Three-dimensional freeform reflector design with a microfacet surface roughness model.

This paper proposes a methodology for the design of freeform reflectors with scattering surfaces. We use microfacets, which are small, tilted mirrors superimposed on a smooth surface. We form a simple model of surface roughness and light scattering based on the orientations of the microfacets. Using a least-squares solver to compute the smooth reflector as a starting point, we can subsequently alter the surface using an optimization procedure to account for the scattering. After optimization, the resulting reflector surface produces the desired scattered light distribution. We verify the resulting reflector using raytracing. This study focuses on freeform systems with a collimated incident beam and a far-field target intensity.

Three-dimensional freeform reflector design with a scattering surface.

We introduce an approach to calculating three-dimensional freeform reflectors with a scattering surface. Our method is based on optimal transport and utilizes a Fredholm integral equation to express scattering. By solving this integral equation through a process analogous to deconvolution, we can recover a typical specular design problem. Consequently, we consider freeform reflector design with a scattering surface as a two-step process wherein the target distribution is first altered to account for scattering, and then the resulting specular problem is solved. We verify our approach using a custom raytracer that implements the surface scattering model we used to derive the Fredholm integral.

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 the 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).

Two-dimensional freeform reflector design with a scattering surface.

We combine two-dimensional freeform reflector design with a scattering surface modeled using microfacets, i.e., small, specular, surfaces representing surface roughness. The model resulted in a convolution integral for the scattered light intensity distribution, which yields an inverse specular problem after deconvolution. Thus, the shape of a reflector with a scattering surface may be computed using deconvolution, followed by solving the typical inverse problem of specular reflector design. We found that the presence of surface scattering resulted in a few percentage difference in terms of reflector radius, depending on the amount of scattering in the system.

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.

Unified mathematical framework for a class of fundamental freeform optical systems.

We present a unified mathematical framework for sixteen fundamental optical systems. The systems have a parallel or point source and a parallel, point, near-field or far-field target. These choices give eight configurations if we use reflectors only and take the minimum number of freeform surfaces required. Similarly, we get eight lens systems if we only use lens surfaces. The mathematical model for each system is based on Hamilton's characteristic functions and conservation of luminous flux. Some configurations lead to standard or generalized Monge-Ampère equations. The remaining systems are described by so-called generated Jacobian equations.

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting.

We study the diffuse transport of light through polymer slabs containing TiO(2) scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470-840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 µm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 µm) consist of clusters of small particles (R<0.13 µm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.