The Reflector Problem and the Inverse-square Law
نویسنده
چکیده
∗ We introduce a model to design reflectors that take into account the inverse-square law for radiation, i.e. it considers how far the reflector is from the source. The radiant intensity at the source and the irradiance distribution at the target are given. We prove the existence of solutions in the near field case, when the input and output energies are prescribed. A uniqueness property will also be shown.The reflectors constructed are weak solutions of a Monge-Ampère type partial differential equation . This is a joint work with Professor Cristian Gutiérrez, and it has been partial funded by NSF grant DMS-1201401. 1
منابع مشابه
Behavior correction of the inverse square law in irradiation room for volumetric source and detector
The inverse-square law is used to calculate the radiation flux at difference distances from the source. This law is applied for point source and point detector in vacuum. This research aims to study the point behavior of volumetric source and detector by undertaking required corrections on inverse-square law through the elimination of scattered neutrons contribution. The measurements have been ...
متن کاملNURBS-based Inverse Reflector Design
Commonly used direct rendering techniques simulate light transport for a complete scene, specified in terms of light sources, geometry, materials, participating media, etc. On the other hand, inverse rendering problems take as input a desired light distribution and try to find the unknown parts of the scene needed to get such light field. The latter kind, where inverse reflector design is inclu...
متن کاملA TRANSIENT TWO-DIMENTIONAL INVERSE ESTIMATION OF THE METAL-MOLD HEAT TRANSFER COEFFICIENT DURING SQUEEZE CASTING of AL-4.5WT%CU
In this paper, a transient, two-dimensional and nonlinear inverse heat conduction problem in solidification process is considered. Genetic algorithm is applied for the identification of the interfacial heat transfer coefficients during squeeze casting of commercial aluminum alloy (Al-4.5wt%Cu) by assuming a priori information regarding the functional form of the unknown heat transfer coefficien...
متن کاملSolving the Monge-Ampère Equations for the Inverse Reflector Problem
The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the target, e.g., a projected image on a screen. This optical problem can mathematically be understood as a problem of optimal transport and equivalently be expressed ...
متن کاملInverse Problems in Imaging Systems and the General Bayesian Inversion Frawework
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Baye...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013