Journal ArticleDOI
Reflector synthesis for generalized far-fields
B S Westcott,A P Norris +1 more
Reads0
Chats0
TLDR
In this paper, a geometric-optics approximation is used to synthesize a reflector surface to produce a generalized far-field when illuminated by a point source, subject to nonlinear boundary conditions.Abstract:
The theoretical foundations of a proposed new method of reflector design are presented The geometric-optics approximation is used to synthesise a reflector surface to produce a generalized far-field when illuminated by a point source The far-field can have a prescribed variation in two variables and source blockage can be removed The technique of differential geometry are used to show that a nonlinear second-order partial differential equation, the Monge-Ampere equation, must be solved subject to nonlinear boundary conditions Particular consideration is given to the special case of fields with even azimuthal symmetry when referred to spherical polar coordinates The method is applicable to problems in optics acoustics and microwave antenna design where shaped beams are requiredread more
Citations
More filters
Journal ArticleDOI
On the design of a reflector antenna
TL;DR: The reflector antenna design problem is reduced to that of finding a minimizer or a maximizer of a linear functional subject to a linear constraint, therefore it becomes an linear optimization problem and algorithms in linear programming apply.
Book ChapterDOI
Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics
TL;DR: In this article, the authors survey some of these problems and describe the current progress in their study and present algorithms for computing solutions numerically, as well as a survey of the current state of the art in these problems.
Journal ArticleDOI
Local estimates for some fully nonlinear elliptic equations
TL;DR: In this paper, a method to derive local estimates for some classes of fully nonlinear elliptic equations is presented. But the method is not suitable for all classes of equations and cannot be applied to a large class of equations.
Journal ArticleDOI
Weak solutions of one inverse problem in geometric optics
TL;DR: In this paper, the authors considered the problem of recovering a closed convex reflecting surface such that for a given point source of light (inside the convex body bounded by the surface) the reflected directions cover a unit sphere with prespecified in advance density.
Go synthesis of offset dual reflectors
TL;DR: In this article, the synthesis of a dual offset reflector system with uniform aperture phase is formulated using mathematically exact equations under the assumptions of geometrical optics and demonstrated the existence of numerical solutions to problems of practical significance.
References
More filters
Book
Extrinsic geometry of convex surfaces
TL;DR: The intrinsic geometry of convex surfaces always becomes the most wanted book and many people are absolutely searching for this book as mentioned in this paper, which means that many love to read this kind of book.
Journal ArticleDOI
Realisation of generalised far fields by reflector synthesis
A P Norris,B.S. Westcott +1 more
TL;DR: In this article, a method of designing reflector surfaces by the geometrical-optics approximation is introduced, in which a given generalised far field is realized when the reflector is illuminated by a point source.
Related Papers (5)
The geometrical optics design of reflectors using complex coordinates
Reflector design for two-variable beam shaping in the hyperbolic case
F. Brickell,B S Westcott +1 more