Abstract

By tooling a spot-illuminated surface to control the flow of specular glints under motion, one can produce holographic view-dependent imagery. This paper develops the differential equations that govern the shape of the specular surfaces, and illustrates how solutions can be constructed for different kinds of motion, lighting, host surface geometries, and fabrication constraints, leading to some unconventional forms of holography.

© 2011 Optical Society of America

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References

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  1. P. Kirkpatrick, “A binocular illusion,” Am. J. Phys. 22, 493(1954).
    [CrossRef]
  2. J. Lott, “Reflections on a gramophone record,” Math. Gaz. 47, 113–118 (1963).
    [CrossRef]
  3. J. Walker, “What do phonograph records have in common with windshield wipers?,” Sci. Am. 261, 106–109 (1989).
    [CrossRef]
  4. W. T. Plummer and L. R. Gardner, “A mechanically generated hologram?,” Appl. Opt. 31, 6585–6588 (1992).
    [CrossRef] [PubMed]
  5. H. Weil, “Improvement in advertising and the like signs,” U.K. patent 37.208/34 (1934).
  6. E. Garfield, “ISI’s ‘World Brain’ by Gabriel Liebermann: the world’s first holographic engraving,” in Essays of an Information Scientist (ISI, 1981), Vol.  5, pp. 348–354.
  7. W. Beaty, “Hand-drawn holograms,” http://amasci.com/amateur/holo1.html.
  8. W. Beaty, “Drawing holograms by hand,” Proc. SPIE 5005, 156–167 (2003).
    [CrossRef]
  9. J. Eichler, L. Dünkel, and O. Gonçalves, “Three-dimensional image construction by curved surface scratches,” Appl. Opt. 42, 5627–5633 (2003).
    [CrossRef] [PubMed]
  10. A. G. Augier and R. B. Sánchez, “Hologravure as a computer-generated and laser engraved scratch hologram,” Opt. Commun. 284, 112–117 (2011).
    [CrossRef]
  11. C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
    [CrossRef]
  12. R. A. Hicks, “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323–330 (2005).
    [CrossRef]
  13. There are also two degenerate solutions: The exterior of an infinitesimal parabolic needle for p at the surface s (ϵ=1) and the interior of a sphere for p at light source i (ϵ→0).
  14. G.-I. Kweon and C.-H. Kim, “Apherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103(2007).
    [CrossRef]
  15. For example, a hologram in which the view circles twice around a 3D head, seeing a different face in each cycle.
  16. ArtPrize, Grand Rapids, Michigan (2009-2010), http://www.artprize.org.

2011

A. G. Augier and R. B. Sánchez, “Hologravure as a computer-generated and laser engraved scratch hologram,” Opt. Commun. 284, 112–117 (2011).
[CrossRef]

2010

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

2007

G.-I. Kweon and C.-H. Kim, “Apherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103(2007).
[CrossRef]

2005

2003

1992

1989

J. Walker, “What do phonograph records have in common with windshield wipers?,” Sci. Am. 261, 106–109 (1989).
[CrossRef]

1963

J. Lott, “Reflections on a gramophone record,” Math. Gaz. 47, 113–118 (1963).
[CrossRef]

1954

P. Kirkpatrick, “A binocular illusion,” Am. J. Phys. 22, 493(1954).
[CrossRef]

Augier, A. G.

A. G. Augier and R. B. Sánchez, “Hologravure as a computer-generated and laser engraved scratch hologram,” Opt. Commun. 284, 112–117 (2011).
[CrossRef]

Beaty, W.

W. Beaty, “Drawing holograms by hand,” Proc. SPIE 5005, 156–167 (2003).
[CrossRef]

W. Beaty, “Hand-drawn holograms,” http://amasci.com/amateur/holo1.html.

Dünkel, L.

Eichler, J.

Gardner, L. R.

Garfield, E.

E. Garfield, “ISI’s ‘World Brain’ by Gabriel Liebermann: the world’s first holographic engraving,” in Essays of an Information Scientist (ISI, 1981), Vol.  5, pp. 348–354.

Gonçalves, O.

Gross, M.

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

Hicks, R. A.

Kim, C.-H.

G.-I. Kweon and C.-H. Kim, “Apherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103(2007).
[CrossRef]

Kirkpatrick, P.

P. Kirkpatrick, “A binocular illusion,” Am. J. Phys. 22, 493(1954).
[CrossRef]

Kweon, G.-I.

G.-I. Kweon and C.-H. Kim, “Apherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103(2007).
[CrossRef]

Lott, J.

J. Lott, “Reflections on a gramophone record,” Math. Gaz. 47, 113–118 (1963).
[CrossRef]

Matusik, W.

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

Plummer, W. T.

Regg, C.

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

Rusinkiewicz, S.

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

Sánchez, R. B.

A. G. Augier and R. B. Sánchez, “Hologravure as a computer-generated and laser engraved scratch hologram,” Opt. Commun. 284, 112–117 (2011).
[CrossRef]

Walker, J.

J. Walker, “What do phonograph records have in common with windshield wipers?,” Sci. Am. 261, 106–109 (1989).
[CrossRef]

Weil, H.

H. Weil, “Improvement in advertising and the like signs,” U.K. patent 37.208/34 (1934).

ACM Trans. Graph.

C. Regg, S. Rusinkiewicz, W. Matusik, and M. Gross, “Computational highlight holography,” ACM Trans. Graph. 29, 170 (2010).
[CrossRef]

Am. J. Phys.

P. Kirkpatrick, “A binocular illusion,” Am. J. Phys. 22, 493(1954).
[CrossRef]

Appl. Opt.

J. Korean Phys. Soc.

G.-I. Kweon and C.-H. Kim, “Apherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103(2007).
[CrossRef]

J. Opt. Soc. Am. A

Math. Gaz.

J. Lott, “Reflections on a gramophone record,” Math. Gaz. 47, 113–118 (1963).
[CrossRef]

Opt. Commun.

A. G. Augier and R. B. Sánchez, “Hologravure as a computer-generated and laser engraved scratch hologram,” Opt. Commun. 284, 112–117 (2011).
[CrossRef]

Proc. SPIE

W. Beaty, “Drawing holograms by hand,” Proc. SPIE 5005, 156–167 (2003).
[CrossRef]

Sci. Am.

J. Walker, “What do phonograph records have in common with windshield wipers?,” Sci. Am. 261, 106–109 (1989).
[CrossRef]

Other

H. Weil, “Improvement in advertising and the like signs,” U.K. patent 37.208/34 (1934).

E. Garfield, “ISI’s ‘World Brain’ by Gabriel Liebermann: the world’s first holographic engraving,” in Essays of an Information Scientist (ISI, 1981), Vol.  5, pp. 348–354.

W. Beaty, “Hand-drawn holograms,” http://amasci.com/amateur/holo1.html.

There are also two degenerate solutions: The exterior of an infinitesimal parabolic needle for p at the surface s (ϵ=1) and the interior of a sphere for p at light source i (ϵ→0).

For example, a hologram in which the view circles twice around a 3D head, seeing a different face in each cycle.

ArtPrize, Grand Rapids, Michigan (2009-2010), http://www.artprize.org.

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Figures (1)

Fig. 1
Fig. 1

Geometry of specular holography. (a) Glints on a curved surface are perceived as an off-surface point. (b) Ideal surface is any of a foliation of quartics (for reflection, conics) with one focus at the light and the other at the point. (c) Equivalent ridged surface is bounded by surfaces from the foliation, the host surface, and a set of cones. (d) Striping of tool paths on a host surface whose swept volume osculates the foliation.

Equations (11)

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n i s i s η 1 + η 2 e s e s ,
tangents normal to local axis:     T s n ,
glints lie on sightline:     ( s p ) ( e p ) ,
tooling conforms to surface:     s H Δ .
0 = s ˙ , i s i s η 1 ± η 2 p s p s
= s ˙ , ( i s ) d ps η 1 ± η 2 d is ( p s ) ,
n i e + e i ( sin θ , cos α , cos θ + sin α ) .
t 1 n × N ( cos α , sin θ , 0 ) .
y ( θ ) = d y d x d x d θ d θ = p z sec α sec θ + C 0 ,
thus     y ( x ) = p z ( sec α ) [ ( x / p z ) 2 + 1 ] 1 / 2 + C 0 .
t 2 t 1 × n ( sin θ , cos α , cos 2 α + sin 2 θ cos θ + sin α ) ,

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