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Laplacian Magic Windows

People Involved

Dr Howard Snelling

Project Description

The ‘magic' comes when light reflected from the mirror is observed as an illuminated patch on a wall, on which appears, unexpectedly, an image of the pattern on the back (figure 3). Underlying the explanation is the fact that during manufacture (casting, cooling and vigorous polishing), a faint reproduction of the relief on the back is transferred to the front [3]. But this leaves unanswered the optics question: how can this relief, invisible to the eye under direct observation, cast such a clear image? A precise theoretical understanding was reached only in the present century [4] (see also [5]): the image is produced by the pattern of curvatures corresponding to the relief on the front face of the mirror, and the intensity of the image is proportional to the Laplacian function of the height function of the relief. This Laplacian image theory, by one of us (MB), is a simple but scarcely explored regime of geometrical optics, leading to predictions that were confirmed by experiment. The theory has been applied, also by one of us (DJ), to image contrast in electron microscopy [6]

Status Project Complete
Value £123,828.00
Project Dates Sep 1, 2017 - Feb 29, 2020

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