Abstract

Modern liquid crystal spatial light modulators (SLMs) are capable of shifting the optical path length by some microns, which corresponds to phase shifts of several multiples of 2π. We use this capability to display freeform optical elements (FOEs) on a SLM, as largely smooth phase variations with only a small number of wrapping lines. These FOEs can be programmed to generate so-called caustic intensity distributions, which may be real images reconstructed at a selected position in front of the SLM surface. In contrast to standard diffractive structures, reconstruction of the freeform images is non-dispersive (i.e. white light images can be programmed), free of speckle, and its efficiency does not depend on the wavelength. These features promise novel applications in image projection, and various application fields of SLMs in microscopy.

© 2017 Optical Society of America

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References

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  1. G. Damberg, J. Gregson, and Wolfgang Heidrich, “High brightness HDR projection using dynamic freeform lensing,” ACM Trans. Graphics 35, 24 (2016).
    [Crossref]
  2. Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graphics 33, 74 (2014).
    [Crossref]
  3. T. Kiser and M. Pauly, “Caustic art,” (No. EPFL-REPORT-196165, 2012).
  4. T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).
  5. M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109–118 (2006).
    [Crossref]
  6. F. Riesz, “Non-linearity and related features of Makyoh (magic-mirror) imaging,” J. Opt. 15, 075709 (2013).
    [Crossref]
  7. G. Damberg and Wolfgang Heidrich, “Efficient freeform lens optimization for computational caustic displays,” Opt. Exp. 23, 10224–10232 (2015).
    [Crossref]
  8. Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
    [Crossref]
  9. C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
    [Crossref]
  10. M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
    [Crossref]
  11. Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
    [Crossref]
  12. F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).
  13. F. Riesz, “A note on Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, N5–N7 (2006).
    [Crossref]
  14. D. Infante-Gómez and H. P. Herzig, “Design, simulation, and quality evaluation of micro-optical freeform beam shapers at different illumination conditions,” Appl. Opt. 55, 8340–8346 (2016).
    [Crossref] [PubMed]
  15. T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
    [Crossref] [PubMed]

2016 (3)

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

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
[Crossref]

D. Infante-Gómez and H. P. Herzig, “Design, simulation, and quality evaluation of micro-optical freeform beam shapers at different illumination conditions,” Appl. Opt. 55, 8340–8346 (2016).
[Crossref] [PubMed]

2015 (1)

G. Damberg and Wolfgang Heidrich, “Efficient freeform lens optimization for computational caustic displays,” Opt. Exp. 23, 10224–10232 (2015).
[Crossref]

2014 (3)

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

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

2013 (2)

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).

F. Riesz, “Non-linearity and related features of Makyoh (magic-mirror) imaging,” J. Opt. 15, 075709 (2013).
[Crossref]

2011 (1)

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

2006 (2)

F. Riesz, “A note on Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, N5–N7 (2006).
[Crossref]

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109–118 (2006).
[Crossref]

1988 (1)

Berry, M. V.

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109–118 (2006).
[Crossref]

Bompas, P.

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

Chen, B. Y.

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Cheng, Y.

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).

Damberg, G.

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

G. Damberg and Wolfgang Heidrich, “Efficient freeform lens optimization for computational caustic displays,” Opt. Exp. 23, 10224–10232 (2015).
[Crossref]

Dobashi, Y.

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Eigensatz, M.

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

Fang, F.

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).

Feng, Z.

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
[Crossref]

Froese, B. D.

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
[Crossref]

George, N.

Gregson, J.

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

Heidrich, Wolfgang

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

G. Damberg and Wolfgang Heidrich, “Efficient freeform lens optimization for computational caustic displays,” Opt. Exp. 23, 10224–10232 (2015).
[Crossref]

Herzig, H. P.

Ijzerman, W. L.

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Infante-Gómez, D.

Iwasaki, K.

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Jakob, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Jarosz, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Kiser, T.

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

T. Kiser and M. Pauly, “Caustic art,” (No. EPFL-REPORT-196165, 2012).

Liang, R.

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
[Crossref]

Matusik, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Nguyen, M. M.

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

Nishita, T.

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Papas, M.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Pauly, M.

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

T. Kiser and M. Pauly, “Caustic art,” (No. EPFL-REPORT-196165, 2012).

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

Prins, C. R.

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Riesz, F.

F. Riesz, “Non-linearity and related features of Makyoh (magic-mirror) imaging,” J. Opt. 15, 075709 (2013).
[Crossref]

F. Riesz, “A note on Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, N5–N7 (2006).
[Crossref]

Rusinkiewicz, S.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Schwartzburg, Y.

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

Stone, T.

Tagliasacchi, A.

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

Ten Thije Boonkkamp, J. H. M.

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Testuz, R.

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

Tukker, T. W.

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Van Roosmalen, J.

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Weyrich, T.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Yue, Y.

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Zhang, X.

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).

ACM Trans. Graphics (3)

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

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

Y. Yue, K. Iwasaki, B. Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graphics 33, 31 (2014).
[Crossref]

Adv. Opt. Techn. (1)

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Techn. 2, 445–453 (2013).

Appl. Opt. (2)

Appl. Opt. Vol. (1)

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. Vol. 55, 4301 (2016).
[Crossref]

Computer Graphics Forum (Proc. of Eurographics, 2011) (1)

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” Computer Graphics Forum (Proc. of Eurographics, 2011),  30, 503–5011 (2011).
[Crossref]

Eur. J. Phys. (2)

F. Riesz, “A note on Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, N5–N7 (2006).
[Crossref]

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109–118 (2006).
[Crossref]

J. Opt. (1)

F. Riesz, “Non-linearity and related features of Makyoh (magic-mirror) imaging,” J. Opt. 15, 075709 (2013).
[Crossref]

Opt. Exp. (1)

G. Damberg and Wolfgang Heidrich, “Efficient freeform lens optimization for computational caustic displays,” Opt. Exp. 23, 10224–10232 (2015).
[Crossref]

SIAM J. Sci. Comput. (1)

C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. Van Roosmalen, W. L. Ijzerman, and T. W. Tukker, “A Monge-Ampère-solver for free-form refelector design,” SIAM J. Sci. Comput. 36, B640–B660 (2014).
[Crossref]

Other (2)

T. Kiser and M. Pauly, “Caustic art,” (No. EPFL-REPORT-196165, 2012).

T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).

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Figures (7)

Fig. 1
Fig. 1 Simulated image reconstructions at various distances behind a FOE. (a): Phase profile of FOE. Gray levels correspond to the optical path length of the FOE in a range between 0 and 50 μm. The FOE consists of 600 × 600 quadratic pixels, each with an edge length of 20 μm. (b)–(f): Image reconstructions at distances of 2 mm, 30 mm, 60 mm, 120 mm, and 200 mm, respectively.
Fig. 2
Fig. 2 Flowchart for FOE calculation. P0(x, y) is the intensity of image template. P1(x, y) is a scaled image, with a maximal intensity of π/λf, which is also the maximal curvature of the successively obtained phase map Φ(x, y). For solving the Poisson equation, a numerical Poisson solver is used. A test propagation of the obtained phase map Φ(x, y) to the image plane at a distance f is done with a wave-optical propagation method (plane wave propagation). The obtained image intensity distribution R(x, y) is visually controlled for sufficient accordance with the template (an automatized check is also possible, testing whether the output image still significantly changes with respect to the previous iteration). If image distortions are not sufficiently suppressed, a new template image P(x, y) is created by interpolation of the recent one at positions determined by the phase gradients Φ x , and Φ y and the propagation distance f.
Fig. 3
Fig. 3 Experimental setup for reconstruction of freeform optical elements displayed on a SLM. A wavelength tunable monochromator (bandwidth between 8 and 15 nm) is used as a light source, which illuminates the reflective SLM surface (working in phase-only modulation mode) through a non-polarizing beam splitter cube. The reflected light passes again through the beam splitter cube and is imaged at a reconstruction distance of 5 cm by a camera (without objective).
Fig. 4
Fig. 4 Images reconstructed from a freeform optical element displayed on a spatial light modulator. (a) Template image to be reconstructed. (b) Corresponding phase mask (covering multiples of 2π) displayed at the SLM. (c),(d),(e) Images reconstructed at a distance of 5 cm behind the SLM, after illumination with incoherent red (660 nm), green (532 nm), and blue (467 nm) light, respectively. (f): Final image composed of the red, green, and blue sub-images.
Fig. 5
Fig. 5 Comparison of an image reconstructed from a FOE, with an image reconstructed from a diffractive structure calculated by the Gerchberg-Saxton algorithm. FOE and diffractive structure have been calculated to reconstruct the letter “R”. (a) Phase distribution of FOE, as displayed on the SLM (phase range between 0 and 8π). (b) reconstructed image. (c) phase distribution of DOE displayed on SLM (phase range between 0 and 2π). (d) reconstructed image. The FOE image is free of speckle, whereas the GS image shows a pronounced speckle field.
Fig. 6
Fig. 6 Comparison of dispersive behavior of images reconstructed from a FOE and a DOE (calculated with GS-algorithm), both displayed at the SLM. Reconstruction has been performed subsequently at 3 wavelength, namely 660 nm (red), 532 nm (green) and 467 nm (blue). The resulting images are composed as an RGB-image by addressing the respective color channels with the reconstructed images.(a): Result of FOE reconstruction. (b) Result of DOE reconstruction. There the size of the red, green and blue image components is different, due to diffractive dispersion.
Fig. 7
Fig. 7 Effect of doubling the phase values of a FOE, and of a GS based hologram. (a): Image reconstructed from a FOE (displayed at the SLM). (b): Image from a FOE with doubled phase amplitude, reconstructed in the same camera plane. (c): Image reconstructed from a diffractive structure calculated with the GS algorithm. (d): Image reconstructed from a diffractive structure with doubled phase values.

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