Beyond trial and error in lighting optics design

llumination optics is an important field in the lighting industry. However, the knowledge is gained merely by experience and stored in the heads of a small group of aging engineers. In practice, optical design for lighting applications is a process of trial and error and thus time-consuming and expensive

Computation of double freeform optical surfaces using a Monge–Ampère solver: Application to beam shaping

In this article, we present a formulation for the design of double freeform lens surfaces to control the intensity distribution of a laser beam with plane wavefronts. Double freefrom surfaces are utilized to shape collimated beams. Two different layouts of the freeform lens optical system are introduced, i.e., a single lens with double freeform surfaces, and two separate lenses with two flat and two freeform surfaces. The freeform lens design problem can be formulated as a Monge–Ampère type differential equation with transport boundary condition, expressing conservation of energy combined with the law of refraction and the constraint imposed on the optical path length between source and target planes. Numerical solutions are computed using a generalized least-squares algorithm which is presented by Yadav et al. (2018). The algorithm is capable to compute two solutions of the Monge–Ampère boundary value problem, corresponding to either c-convex or c-concave freeform surfaces for both layouts. The freeform surfaces are validated for several numerical examples using a ray-tracer based on Quasi-Monte Carlo simulation.</p

Full linear multistep methods as root-finders

Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented. A general analysis is provided based on inverse polynomial interpolation, which is used to prove a fundamental barrier on the convergence rate of any LMM-based method. We show, using numerical examples, that full LMM-based methods perform excellently. Finally, we also provide a robust implementation based on Brent's method that is guaranteed to converge.Comment: 20 pages, 1 figur

Alternative computation of the Seidel aberration coefficients using the Lie algebraic method

We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction, and reflection in phase space. The method offers a systematic way to find aberration coefficients of any order for arbitrary rotationally symmetric optical systems. The coefficients from the Lie method are linked to the Seidel aberration coefficients. Furthermore, the property of summing individual surface contributions is preserved by the Lie algebraic theory. Two examples are given to validate the proposed methodology with good results.</p

An inverse method for the design of TIR collimators to achieve a uniform color light beam

Color over Angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the di¿erential equations arising from this method and verify the results using Monte-Carlo raytracing

Color homogeneity in LED spotlights

LED is a rising technology in the field of lighting. Halogen spotlights are nowadays replaced by LED spotlights because of their energy efficiency and long lifetime. However, color variation in the light output is a common problem. Poorly designed LED spotlights tend to have yellowish or bluish rings in the beam, which is undesirable. In this article we outline a method to design an optical component that annihilates this color variation

An inverse method for color uniformity in white LED spotlights

Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is an improved version of an earlier method [1], and provides more design freedom. We derive a mathematical model for color mixing in a collimator and present a numerical algorithm to solve it. We verify the results using Monte-Carlo ray tracing

Fresnel reflections in inverse freeform lens design

In this paper we propose a method to design a freeform lens including the effect of Fresnel reflections on the transmitted intensity. This method is elaborated for a lens with one freeform surface shaping a far-field target from a point source or collimated input beam. It combines the optical mapping with the energy balance incorporating the loss due to Fresnel reflections, which leads to a generalized Monge–Ampère equation. We adapt a least-squares solver from previous research to solve the model numerically. This is then tested with a theoretical example and a test case related to road lighting