arXiv subjects

Wilbert L. IJzerman

Publications and source records attributed to Wilbert L. IJzerman.

11 recordsLinked to original sources

arXiv2025

Design of a three-dimensional parallel-to-point imaging system based on inverse methods

We present an inverse method for designing a three-dimensional imaging system comprising of freeform optical surfaces. We impose an imaging condition on the optical map and combine it with the law of conservation of energy to conclude that the ratio of energy distributions at the source and target of an imaging system must be constant. A mathematical model for the design of a parallel-to-point system consisting of two freeform reflectors is presented. A Schwarzschild telescope, a classical design known for maximum correction of third-order aberrations, is utilized to specify the design parameters in the mathematical model, enabling us to compute an inverse freeform imaging system. The performance of both designs is compared by ray tracing various parallel beams of light and determining the corresponding spot sizes of the image. We demonstrate that our inverse freeform design is superior to the classical design.

physics.optics↗

arXiv2025

An Inverse Method for the Design of Freeform Double-Reflector Imaging Systems

We propose an inverse method to design two-dimensional freeform imaging systems. We present the mathematical model to design a parallel-to-point double-reflector imaging system using inverse methods from nonimaging optics. We impose an imaging condition on the energy distributions at the source and target of the optical system. Our freeform design is compared to the classical Schwarzschild telescope, which is well-known for minimizing third-order aberrations. A raytracer using quasi-interpolation is employed to test the performance of both designs by comparing the spot sizes corresponding to on-axis and off-axis light rays. We show that the inverse freeform design outperforms the classical design.

physics.optics↗

arXiv2023

Wavefront shaping through a free-form scattering object

Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are studied are slabs or wave-guides. In this paper, we study how macroscopic changes in the sample shape affect light scattering using the wavefront shaping technique. Using a flexible scattering material, we optimize the intensity of light in a focusing spot using wavefront shaping and record the optimized pattern, comparing the enhancement for different curvatures and beam radii. We validate our hypothesis that wavefront shaping has a similar enhancement regardless of the free-form shape of the sample and thus offers relevant potential for industrial applications. We propose a new figure of merit to evaluate the performance of wavefront shaping for different shapes. Surprisingly, based on this figure of merit, we observe that for this particular sample, wavefront shaping has a slightly better performance for a free-form shape than for a slab shape.

physics.optics↗

arXiv2023

Design of two-dimensional reflective imaging systems: An approach based on inverse methods

Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging optics and optimize them to obtain a system that produces minimal aberrations. This is done by minimizing a merit function that quantifies aberrations and is dependent on the energy distributions at the source and target of an optical system, which are input parameters essential for inverse freeform design. The proposed method is tested for two configurations: a single-reflector system and a double-reflector system. Classical designs consisting of aspheric elements are well-known for their ability to minimize aberrations. We compare the performance of our freeform optical elements with classical designs. The optimized freeform designs outperform the classical designs in both configurations.

physics.optics↗

arXiv2023

Enhanced Secrecy in Optical Communication using Speckle from Multiple Scattering Layers

We study the secrecy of an optical communication system with two scattering layers, to hide both the sender and receiver, by measuring the correlation of the intermediate speckle generated between the two layers. The binary message is modulated as spatially shaped wavefronts, and the high number of transmission modes of the scattering layers allows for many uncorrelated incident wavefronts to send the same message, making it difficult for an attacker to intercept or decode the message and thus increasing secrecy. We collect 50,000 intermediate speckle patterns and analyze their correlation distribution using Kolmogorov-Smirnov (K-S) test. We search for further correlations using the K-Means and Hierarchical unsupervised classification algorithms. We find no correlation between the intermediate speckle and the message, suggesting a person-in-the-middle attack is not possible. This method is compatible with any digital encryption method and is applicable for codifications in optical wireless communication (OWC).

physics.optics↗

arXiv2023

An Iterative Least-Squares Method for the Hyperbolic Monge-Ampère Equation with Transport Boundary Condition

A least-squares method for solving the hyperbolic Monge-Ampère equation with transport boundary condition is introduced. The method relies on an iterative procedure for the gradient of the solution, the so-called mapping. By formulating error functionals for the interior domain, the boundary, both separately and as linear combination, three minimization problems are solved iteratively to compute the mapping. After convergence, a fourth minimization problem, to compute the solution of the Monge-Ampère equation, is solved. The approach is based on a least-squares method for the elliptic Monge-Ampère equation by Prins et al., and is improved upon by the addition of analytical solutions for the minimization on the interior domain and by the introduction of two new boundary methods. Lastly, the iterative method is tested on a variety of examples. It is shown that, when the iterative method converges, second-order global convergence as function of the spatial discretization is obtained.

math.NA↗

arXiv2021

Modelling Surface Light Scattering in the Context of Freeform Optical Design

We present a novel approach of modelling surface light scattering in the context of freeform optical design. The model relies on energy conservation and optimal transport theory. For isotropic scattering in cylindrically or rotationally symmetric systems with in-plane scattering, the scattered light distribution can be expressed as a convolution between a scattering function, which characterises the optical properties of the surface, and a specular light distribution. Deconvolving this expression allows for traditional specular reflector design procedures to be used, whilst accounting for scattering.

physics.optics↗

arXiv2021

Numerical Methods for the Hyperbolic Monge-Ampère Equation Based on the Method of Characteristics

We present three alternative derivations of the method of characteristics (MOC) for a second order nonlinear hyperbolic partial differential equation. The MOC gives rise to two mutually coupled systems of ordinary differential equations. As a special case we consider the Monge-Ampère equation, for which we solve the system of ODE's using explicit one-step methods (Euler, Runge-Kutta) and spline interpolation. Numerical examples demonstrate the performance of the methods.

math.NA↗

arXiv2019

Systematic design of the color point of a white LED

Lighting is a crucial technology that is used every day. The introduction of the white light emitting diode (LED) that consists of a blue LED combined with a phosphor layer, greatly reduces the energy consumption for lighting. Despite the fast-growing market white LED's are still designed using slow, numerical, trial-and-error algorithms. Here we introduce a radically new design principle that is based on an analytical model instead of a numerical approach. Our design model predicts the color point for any combination of design parameters. In addition the model provides the reflection and transmission coefficients - as well as the energy density distribution inside the LED - of the scattered and re-emitted light intensities. To validate our model we performed extensive experiments on an emblematic white LED and found excellent agreement. Our model provides for a fast and efficient design, resulting in reduction of both design and production costs.

physics.optics↗

arXiv2017

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.

math.NA↗

arXiv2017

Embedded WENO: a design strategy to improve existing WENO schemes

Embedded WENO methods utilize all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu (J. Comput. Phys. 126 (1996)) and on the WENO-Z scheme of Borges et al. (J. Comput. Phys. 227 (2008)) are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

math.NA↗