Abstract

A visually striking image phenomenon has been noticed during mechanical abrasion of a plane nickel optical surface. After the lap was removed and the surface was cleaned, two clear ghost images of the absent lap were visible in full detail, in each of four abrasion test areas. In a binocular view these ghost images were plainly situated above and below the actual optical surface, an appearance commonly associated with a reflection hologram. A theory is offered to explain the phenomenon by simple geometry.

© 1992 Optical Society of America

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References

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  1. M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 263 ff.

Kerker, M.

M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 263 ff.

Other

M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 263 ff.

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Figures (7)

Fig. 1
Fig. 1

Four regions of mechanically abraded surface viewed by reflected diffuse light. Dark areas show wear; the lighter annulus is the path followed by the hollow center of the lap.

Fig. 2
Fig. 2

Crossed-eye stereogram of the abraded surface illuminated by a small tungsten source high and to the right of the camera. Each wear pattern shows two out-of-surface ghost images of the abrading lap.

Fig. 3
Fig. 3

Geometry to illustrate the scattering properties of a fine, smooth engraved scratch on a metal optical surface. Light striking the scratch at an angle ϕ with its axis, from any azimuth on the cone to the left, will be spread over the forward cone to the right, at the same half-angle ϕ.

Fig. 4
Fig. 4

Viewing geometry for an explanation of the ghost lap images. Here we consider the appearance of a single scribed circle of radius a under illumination from direction L.

Fig. 5
Fig. 5

With vertical illumination, the single engraved circle presents bright glints, at the points noted, to a binocular observer.

Fig. 6
Fig. 6

Merged space image of points A and C from Fig. 5 will be an image at depth z below the surface, while the merged space image of B and D will appear at height z′ above the surface.

Fig. 7
Fig. 7

Points C1 and C2 are centers of circles of radius a formed by two sharp grains at the near and far edges of the orbited lap. The corresponding merged images that appear beneath the optical surface are G1 and G2, while H1 and H2 are the corresponding merged images that appear above the surface. The ghost images of the lap extend from G1 to G2 and from H1 to H2, formed in full pictorial detail by a myriad of scribed circles, all of the same radius a, having centers distributed across the region from C1 to C2.

Equations (6)

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E ^ · S ^ = - L ^ · S ^
E = ( r - a cos Θ ) ι ^ + ( q - a sin Θ ) j ^ + h k ^
S ^ = - sin Θ ι ^ + cos Θ j ^ .
E · S ^ = - ( r - a cos Θ ) sin Θ + ( q - sin Θ ) cos Θ = 0.
tan Θ = q / r .
z = a h / d ,             z = a h / d ,

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