Abstract

Moiré is an appealing visual effect observable when two or more repetitive patterns are superposed. Fabrication of moiré effects has already proven to be useful in a range of applications, from art to engineering. Here, we introduce a method for designing and fabricating level-line moirés on curved surfaces. These moiré shapes are obtained by superposing a partly absorbing layer and a layer formed by an array of cylindrical lenses or by two layers of cylindrical lenses. We formulate the problem of placing an array of cylindrical lenses on a curved surface as a design problem with a small number of dimensions. The range of possible solutions can therefore be explored by a human observer. We demonstrate the quality of our method by rendered simulations and by fabrication. The resulting static displays can be manufactured using different fabrication techniques, from multi-material 3D printing to molding.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Amidror, The Theory of the Moiré Phenomenon: Volume I: Periodic Layers, vol. 38 (Springer Science & Business Media, 2009).
  2. D. Post, B. Han, and P. Ifju, Moiré Interferometry (SpringerUS, 1994), pp. 135–226.
  3. C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
    [Crossref]
  4. J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
    [Crossref]
  5. T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
    [Crossref]
  6. T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
    [Crossref]
  7. O. Bryngdahl, “Moiré: formation and interpretation,” J. Opt. Soc. Am. 64(10), 1287–1294 (1974).
    [Crossref]
  8. R. D. Hersch and S. Chosson, “Band moiré images,” in ACM Trans. Graph., vol. 23 (ACM, 2004), pp. 239–247.
  9. M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
    [Crossref]
  10. H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
    [Crossref]
  11. V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
    [Crossref]
  12. W. Zheng, S. Shen, Y. Gao, N. Liu, and Y. Liu, “Design methodology for moiré magnifier based on micro-focusing elements,” Opt. Express 25(25), 31746–31757 (2017).
    [Crossref]
  13. T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
    [Crossref]
  14. M. Papas, W. Jarosz, W. Jakob, S. Rusinkiewicz, W. Matusik, and T. Weyrich, “Goal-based caustics,” in Computer Graphics Forum, vol. 30 (Wiley Online Library, 2011), pp. 503–511.
  15. Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graph. 33(3), 1–7 (2014).
    [Crossref]
  16. Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
    [Crossref]
  17. J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
    [Crossref]
  18. H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
    [Crossref]
  19. J. S. Marsh, “Contour plots using a moiré technique,” Am. J. Phys. 48(1), 39–40 (1980).
    [Crossref]
  20. S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
    [Crossref]
  21. E. Hecht, Optics, 5e (Pearson Education India, 2017).
  22. M. P. do Carmo, Differential geometry of curves and surfaces. (Prentice Hall, 1976).
  23. Blender, Blender - a 3D modelling and rendering package, Blender Foundation, Blender Institute, Amsterdam (2019).
  24. D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
    [Crossref]
  25. Stratasys, “Objet connex3: How to maximize multi-material and color possibilities,” (2014).
  26. V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
    [Crossref]
  27. G. Oster, M. Wasserman, and C. Zwerling, “Theoretical interpretation of moiré patterns,” J. Opt. Soc. Am. 54(2), 169–175 (1964).
    [Crossref]

2020 (1)

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

2019 (3)

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
[Crossref]

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

2017 (2)

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

W. Zheng, S. Shen, Y. Gao, N. Liu, and Y. Liu, “Design methodology for moiré magnifier based on micro-focusing elements,” Opt. Express 25(25), 31746–31757 (2017).
[Crossref]

2014 (2)

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graph. 33(3), 1–7 (2014).
[Crossref]

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

2013 (3)

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

2011 (1)

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

2010 (1)

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

2009 (1)

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

1998 (1)

H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
[Crossref]

1994 (1)

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

1980 (1)

J. S. Marsh, “Contour plots using a moiré technique,” Am. J. Phys. 48(1), 39–40 (1980).
[Crossref]

1974 (1)

1964 (1)

Alda, J.

H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
[Crossref]

Amidror, I.

I. Amidror, The Theory of the Moiré Phenomenon: Volume I: Periodic Layers, vol. 38 (Springer Science & Business Media, 2009).

Babaei, V.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

Besson, T.

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

Bickel, B.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Brugger, J.

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

Bryngdahl, O.

Cadarso, V. J.

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

Chellappan, K. V.

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

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. Graph. 33(3), 1–7 (2014).
[Crossref]

Chosson, S.

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

R. D. Hersch and S. Chosson, “Band moiré images,” in ACM Trans. Graph., vol. 23 (ACM, 2004), pp. 239–247.

Dean, C. R.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Didyk, P.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

do Carmo, M. P.

M. P. do Carmo, Differential geometry of curves and surfaces. (Prentice Hall, 1976).

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. Graph. 33(3), 1–7 (2014).
[Crossref]

Erden, E.

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

Flauraud, V.

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

Forsythe, C.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Fujigaki, M.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Gao, Y.

W. Zheng, S. Shen, Y. Gao, N. Liu, and Y. Liu, “Design methodology for moiré magnifier based on micro-focusing elements,” Opt. Express 25(25), 31746–31757 (2017).
[Crossref]

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Ghahari, F.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Han, B.

D. Post, B. Han, and P. Ifju, Moiré Interferometry (SpringerUS, 1994), pp. 135–226.

Hecht, E.

E. Hecht, Optics, 5e (Pearson Education India, 2017).

Heinzle, S.

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

Hersch, R. D.

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

R. D. Hersch and S. Chosson, “Band moiré images,” in ACM Trans. Graph., vol. 23 (ACM, 2004), pp. 239–247.

Hunt, R.

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

Hutley, M.

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

Ifju, P.

D. Post, B. Han, and P. Ifju, Moiré Interferometry (SpringerUS, 1994), pp. 135–226.

Ishigami, M.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

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. Graph. 33(3), 1–7 (2014).
[Crossref]

J. Hone, K

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Jakob, W.

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

Kamal, H.

H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
[Crossref]

Katoch, J.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Kautz, J.

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

Kim, P.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Koshino, M.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Krivánek, J.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Liu, N.

Liu, Y.

Lu, Y.

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

Maher, P.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Marsh, J. S.

J. S. Marsh, “Contour plots using a moiré technique,” Am. J. Phys. 48(1), 39–40 (1980).
[Crossref]

Matusik, W.

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

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

Mérigot, Q.

J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
[Crossref]

Meyron, J.

J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
[Crossref]

Moon, P.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Morimoto, Y.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Myszkowski, K.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Nindel, T.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

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. Graph. 33(3), 1–7 (2014).
[Crossref]

Oster, G.

Papas, M.

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

Pauly, M.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

Peers, P.

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

Post, D.

D. Post, B. Han, and P. Ifju, Moiré Interferometry (SpringerUS, 1994), pp. 135–226.

Ramos, J.

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

Ri, S.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Rittig, T.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Rusinkiewicz, S.

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

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

Savander, P.

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

Schwartzburg, Y.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

Shen, S.

Shepard, L.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Sidler, K.

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

Stevens, R.

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

Sumin, D.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Surman, P.

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

Tagliasacchi, A.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

Taniguchi, T.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Testuz, R.

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

Thibert, B.

J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
[Crossref]

Tompkin, J.

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

Urey, H.

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

Voelkel, R.

H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
[Crossref]

Walger, T.

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “1d moiré shapes by superposed layers of micro-lenses,” Opt. Express 27(26), 37419–37434 (2019).
[Crossref]

Wang, L.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Wasserman, M.

Watanabe, K.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Webster, G.

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

Weyrich, T.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

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

Wilkie, A.

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[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. Graph. 33(3), 1–7 (2014).
[Crossref]

Zheng, W.

Zwerling, C.

ACM Trans. Graph. (6)

J. Tompkin, S. Heinzle, J. Kautz, and W. Matusik, “Content-adaptive lenticular prints,” ACM Trans. Graph. 32(4), 1 (2013).
[Crossref]

Y. Yue, K. Iwasaki, B.-Y. Chen, Y. Dobashi, and T. Nishita, “Poisson-based continuous surface generation for goal-based caustics,” ACM Trans. Graph. 33(3), 1–7 (2014).
[Crossref]

Y. Schwartzburg, R. Testuz, A. Tagliasacchi, and M. Pauly, “High-contrast computational caustic design,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

J. Meyron, Q. Mérigot, and B. Thibert, “Light in power: a general and parameter-free algorithm for caustic design,” ACM Trans. Graph. 37(6), 1–13 (2019).
[Crossref]

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28(3), 1–6 (2009).
[Crossref]

D. Sumin, T. Rittig, V. Babaei, T. Nindel, A. Wilkie, P. Didyk, B. Bickel, J. Křivánek, K. Myszkowski, and T. Weyrich, “Geometry-aware scattering compensation for 3D printing,” ACM Trans. Graph. 38(4), 1–14 (2019).
[Crossref]

Am. J. Phys. (1)

J. S. Marsh, “Contour plots using a moiré technique,” Am. J. Phys. 48(1), 39–40 (1980).
[Crossref]

Exp. Mech. (1)

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

IEEE Comput. Grap. Appl. (1)

V. Babaei, J. Ramos, Y. Lu, G. Webster, and W. Matusik, “Fabsquare: Fabricating photopolymer objects by mold 3d printing and uv curing,” IEEE Comput. Grap. Appl. 37(3), 34–42 (2017).
[Crossref]

J. Opt. Soc. Am. (3)

T. Walger, T. Besson, V. Flauraud, R. D. Hersch, and J. Brugger, “Level-line moirés by superposition of cylindrical microlens gratings,” J. Opt. Soc. Am. 37(2), 209–218 (2020).
[Crossref]

G. Oster, M. Wasserman, and C. Zwerling, “Theoretical interpretation of moiré patterns,” J. Opt. Soc. Am. 54(2), 169–175 (1964).
[Crossref]

O. Bryngdahl, “Moiré: formation and interpretation,” J. Opt. Soc. Am. 64(10), 1287–1294 (1974).
[Crossref]

Light: Sci. Appl. (1)

V. J. Cadarso, S. Chosson, K. Sidler, R. D. Hersch, and J. Brugger, “High-resolution 1d moirés as counterfeit security features,” Light: Sci. Appl. 2(7), e86 (2013).
[Crossref]

Nature (1)

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, L. Shepard, K J. Hone, and P. Kim, “Hofstadter’s butterfly and the fractal quantum hall effect in moiré superlattices,” Nature 497(7451), 598–602 (2013).
[Crossref]

Opt. Eng. (1)

H. Kamal, R. Voelkel, and J. Alda, “Properties of moiré magnifiers,” Opt. Eng. 37(11), 3007–3014 (1998).
[Crossref]

Opt. Express (2)

Proc. IEEE (1)

H. Urey, K. V. Chellappan, E. Erden, and P. Surman, “State of the art in stereoscopic and autostereoscopic displays,” Proc. IEEE 99(4), 540–555 (2011).
[Crossref]

Pure Appl. Opt. (1)

M. Hutley, R. Hunt, R. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3(2), 133–142 (1994).
[Crossref]

Other (8)

R. D. Hersch and S. Chosson, “Band moiré images,” in ACM Trans. Graph., vol. 23 (ACM, 2004), pp. 239–247.

I. Amidror, The Theory of the Moiré Phenomenon: Volume I: Periodic Layers, vol. 38 (Springer Science & Business Media, 2009).

D. Post, B. Han, and P. Ifju, Moiré Interferometry (SpringerUS, 1994), pp. 135–226.

E. Hecht, Optics, 5e (Pearson Education India, 2017).

M. P. do Carmo, Differential geometry of curves and surfaces. (Prentice Hall, 1976).

Blender, Blender - a 3D modelling and rendering package, Blender Foundation, Blender Institute, Amsterdam (2019).

Stratasys, “Objet connex3: How to maximize multi-material and color possibilities,” (2014).

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

Supplementary Material (10)

NameDescription
» Visualization 1       Visualization 1, Good and Bad Comparison
» Visualization 2       Visualization 2, Dual-lens Graces on Saddle Simulation
» Visualization 3       Visualization 3, Dual-lens David on Saddle Simulation
» Visualization 4       Visualization 4, David on Paraboloid Fabrication
» Visualization 5       Visualization 5, Flower on Paraboloid Fabrication
» Visualization 6       Visualization 6, Mosque on Saddle Fabrication
» Visualization 7       Visualization 7, David on Saddle Fabrication
» Visualization 8       Visualization 8, Dual-lens Graces on Saddle Fabrication
» Visualization 9       Visualization 9, Dual-lens David on Saddle Fabrication
» Visualization 10       Visualization 10, Silicone Cast of Dual-lens moiré

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1.
Fig. 1. (a) Elevation profile extracted from a gray-level image, (b) base layer shifted according to the elevation profile, (c) revealing layer, and (d) superposition of the base and revealing layers yielding the level-line moiré (taken with permission from [6]).
Fig. 2.
Fig. 2. Top row: (a) elevation profile formed by a gray-level image, (b) base layer shifted according to the elevation profile, (c) a closer view of the base layer. Bottom row: superposition of the base and revealing layers yielding the level-line moiré, shown at different tilt angles.
Fig. 3.
Fig. 3. Comparison between a low (left) and high (right) quality level-line moiré, see Visualization 1
Fig. 4.
Fig. 4. (a) A cylindrical lens array on top of a base layer. (b) Cross section of a single cylindrical lenslet with $r$: lens radius, $w$: lens pitch (or width), $h$: sag-height, $f_{l}$: focal length, and $d$: lens body thickness.
Fig. 5.
Fig. 5. (a) Three steps in creating surface moiré. (b) Lenses with equal radius ($r$) are fitted, resulting in different angular field of views (AFOV). (c) By adapting the radius of each lens, the angular field of view $\alpha$ remains constant.
Fig. 6.
Fig. 6. (a) Inspired by [4], we design a base surface (in green) that is both parallel to the individual lenses and in their focal plane. (b) The rendered simulation of such a design. The nonsmooth base-layer causes artifacts. (c) For a given lens surface, we can compute the offset surface (blue), the focal surface (red) and one of the interpolation surfaces (green).
Fig. 7.
Fig. 7. Cross-section of a transparent device formed by two gratings of transparent cylindrical lenses with light rays oriented towards the eye of an observer having (a) an unshifted base and (b) a base shifted by quarter of the lens repetition period (schematic view).
Fig. 8.
Fig. 8. Design space explored by varying the weighting parameter $a$ and the distance parameter $d$, see formula 9.
Fig. 9.
Fig. 9. Elevation profiles. (a) David. (b) Mosque. (c) Flower. (d) Graces.
Fig. 10.
Fig. 10. Dual-lens surface moiré simulation: (a) and (b) show the Graces level-line moiré on a saddle surface, Visualization 2; (c) and (d) show the David’s level-line moiré on a saddle surface,Visualization 3.
Fig. 11.
Fig. 11. 3D printed Parametric surfaces from 2 different angles each, (a) Paraboloid with David elevation profile, Visualization 4. (b) Paraboloid with Flower elevation profile, Visualization 5. (c) Saddle with Mosque elevation profile, Visualization 6. (d) Saddle with David elevation profile, Visualization 7.
Fig. 12.
Fig. 12. (a) and (b) 3D printed dual-lens surface moiré from 2 different angles each, Visualization 8 and Visualization 9 (c) Silicone cast of a dual-lens moiré, illuminated with a green light, from 2 different angles. Visualization 10.
Fig. 13.
Fig. 13. Superposition of a revealer (gray) and a base (black). The transparent lines of the revealer are indexed with $r$. The black lines of the base are indexed with $b$. The moiré fringe lines are indexed with $m$.
Fig. 14.
Fig. 14. A parameterized curve $\gamma (t)$ in three dimensional space.

Equations (20)

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

( r h ) 2 = r 2 ( w / 2 ) 2
f l = η l η l η a i r r
h = r r 2 ( w 2 ) 2
P : f ( u , v ) .
s i n ( α / 2 ) = w 2 r .
Q : g ( u , v ; d ) = f ( u , v ) d n f ( u , v )
n f = f u × f v f u × f v .
R : h ( u , v ) = f ( u , v ) n f ( u , v ) η l η l η a i r r s | f u | .
S : s ( u , v ; a , d ) = ( 1 a ) g ( u , v ; d ) + a h ( u , v ) .
m = r b
ρ ( x , y ) = r T r
β ( x , y ) = b T b
ρ ( x , y ) T r β ( x , y ) T b = m
y = r T
y g ( x , y ) = b T
m = y T y g ( x , y ) T = g ( x , y ) T g ( x , y ) = m T
Δ s | Δ γ | = | γ ( t + Δ t ) γ ( t ) | = | d γ d t Δ t + 1 2 d 2 γ d t 2 ( Δ t ) 2 | | d γ d t | Δ t .
d s = | d γ d t | d t = | γ ˙ | d t = γ ˙ . γ ˙ d t .
d s = | d γ d t | d t = | f u d u d t + f v d v d t | d t = ( f u u ˙ + f v v ˙ ) . ( f u u ˙ + f v v ˙ ) d t = f u . f u . u ˙ . u ˙ + 2 f u . f v . u ˙ . v ˙ + f v . f v . v ˙ . v ˙ d t
d s = f u . f u . u ˙ . u ˙ + 0 + 0 . d t = | f u | d u | d s d u | = | f u |