Demystifying the sequential ray-tracing algorithm

A narcissus calculating method for cryogenic infrared imaging systems is proposed in this paper. The accuracy is largely improved compared to the traditional paraxial analysis, as ray blocking of the optical opertures is taken into account and real ray data are used during the calculation. The narcissus distribution on the full focal plane can be obtained via analyzing field by field. Meanwhile, it can be implemented simply and fast as sequential ray tracing is utilized and rays only pass through three surfaces during the cold return statistics for every retro-reflecting surface. According to this method, a general narcissus calculation package was realized using the macro language of optical design software Code V. The performance of the new method was tested by calculating an example system using this package and comparing it with traditional methods. The results showed that the new method produced the same result accuracy and information quantity as the nonsequential ray trace, while the whole analysis took only 5 s, which was significantly shortened compared with the nonsequential ray trace, which took about 30 min.

Polarization ray tracing, which consist of several extensions to geometrical ray tracing, calculates the evolution of polarization states along ray paths and determines the intrinsic polarization properties, such as diattenuation and retardance, associated with ray paths. This paper compares the suitability of the Jones, Mueller, and a three-dimensional polarization ray tracing calculi, examining the issues of local versus global coordinates, amplitude versus phase representations, inclusion of the wavefront aberration function, partially polarized light, measurements of images by polarimeters, and diffraction image formation by low and high numerical aperture beams.

The error resulting from using the well known paraxial approximation instead of Snell's law of refraction is visualized geometrically.

Manipulation of acoustic wavefronts by thin and planar devices, known as metasurfaces, has been extensively studied, in view of many important applications. Reflective and refractive metasurfaces are designed using the generalized reflection and Snell's laws, which tell that local phase shifts at the metasurface supply extra momentum to the wave, presumably allowing arbitrary control of reflected or transmitted waves. However, as it has been recently shown for the electromagnetic counterpart, conventional metasurfaces based on the generalized laws of reflection and refraction have important drawbacks in terms of power efficiency. This work presents a new synthesis method of acoustic metasurfaces for anomalous reflection and transmission that overcomes the fundamental limitations of conventional designs, allowing full control of acoustic energy flow. The results show that different mechanisms are necessary in the reflection and transmission scenarios for ensuring perfect performance. Metasurfaces for anomalous reflection require non-local response, which allows energy channeling along the metasurface. On other hand, for perfect manipulation of anomalously transmitted waves, local and non-symmetric response is required. These conclusions are interpreted through appropriate surface impedance models which are used to find possible physical implementations of perfect metasurfaces in each scenario. We hope that this advance in the design of acoustic metasurfaces opens new avenues not only for perfect anomalous reflection and transmission but also for realizing more complex functionalities, such as focusing, self-bending or vortex generation.

In this paper, we present a semi-analytical simplified approach based on the ray tracing method to estimate radiated electric fields associated with lightning return strokes, taking into account ionospheric reflections. The field transfer function at each frequency and each grazing angle is determined by applying the generalized Snell's law of refraction, and the antenna radiation pattern concept is used to obtain the source illumination efficiency, from which the radiated field is derived. The proposed method is validated using as reference full-wave FDTD simulations.

The fundamental laws of wave propagation at an interface, the laws of reflection, refraction, and diffraction are arrived at from a consideration of wave scattering from an array of scattering centers. It is shown that the number, spacing, and dimension of the scattering centers decide whether the laws of reflection and refraction or the more comprehensive law of normal scattering is obeyed. An exact equation for the summation of the phases and amplitudes of scattered waves arriving at a point is developed. Scattered ray directions are arrived at from the analytical behavior of this equation, and the region of validity of the solutions is discussed. It is shown that the length of the array plays as important a role as the spacing of the scattering centers. The modulation of diffracted ray intensity with an increase in scattering center size is identified and investigated. An expression for far-field distance is arrived at based on numerical simulation and is valid for all scattered angles.

Metasurfaces, planar metamaterials consisting of a single layer or several layers of artificial structures, not only form the basis for fundamental physics research but also have considerable technological significance. Metasurfaces can locally modify the optical property within a subwavelength range, which can facilitate device miniaturization and system integration. Metasurfaces have shown extraordinary capabilities in the local manipulation of the light's amplitude, phase, and polarization, leading to a plethora of novel applications such as generalized Snell's law of refraction and photonic spin Hall effect. This progress report is focused on the recent advancements in the fundamental research of geometric metasurfaces and their applications in ultrathin optical devices, including planar metalenses, helicity multiplexed holograms, functionality switchable devices, polarization beam splitters, vector beam generation, arbitrary polarization control, and so on. The compactness, ease of fabrication, and unusual functionalities of these devices render geometric optical metasurface devices very attractive for new applications such as encryption, imaging, anti‐counterfeiting, optical communications, quantum science, and fundamental physics. This paper aims to bring readers some new insights, and to broaden the applications of geometric metasurfaces in more research fields of science and technology.

Ray tracing is a method that allows the creation of stunning photo‐realistic images on a computer. Most ray tracing programs can model any three‐dimensional object which can be described by mathematical formulae. Looking closely at ray tracing many situations can be found where this technique can be useful. In this article a widely available shareware ray tracing program, PovRay, is described. Some ideas how PovRay can be used in teaching and 3D geometry, physics, and other high school and university subjects.

Modelling plays a major role in the evolution of scientific knowledge and is an objective for students' literacy in science. The emergence of accessible and powerful computational technologies imposes the development of a specific curriculum focusing on the study of science by computer modelling. This paper presents the results of investigating the possibilities of integration of computational modelling activities in Physics lessons, at high school level. Through the activities we propose here we will highlight the generality and transferability of models, by applying a unique mathematical model to solve problems that, at first sight, have nothing in common. The simulations we built with GeoGebra software and VPython programming language can be tailored both to the study of optical phenomena such as inferior or higher mirage, and to solving the famous problem of the brachistochrone. The interdisciplinary learning context, based on problem solving, calls for the application of knowledge from various fields: trigonometric and algebraic calculus, Euclidian geometry elements, Snell's law of refraction, energy conservation law, knowledge of programming and use a graphical software in modelling. The problem which students start from when investigating requires determining the fastest path between two points, separated by strips in which the propagation speeds are different. Using the achieved models, students can infer that in the case of the non-friction sliding motion, the cycloid is the fastest path. The simulations of motions were performed with GeoGebra, based on the kinematic equations, and with the VPython programming language, using the dynamic equations. The proposed modelling activities foster the development of students' transversal and transferable skills in mathematics, physics and computational technology.

We investigate the spectral reflectivity of photonic crystals assembled with silica spheres. The propagation of electromagnetic wave can be controlled by periodic structures known as photonic crystals. Therefore photonic crystals are anticipated for advanced control of thermal radiation beyond solid state properties. The close-packed photonic crystals well-defined thickness are rapidly made on a Si wafer by using self-assembly of colloidal silica spheres. We measure spectral reflectivities of the samples with an FT-IR (Fourier Transform - Infrared Spectroscopy). The spectral reflectivity is enhanced at specific wavelength designed with numerical analysis. The peak of spectral reflectivity shifts to shorter wavelength with increasing incident angle. The angular dependency of the spectral reflectivity can be roughly calculated by the modified Bragg's equation taking into account Snell's law of refraction. We show that the reflectivity in infrared range is well enhanced by using large photonic crystals assembled with silica micro-spheres.

The influence of surface roughness on the refraction effect for X-rays at gracing incidence was investigated using a set of brass samples with different surface roughnesses. For each sample Bragg peak positions were measured varying the incidence angle. The refraction effect at the sample surface was calculated and compared with theoretical values derived from Snell's law of refraction. Peak shift due to residual stress was also taken into account.

Light travels at different speeds through different materials causing it to bend according to Snells law Here light is represented by traveling wave fronts coming from a light source above the boundary between two materials

It is often advantageous to acquire pulse-echo ground-penetrating radar (GPR) measurements from antennas that are offset from the air-ground interface by a nonnegligible distance, either because the ground's surface is rough, or because measurements must be collected remotely. This paper describes the effects of incorrectly estimating the location of the air-ground interface on GPR images created with the plane-to-plane backpropagation (PPB) method. To compensate for a nonplanar air-ground interface, the wideband time-domain synthetic aperture method is reviewed and reformulated, using Snell's law of refraction, to account for measurements taken some distance above an undulating interface. A modification of the PPB algorithm that accounts for a nonplanar interface is also formulated, and examples of imaging with both methods are given to validate, the algorithms' performance for surface variations that are relatively smooth with respect to the radar waveform wavelengths. Additionally, a method for inferring the surface topography from the radar returns is described. Finally, the modified PPB is demonstrated by imaging buried targets sensed in field-acquired data.

Ray tracing has been traditionally used with applications for media and entertainment (3D animation, rendering), product development (CAD/CAM/CAE), life sciences (medical, molecular), energy, and other operations. The ray-tracing programs are used by engineers and artist proposing a project concept or new product design, by designers who bring the first renditions of the project or product for evaluation, by manufacturing people who build and test the project, or product virtually in the computer. And then when everything is proven and acceptable, marketing people use ray tracing to create images to sell the product. Ray tracing is used in all four stages from project concept to fulfillment. The concept of virtual prototyping and in the film industry pre-viz has been embraced by most industries and has saved millions of dollars by eliminating redos and expensive after-sales repairs.

Site-specific ultrawideband propagation modeling involves dealing with frequency variations of the propagation mechanisms and antenna patterns in the ray tracing program. Typically, electromagnetic field calculations have to be performed in a lot of frequencies to accurately construct the frequency response of the channel at a receiving point. This imposes a heavy computational burden on ray tracing specially in calculating the coverage map or finding the statistics of channel parameters where the number of receiving locations is large. In this paper, the computational complexity of ray tracing in ultrawideband propagation modeling is reduced by using cubic B-spline interpolation. The frequency response of the channel at each receiving point is obtained by calculating the electromagnetic fields at a limited number of frequencies and then interpolating the results using cubic B-splines. A speedup of about four times in simulating a typical residential environment is achieved. Besides, the accuracy of the results is maintained due to excellent characteristics of the cubic B-spline interpolation.