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)

Focusing light through a free-form scattering medium

Imaging and transport light through scattering opaque media is a hot topic pursued in multiple fields, ranging from nanotechnology to life sciences. A promising technique to do this is wavefront shaping (WFS), where the light propagation through a scattering medium is controlled by interference [1][2]. Recently, the potential of WFS was even extended to, for instance, time-varying samples [3][4]. In most cases to date, WFS has been done on the quintessential scattering sample geometry, namely in slabs. Real-world applications, however, require samples to have any shape – “free-form scattering optics” – that defies current theories. Here, we present the study of an opaque sample of TiO2 particles suspended in silicone. Exploiting the flexibility of silicone, we are able to modify the geometry of the sample and measure the enhancement of the intensity η in a point of the speckle pattern. Using this opportunity, we compare the performance of a flat and a free form sample. These experimental measurements will be compared with a newly formulated theory of light transport in free form scattering media

Computing aberration coefficients for plane-symmetric reflective systems: A Lie algebraic approach

We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to arbitrary order. The presented method provides a systematic and rigorous approach to the derivation, treatment and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirror examples

An ADER discontinuous Galerkin method on moving meshes for Liouville's equation of geometrical optics

Liouville's equation describes light propagation through an optical system. It governs the evolution of an energy distribution on phase space. This energy distribution is discontinuous across optical interfaces. Curved optical interfaces manifest themselves as moving boundaries on phase space. In this paper, an ADER discontinuous Galerkin (DG) method on a moving mesh is applied to solve Liouville's equation. In the ADER approach a temporal Taylor series is computed by replacing temporal derivatives with spatial derivatives using the Cauchy-Kovalewski procedure. The result is a fully discrete explicit scheme of arbitrary high order of accuracy. A moving mesh is not sufficient to be able to solve Liouville's equation numerically for the optical systems considered in this article. To that end, we combine the scheme with a new method we refer to as sub-cell interface method. When dealing with optical interfaces in phase space, non-local boundary conditions arise. These are incorporated in the DG method in an energy-preserving manner. Numerical experiments validate energy-preservation up to machine precision and show the high order of accuracy. Furthermore, the DG method is compared to quasi-Monte Carlo ray tracing for two examples showing that the DG method yields better accuracy in the same amount of computational time.</p

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

An Iterative Least-Squares Method for the Hyperbolic Monge-Amp\`ere Equation with Transport Boundary Condition

A least-squares method for solving the hyperbolic Monge-Amp\`ere 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-Amp\`ere equation, is solved. The approach is based on a least-squares method for the elliptic Monge-Amp\`ere 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.Comment: 30 pages, 24 figure

A global experiment on motivating social distancing during the COVID-19 pandemic

Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

A global experiment on motivating social distancing during the COVID-19 pandemic

Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e. a controlling message) compared to no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly-internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared to the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly-internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing: Controlled motivation was associated with more defiance and less long-term behavioral intentions to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

Illumination freeform design using Monge-Ampère equations

As a generic model for freeform optical systems, we combine the optical map and the luminous flux conservation law into a generalized Monge-Ampère equation. We sketch a least-squares solution strategy

Determination of the Diffusion Parameters of an Optically Thin Scattering Sample Through Time-resolved Transmission

The color-converting phosphor diffusers in white LEDs are optically thin and hence are hard to characterize. We show that separating of direct from diffuse transmission in time-resolved experiments results in less than 20% error in determining the diffusion parameters using the diffusion approximation