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
    [Crossref]
  7. R. Wester, G. Müller, A. Völl, M. Berens, J. Stollenwerk, and P. Loosen, “Designing optical free-form surfaces for extended sources,” Opt. Express 22, A552–A560 (2014).
    [Crossref] [PubMed]
  8. Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
    [Crossref]
  9. R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
    [Crossref]
  10. S. Sorgato, R. Mohedano, J. Chaves, M. Hernández, J. Blen, D. Grabovičkić, P. Benítez, J. C. Miñano, H. Thienpont, and F. Duerr, “Compact illumination optic with three freeform surfaces for improved beam control,” Opt. Express 25, 29627–29641 (2017).
    [Crossref] [PubMed]
  11. D. Ma, Z. Feng, and R. Liang, “Deconvolution method in designing freeform lens array for structured light illumination,” Appl. Opt. 54, 1114–1117 (2015).
    [Crossref] [PubMed]
  12. M. V. Berry, “Laplacian magic windows,” J. Opt. 1906LT01 (2017).
    [Crossref]
  13. W. L. Wolfe, Introduction to radiometry(SPIE, 1998).
    [Crossref]

2018 (2)

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

2017 (2)

2016 (1)

G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
[Crossref]

2015 (1)

2014 (2)

R. Wester, G. Müller, A. Völl, M. Berens, J. Stollenwerk, and P. Loosen, “Designing optical free-form surfaces for extended sources,” Opt. Express 22, A552–A560 (2014).
[Crossref] [PubMed]

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

2011 (1)

2002 (1)

Benítez, P.

Berens, M.

Berry, M. V.

M. V. Berry, “Laplacian magic windows,” J. Opt. 1906LT01 (2017).
[Crossref]

Blen, J.

Bräuer, A.

Chaves, J.

Damberg, G.

G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
[Crossref]

Duerr, F.

Feng, Z.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

D. Ma, Z. Feng, and R. Liang, “Deconvolution method in designing freeform lens array for structured light illumination,” Appl. Opt. 54, 1114–1117 (2015).
[Crossref] [PubMed]

Grabovickic, D.

Gregson, J.

G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
[Crossref]

Heidrich, W.

G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
[Crossref]

Hernández, M.

IJzerman, W.

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

Liang, R.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

D. Ma, Z. Feng, and R. Liang, “Deconvolution method in designing freeform lens array for structured light illumination,” Appl. Opt. 54, 1114–1117 (2015).
[Crossref] [PubMed]

Liu, S.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Loosen, P.

Ma, D.

Michaelis, D.

Miñano, J. C.

Mohedano, R.

Müller, G.

Muschaweck, J.

Oliker, V.

V. Oliker, Trends in nonlinear analysis(Springer, 2003), chap. 3.

Pauly, M.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

Prins, C.

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

Ries, H.

Schreiber, P.

Schwartzburg, Y.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

Sorgato, S.

Stollenwerk, J.

Tagliasacchi, A.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

ten Thije Boonkkamp, J.

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

Testuz, R.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

Thienpont, H.

Tukker, T.

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

van Roosmalen, J.

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

Völl, A.

Wester, R.

Wolfe, W. L.

W. L. Wolfe, Introduction to radiometry(SPIE, 1998).
[Crossref]

Wu, R.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

Zhang, H.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zhao, Z.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zheng, H.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zheng, Z.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

ACM Trans. Graph. (2)

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33, 74 (2014).
[Crossref]

G. Damberg, J. Gregson, and W. Heidrich, “High brightness hdr projection using dynamic freeform lensing,” ACM Trans. Graph. 35, 24 (2016).
[Crossref]

Appl. Opt. (1)

J. Opt. (1)

M. V. Berry, “Laplacian magic windows,” J. Opt. 1906LT01 (2017).
[Crossref]

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

Laser Photonics Rev. (1)

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser Photonics Rev. 12, 1700310 (2018).
[Crossref]

Opt. Commun. (1)

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for led uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (3)

W. L. Wolfe, Introduction to radiometry(SPIE, 1998).
[Crossref]

C. Prins, J. ten Thije Boonkkamp, J. van Roosmalen, W. IJzerman, and T. Tukker, “A numerical method for the design of free-form reflectors for lighting applications,” Tech. Rep. CASA-report 1322 (2013).

V. Oliker, Trends in nonlinear analysis(Springer, 2003), chap. 3.

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Figures (4)

Fig. 1
Fig. 1 Dilation of a ray bundle from optical surface element dA to projection surface element dB (derived in §2.2–§2.3; see §2.1 for the variable meanings).
Fig. 2
Fig. 2 Algorithmic summary: In the zero-étendue case (left and §3.1–3.2), rays from the incident wavefront propagate through the optic to determine sampling locations on the projection surface. In §3.1, sampled target irradiance intensities are pulled back along the exitent rays to the optical surface and compared with incident intensities from the wavefront to estimate local curvatures for the optic via Eq. (6). In §3.2, both target and actual irradiances are pulled back and compared to obtain a field of curvature corrections via Eq. (8). For positive-étendue light-fields (right and §3.3), the physics are reversed: Pseudo-rays from test points on the target determine sampling locations and directions on a radiant surface. The pushforward of energy flows along theserays forms a system of linear equations in that connects irradiance errors to curvature corrections (Eq. (12)).
Fig. 3
Fig. 3 Two mirrors estimated via Eq. (8) to produce the same irradiance, but from different base surfaces, as per schematic ray transport diagrams. Grayscale shading on the mirror surfaces indicates local surface curvature.
Fig. 4
Fig. 4 Axonometric view of an “E”-projecting lens tailored via Eq. (11). The radiant surface (left) simulates two lens-embedded LEDs that subtend between 9° and 22° when viewed from points on the tailored exit surface (middle). The total distance from the radiant to the irradiant surface (right) is 2 lens-widths = 2 . The inset shows the irradiance obtained from a surface designed for a point source, comparably illuminated by the LEDs.

Tables (1)

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Table 1 Variables and their meanings.

Equations (13)

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n n r i r i r e r e , equivalently , n t , r i r e = t , r e r i  since t , n = 0 .
r e n r i + ( 1 n ) n = ( ( n 1 ) z n w , 1 ) .
s / u = d B / d A .
d B cos  θ B = ( 1 + r 2 q + r 2 ( ( x x q ) ( y y q ) ( x y q ) 2 ) cos  θ Q d A .
d B d A = 1 + r 2 q cos  θ B / cos  θ Q = ( 1 + r 2 ( ( n 1 ) z n w ) ) / o ,
2 z = 1 n 1 ( m r + n 2 w ) ,
u = s d A d B c = s ¯ o 1 + r 2 ( ( n 1 ) ( c + z ) n w ) ,
2 c = s ¯ o ( n 1 ) r ( 1 u 1 u ^ ) = 1 u ( u ^ u ) ( n 1 ) r d B ¯ d A ,
I p d T = Ω s p d A = Ω ( l p ( cos  θ Q , p r p ) 2 cos  θ B , p d B p ) cos  θ A , p d A   ,
I p d T = Ω ( l p o p r p 2 ( 1 ( n 1 1 ) r p 2 ( c + z + n n 1 w p ) ) d T ) d A .
I p I ^ p = Ω n 1 n l p o p r p 2 c d A .
vec ( n 1 n l p o p r p d A ) , vec ( 2 c ) = I p I ^ p ,
K ( c ) = F 1 ( F ( K ( f ) ) F ( L ) 1 ) .

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