The increasing efficiency of high power LEDs has resulted in many new applications in general lighting. To
take full advantage of the properties of LEDs, free-form surfaces can be utilized to create compact non imaging
optical systems with high efficiencies and high degrees of freedom for optical designers. One of the commonly
used methods to do optical design for this kind of systems is optimization. Appling this powerful tool allows
the enhancement of given optical elements to achieve a desired performance. In this way, free form surfaces
which are usually represented by NURBS, can be optimized and applied even close to an extended LED light
source. However, using optimization for free-form surfaces is far from being straight-forward and requires a lot of
experience mostly due to the high amount of possible optimization variables for NURBS. This comes along with
high, computational effort and difficulties concerning the choice of boundary conditions and merit functions. This
contribution presents a novel non-imaging optical design approach using the concept of free-form deformation
(FFD) in conjunction with customized optimization algorithms to create efficient optical free-form surfaces for
extended LED light sources. Within this framework, specific coordinate system transformations are used to
modify the global shape of free-form surfaces. In this way, optimization techniques relying on relatively few and
easily accessible variables can be applied successfully. All presented concepts are implemented in a flexible and
fully automated FFD optimization software tool incorporating a commercial raytracer and numerical optimization
techniques. Several examples are presented in detail and the scope of FFD based optimization is demonstrated.
Finite element methods (FEM) for the rigorous electromagnetic solution of Maxwell's equations are known to be
very accurate. They possess a high convergence rate for the determination of near field and far field quantities
of scattering and diffraction processes of light with structures having feature sizes in the range of the light
wavelength. We are using FEM software for 3D scatterometric diffraction calculations allowing the application
of a brilliant and extremely fast solution method: the reduced basis method (RBM). The RBM constructs a
reduced model of the scattering problem from precalculated snapshot solutions, guided self-adaptively by an error
estimator. Using RBM, we achieve an efficiency accuracy of about 10-4 compared to the direct problem with
only 35 precalculated snapshots being the reduced basis dimension. This speeds up the calculation of diffraction
amplitudes by a factor of about 1000 compared to the conventional solution of Maxwell's equations by FEM.
This allows us to reconstruct the three geometrical parameters of our phase grating from "measured" scattering
data in a 3D parameter manifold online in a minute having the full FEM accuracy available. Additionally, also
a sensitivity analysis or the choice of robust measuring strategies, for example, can be done online in a few
minutes.
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