Deterministic Approximations of Random Reflectors
Within classical optics, one may add microscopic "roughness'' to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly microscopic) one obtains a flat surface that reflec...
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| Format: | Article |
| Language: | en_US |
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American Mathematical Society (AMS)
2015
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| Online Access: | http://hdl.handle.net/1721.1/93154 https://orcid.org/0000-0002-5951-4933 |
| Summary: | Within classical optics, one may add microscopic "roughness'' to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly microscopic) one obtains a flat surface that reflects randomly, i.e., the transition from incoming to outgoing ray is described by a probability kernel (whose form depends on the nature of the microscopic roughness).
We consider two-dimensional optics (a.k.a. billiards) and show that every random reflector on a line that satisfies a necessary measure-preservation condition (well established in the theory of billiards) can be approximated by deterministic reflectors in this way. |
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