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    Nonlinear PDE and Optical Surfaces Design

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    TETDEDXSabra-temple-0225E-12235.pdf
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    Genre
    Thesis/Dissertation
    Date
    2015
    Author
    Sabra, Ahmad
    Advisor
    Gutiérrez, Cristian E., 1950-
    Committee member
    Mitrea, Irina
    Mendoza, Gerardo A.
    Hicks, R. Andrew
    Department
    Mathematics
    Subject
    Mathematics
    Optics
    Geometric Optics
    Irradiance
    Monge Ampere
    Reflectors
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/3508
    
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    DOI
    http://dx.doi.org/10.34944/dspace/3490
    Abstract
    We introduce two models to design near field reflectors in R^3 that solve an inverse problem in radiometry, taking into account the inverse square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from the source to avoid obstruction. In the second model, the reflectors are neither convex nor concave and do not block the rays even if they are close to the source.
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