Abstract

Phase-only light modulation shows great promise for many imaging applications, including future projection displays. While images can be formed efficiently by avoiding per-pixel attenuation of light most projection efforts utilizing phase-only modulators are based on holographic principles which rely on interference of coherent laser light and a Fourier lens. Limitations of this type of an approach include scaling to higher power as well as visible artifacts such as speckle and image noise.

We propose an alternative approach: operating the spatial phase modulator with broadband illumination by treating it as a programmable freeform lens. We describe a simple optimization approach for generating phase modulation patterns or freeform lenses that, when illuminated by a collimated, broadband light source, will project a pre-defined caustic image on a designated image plane. The optimization procedure is based on a simple geometric optics image formation model and can be implemented computationally efficient. We perform simulations and show early experimental results that suggest that the implementation on a phase-only modulator can create structured light fields suitable, for example, for efficient illumination of a spatial light modulator (SLM) within a traditional projector. In an alternative application, the algorithm provides a fast way to compute geometries for static, freeform lens manufacturing.

© 2015 Optical Society of America

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References

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  1. L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [Crossref]
  2. P. R. Haugen, H. Bartelt, and S. K. Case, “Image formation by multifacet holograms,” Appl. Opt. 22, 2822–2829 (1983).
    [Crossref] [PubMed]
  3. G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.
  4. M. Berry, “Oriental magic mirrors and the laplacian image,” Eur. J. Phys. 27, 109 (2006).
    [Crossref]
  5. M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.
  6. T. Kiser, M. Eigensatz, M. M. Nguyen, P. Bompas, and M. Pauly, Architectural Caustics - Controlling Light with Geometry (Springer, 2013).
  7. Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM T. Graphic. 33, 74 (2014).
    [Crossref]
  8. Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.
  9. Y. Ohno, “Color rendering and luminous efficacy of white led spectra,” in “Optical Science and Technology, the SPIE 49th Annual Meeting,” (International Society for Optics and Photonics, 2004), pp. 88–98.

2014 (1)

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

2006 (1)

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

1983 (1)

1969 (1)

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Bartelt, H.

Berry, M.

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

Bompas, P.

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

Case, S. K.

Chen, B.-Y.

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

Damberg, G.

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

Dobashi, Y.

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

Eigensatz, M.

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

Haugen, P. R.

Heidrich, W.

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

Hirsch, P.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Iwasaki, K.

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

Jakob, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

Jarosz, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

Jordan, J.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Kiser, T.

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

Lesem, L.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Matusik, W.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

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, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

Ohno, Y.

Y. Ohno, “Color rendering and luminous efficacy of white led spectra,” in “Optical Science and Technology, the SPIE 49th Annual Meeting,” (International Society for Optics and Photonics, 2004), pp. 88–98.

Papas, M.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

Pauly, M.

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

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

Rusinkiewicz, S.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

Schwartzburg, Y.

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

Seetzen, H.

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

Tagliasacchi, A.

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

Testuz, R.

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

Ward, G.

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

Weyrich, T.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

Whitehead, L.

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

Yue, Y.

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

ACM T. Graphic. (1)

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

Appl. Opt. (1)

Eur. J. Phys. (1)

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

IBM J. Res. Dev. (1)

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[Crossref]

Other (5)

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Pixel art with refracted light by rearrangeable sticks,” in “Computer Graphics Forum,” (Wiley Online Library, 2012), vol. 31, pp. 575–582.

Y. Ohno, “Color rendering and luminous efficacy of white led spectra,” in “Optical Science and Technology, the SPIE 49th Annual Meeting,” (International Society for Optics and Photonics, 2004), pp. 88–98.

M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in “Computer Graphics Forum,” (Wiley Online Library, 2011), vol. 30, pp. 503–511.

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

G. Damberg, H. Seetzen, G. Ward, W. Heidrich, and L. Whitehead, “3.2: High dynamic range projection systems,” in “SID Symposium Digest of Technical Papers,” (Wiley Online Library, 2007), vol. 38, pp. 4–7.

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Figures (9)

Fig. 1
Fig. 1

Geometry for image formation model: Phase modulation in lens plane at focal distance f from image plane resulting in curvature of the wavefront (phase function p(x)).

Fig. 2
Fig. 2

Intensity change due to distortion of a differential area dx.

Fig. 3
Fig. 3

Algorithm progression for six iterations: target i gets progressively distorted by backwards warping onto lens plane i p ( k ) as phase function p(k) converges towards a solution. The 3D graphic depicts the final lens height field.

Fig. 4
Fig. 4

LuxRender simulation results of a caustic image caused by an acrylic freeform lens. The inset shows the absolute intensity difference between simulated and original image, where the original image is encoded in the interval [0–1], and 0 in the difference map (green) means no difference. There are three possible sources of error: reflections off the edges of the physically thick lens (vertical and horizontal lines, misalignment and scaling of the output relative to the original (manual alignment) and the nature of the light source (not perfectly collimated).

Fig. 5
Fig. 5

Binary test pattern (left) and resulting lens height field (right) used in the wave optics simulation.

Fig. 6
Fig. 6

Spectra of standard white 3-LED (RGB) [9] (dotted graph) and the CIE standard observer color matching functions (solid graph) used in the wave optics simulation.

Fig. 7
Fig. 7

Wave optics simulation for a test lens using standard white 3-LED (RGB) spectra. The simulation was performed at 5nm intervals and mapped to a RGB color space for print.

Fig. 8
Fig. 8

3D printed refractive lens (left), broadband LED spotlight and rear-projection screen with image (right). Differences to the simulation results in Fig. (4) partially stem from an increased beam divergence compared to an ideal light source as well as limitations in the manufacturing process (3D printer).

Fig. 9
Fig. 9

Left: Wrapped phase function p(x) from Fig. (3). Right: Experimental test set-up using a phase modulator, a partially collimated, low power white LED light source and a small front projection screen. Light from an LED reflects off a phase modulator at an angle of 5 degrees and onto a projection screen at the focal distance of our lens computation. The resulting caustic image resembles the target image, but appears slightly blurry, distorted and at lower contrast compared to the simulations. This can be attributed to the broadband nature of light (the image would be sharper for separate lenses for red, green and blue LED light), and the degree of collimation of the incoming beam.

Tables (2)

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Algorithm 1 Freeform lens optimization

Tables Icon

Table 1 Run times of Algorithm 1 using five iterations for a set of different test images and image resolutions.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

u ( x ) x + f p ( x ) .
i ( u ( x ) ) = d x d u i 0 = 1 m ( x ) i 0 ,
m ( x ) = ( x u ( x ) ) × ( y u ( x ) ) 1 + f 2 p ( x ) .
i ( x + f p ( x ) ) = 1 1 + f 2 p ( x ) .
i ( x + f p ( x ) ) 1 f 2 p ( x ) ,
p ^ ( x ) = argmin p ( x ) x ( i p ( x ) 1 + f 2 p ( x ) ) 2 d x .
p ( x ) x ϕ = θ o θ i .
1 n = sin θ i sin θ o θ i θ o .
h ( x ) = h 0 + 1 n 1 p ( x ) ,

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