Generating-function approach for double freeform lens design

Abstract

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Fresnel reflections in inverse double freeform lens design

“…We will give a brief summary of the derivation of the equations governing the path of a ray through the optical system. The derivations for these equations are given by Romijn et al [9]. For the first surface, there is a relation between x and y 1 , given by…”

“…This first surface can be computed from an intermediate distribution. This is done, for example, by the least-squares algorithm in [9], which we adapt in the current paper. Similarly, Shen et al compute the first surface from an intermediate distribution and subsequently compute the second surface [10].…”

“…A further generalization of the Monge-Ampère equations, called the generated Jacobian equation, was used to extend the least-squares algorithm to these layouts [13]. It is this so-called generated Jacobian least-squares (GJLS) algorithm that is also used to design double freeform lenses with a point source and a far-field target [9]. An overview of optical systems and the corresponding versions of the least-squares algorithm is given by Anthonissen et al [14].…”

“…In Section 2.C, we derive an expression for the transmittance of the flux through the double freeform lens, and in Section 2.D we describe the energy balance between the source and target. After that, in Section 3, we briefly elaborate on the algorithm, focusing on the changes compared to [9]. We finally evaluate the results of this algorithm in Section 4.…”

A Convergent Quadrature Based Method For The Monge-Ampère Equation

“…Recent years have seen a growing interest in Monge-Ampère type equations in the context of a diverse range of problems including design of optical systems [31], geophysics [12], mesh generation [7], medical image processing [17], meteorology [10], and data science [29]. This has encouraged the design of many new methods for the Monge-Ampère equation including [3,6,11,13,30].…”