Abstract

Scratches on the surface of transparent or nontransparent media reflect, refract, or diffract incident light. Under parallel illumination each length element of a scratch produces a fan beam (in the absence of diffuse scattering). Looking at a curved scratch, the right and left eyes are hit by different fan beams. Thus each eye sees a separate light spot on the scratch, which is the origin of the fan beam. In certain circumstances these spots can be stereoscopically combined by both eyes and only one light spot in space is seen. Three-dimensional images can be created by a large number of such spots originating from circular or semicircular scratches. These scratches can easily be produced on the surface of Plexiglas or other materials by using a compass. Some experiments and the theory of the so-called scratchograms are given. A comparison with holographic images is made.

© 2003 Optical Society of America

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References

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  1. W. J. Beaty, “Hand-drawn holograms,” http://www.amasci.com/amateur/holo1.html .
  2. N. H. Abramson, “Incoherent holography,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 153–164 (2000).
    [CrossRef]
  3. H. Weil, “Improvement in advertising and like signs,” UK patent37208/34 (December1934).
  4. W. Plummer, L. Gardner, “A mechanically generated hologram,” Appl. Opt. 31, 6585–6588 (1992).
    [CrossRef] [PubMed]
  5. P. Hariharan, Optical Holography (Cambridge University, Cambridge, UK, 1987).

1992 (1)

Abramson, N. H.

N. H. Abramson, “Incoherent holography,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 153–164 (2000).
[CrossRef]

Gardner, L.

Hariharan, P.

P. Hariharan, Optical Holography (Cambridge University, Cambridge, UK, 1987).

Plummer, W.

Weil, H.

H. Weil, “Improvement in advertising and like signs,” UK patent37208/34 (December1934).

Appl. Opt. (1)

Other (4)

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

N. H. Abramson, “Incoherent holography,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 153–164 (2000).
[CrossRef]

H. Weil, “Improvement in advertising and like signs,” UK patent37208/34 (December1934).

P. Hariharan, Optical Holography (Cambridge University, Cambridge, UK, 1987).

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Figures (8)

Fig. 1
Fig. 1

Parallel illumination of a scratch with length element at P, producing a fan beam. The plane of the fan beam is shown by the direction of the incident light beam s and the radius of curvature R. Every length element of the scratch is the origin of such a fan beam.

Fig. 2
Fig. 2

Intensity distribution of the fan beam produced by circular scratches (width of Fig. 2, 17 cm). (a) Circular scratch R in millimeters. The width of the scratch is ∼0.06 mm. The scratch is illuminated approximately in a perpendicular direction by a laser beam ∼0.7 mm in diameter. The distance between the screen and the scratch is 10 cm. (The central spot of the laser beam passes a hole.) The fan beam is created by diffraction, refraction, and reflection. (b) Circular scratch with a semicircular profile (diameter, 3 mm) R of 4 cm. The scratch is illuminated in a perpendicular direction by a laser beam ∼3 mm in diameter. The distance between the screen and the scratch is 10 cm. The fan beam is created by refraction and reflection.

Fig. 3
Fig. 3

Light spots from a circular scratch [as in Fig. 2(b)] illuminated by a spot light at a 3.5-m distance (nearly parallel light). (The angle of illumination with the horizontal plane, ε z = 20°; angle of observation with the horizontal plane, -6°): (a) camera in the left-eye position, (b) camera in the right-eye position (eye distance, 7 cm).

Fig. 4
Fig. 4

A semicircular scratch as each eye is hit by a different fan beam. At the origin of the fan beams a light spot is visible. Each eye sees a different spot. A light point in space can be seen by stereoscopic viewing.

Fig. 5
Fig. 5

Coordinate system with the origin at the central point between the eyes. A circular scratch is shown at (x s , y s , z s ). It is projected by the parallel incident light beam into the xy plane. The fan beams entering each eye and the light spots on the scratch are constructed. In the equations of Figs. 5 and 6, absolute values are used, in contrast to Eq. (1)].

Fig. 6
Fig. 6

The yz plane in Fig. 5.

Fig. 7
Fig. 7

The xz plane in Fig. 5. A circular scratch produces two stereoscopic light points behind and in front of the scratch.

Fig. 8
Fig. 8

Construction of stereoscopic 3D images by using circular scratches. The corner points of the cube are created by four circular scratches yielding four points, ○, in front of the z s plane (the plane of the scratch) and, □, four points behind. Changing the radius connects the corner points in front and behind the z s plane. Scratches with the same radius connect the other corner points.

Equations (11)

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xp=-zs tan εztan εx+xs, yp=-zs tan εz+ys.
ξ=A sin ηxp2+yp21/2-A2cos η.
ξ=-Aypxp2+yp2+Axp2-Aypxp2+yp2.
Δs=Δs sin η=Rξ sin η.
d=zs+dA Δs=zsΔsA1-Δs/AzsΔsA.
dyp2xp2+yp23/2 Rzs=zs tan εz-ys2zstan εztan εx-xs2+zs tan εz-ys23/2 zsR.
d=Rtan εz-ys+Rzs,
dd.
dd=R1-R/zsR.
d=zs tan εz-ys2K1-Rzs tan εz-ys2K Rzs
K=zstan εztan εx-xs2+zs tan εz-ys23/2.

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