Freeform surfaces are widely used in optical design, due to the high design degree of freedom. The aberration theory of freeform optics can better lead designers to obtain a good structure. However, the existing aberration theory of freeform optics is only suitable for the optical system with a relatively small field of view (FOV). In this case, each field area (footprint) shows approximately the same shape and size, and positions of footprints across a surface have a linear relationship with fields. A wide FOV freeform optical system is analyzed in this paper. Parameters of all fields based on real-ray trace and non-linear interpolation can be employed to calculate the aberration generated by freeform terms. Then, to correct aberrations, coefficients of freeform terms are calculated using the least-square fitting method. By bringing back the coefficients to the optical system, the result shows great performance when using non-linear interpolation.
Designing a general method of freeform optics for illuminating hard-to-reach areas is a challenging but rewarding issue. Most of the current designs of freeform illumination optics are valid in the applications in which the region of interest is easily accessible. However, there are some applications in which the region of interest is inaccessible due to the obstacles that cannot be removed and high-quality illumination is still needed (this is usually the case in endoscopic lighting). In this paper, we present a general formulation of designing freeform lenses for illuminating hard-to-reach areas. In this method, the freeform lens consists of two elaborately designed surfaces, by which both the irradiance distribution and wave-front of the light beam are manipulated in a desired manner. The light beam after refraction by the freeform lens is further guided through a light-guiding system to produce a prescribed illumination on a target plane which is inaccessible. Here, the light-guiding system can be a light-guiding element [e.g., a gradient refractive index (GRIN) lens] or an optical system that consists of several optical components. The properties of the light-guiding system are taken into account in the tailoring of the freeform lens profiles to guarantee the prescribed illumination on the target plane. The result shows that the design of freeform optics for illuminating hard-to-reach areas in the presence of a light-guiding system can still be formulated into an Monge–Ampère equation (MA) with a nonlinear boundary condition. Two examples are given to demonstrate the elegance of this method in designing freeform optics for illuminating hard-to-reach areas.
It is a meaningful but challenging issue that designing illumination optics for extended sources directly. A number of direct design methods developed specifically to deal with prescribed intensity designs usually fail to produce satisfactory illumination in the near field where the influence of lens size on the irradiance distribution cannot be ignored. In this paper, a direct method of designing aspherical lenses for extended sources is introduced to achieve specified irradiance characteristics. And various types of prescribed irradiance distributions are shown in this paper to verify the broad applicability and high efficiency of the direct design method, especially two examples of producing discontinuous irradiance distributions are analyzed in detail.
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