Abstract
Current freeform illumination optical designs are mostly focused on producing prescribed irradiance distributions on planar targets. Here, we aim to design freeform optics that could generate a desired illumination on a curved target from a point source, which is still a challenge. We reduce the difficulties that arise from the curved target by involving its varying z-coordinates in the iterative wavefront tailoring (IWT) procedure. The new IWT-based method is developed under the stereographic coordinate system with a special mesh transformation of the source domain, which is suitable for light sources with light emissions in semi space such as LED sources. The first example demonstrates that a rectangular flat-top illumination can be generated on an undulating surface by a spherical-freeform lens for a Lambertian source. The second example shows that our method is also applicable for producing a non-uniform irradiance distribution in a circular region of the undulating surface.
Highlights
Manipulating the irradiance distributions of artificial light sources are very crucial for lighting and laser applications
Komissarov, Boldyrev and later, Schruben showed that the design of a freeform reflector for a point source could be formulated as a second order nonlinear partial differential equation (PDE) of Monge-Ampère (MA) type[4,5]
A new iterative wavefront tailoring (IWT)-based method is proposed for designing freeform lenses that can produce prescribed irradiance distributions on curved targets
Summary
Manipulating the irradiance distributions of artificial light sources are very crucial for lighting and laser applications. Freeform optics design for irradiance tailoring on a given target is a very difficult inverse problem. Komissarov, Boldyrev and later, Schruben showed that the design of a freeform reflector for a point source could be formulated as a second order nonlinear partial differential equation (PDE) of Monge-Ampère (MA) type[4,5]. The first type is the energy conservation between the source intensity and the target irradiance. Schruben did not present the final expression of the MA equation and gave no hint on the numerical calculation. This is probably because that the derivation process is too complicated and the final MA equation is very difficult to solve. Ries and Muschaweck created a different formulation process and solved a set of equivalent nonlinear PDEs, but they kept silent on the numerical techniques[7]
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