Controlling light with freeform optics: Recent progress in computational methods for optical design of freeform lenses with prescribed irradiance properties

摘要

Optical devices utilizing freeform optical surfaces have many applications in illumination and beam shaping. In a typical application the optical surface is required to redirect and reshape the radiance pattern of the source so that the output irradiance is concentrated on a given target set and has a prescribed pattern. Problems of this kind are referred to as the "prescribed irradiance problems". Their solutions define the shapes of required optical surfaces. The freeform must be used when the shapes of the sources and/or targets and input and/or output radiation patterns lack special symmetries such as rotational or rectangular. When such symmetries are not available traditional designs lead to highly energy inefficient devices. It is known that often (especially for small and collimated sources) the prescribed irradiance problems can be reduced to finding solutions to strongly nonlinear partial differential equations (PDE's). The theory and computational methods for solving reliably these equations require the most advanced mathematical tools many of which still have to be developed. In recent years there has been a large surge of publications in which various techniques for solving the prescribed irradiance problems were proposed. However, most of these techniques have limited validity as they can be justified only aposteriori, that is, only in cases if some "candidate" solution can be found. By contrast, we have developed a new approach not suffereing from such defect. In our approach we avoid direct use of PDE's. Instead, we combine basic physical and variational principles to develop reliable (and provably convergent) methods for solving wide classes of prescribed irradiance problems. In this paper we present the results of applying this approach to the design problem in which we wish to design a freeform single lens converting a collimated light beam into an output beam irradiating at a given target in the near-field in three-dimensional space with prescribed irradiance pattern. The developed methods are very general and applicable to near- and far-field problems. They can also be used to design optical systems with two freeform lenses, thus permitting control of the output irradiance and optical path length. These methods apply also to optical systems with small or collimated sources and one or two reflectors.