The Inverse Scattering Problem in Geometrical Optics and the Design of Reflectors: January, 1958 (Classic Reprint) - Hardcover

Joseph B. Keller

9780265840450: The Inverse Scattering Problem in Geometrical Optics and the Design of Reflectors: January, 1958 (Classic Reprint)

Hardcover

ISBN 10: 0265840457 ISBN 13: 9780265840450

Publisher: Forgotten Books, 2017

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Turn scattered light into a blueprint for mirrors.

This classic study shows how, in geometrical optics, the shape of a reflector can be determined from how it scatters and reflects light. It covers two and three dimensions, explaining how the curvature and surface properties drive the direction and intensity of reflected rays.

In clear, practical terms, the work derives formulas that link the differential scattering cross section and the reflection coefficient to the reflector’s shape. It includes concrete examples, such as circular reflectors and surfaces of revolution, and discusses both direct and inverse problems. The methods illuminate how design problems involving reflectors can be approached as inverse problems, with insights for optical system design.

How energy conservation underpins the relation between incident and reflected light
Parametric equations that describe reflector shapes from scattering data
Examples showing concave vs. convex surfaces and their implications
Conditions under which unique determination of the shape is possible

Ideal for readers of mathematical physics and optical design, who want a rigorous yet applicable treatment of reflector geometry and light scattering.
The Inverse Scattering Problem in Geometrical Optics and the Design of Reflectors

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