Ray-tracing Program Research Articles

Oblique-Incidence Interferometric Measurement of Optical Surface Based on a Liquid-Crystal-on-Silicon Spatial Light Modulator

An oblique-incidence interferometric measurement method is proposed to measure and adjust optical surfaces with a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). The optical system only consists of an interferometer and an LCoS-SLM with precision mounts. It could reduce the measuring cost and time consumption due to the programmable function of the LCoS-SLM and offer the ability to align the optical system. The oblique-incidence measurement theory and optical system adjustment method are established based on an off-axis paraboloid model. The ray-tracing program to calculate the compensation phase map in the measurement is proposed with math models. In the optical alignment step, the off-axis paraboloid model is used to apply the LCoS-SLM as a phase compensator to generate a focusing spot or light spot array to adjust the measured optical surface. And in the interferometric measurement step, the calculated compensation phase map from the ray-tracing calculation is loaded on the LCoS-SLM using the same optical setup as the optical alignment step without any mechanical adjustment. Two interference measurement experiments of typical optical surfaces were carried out to verify the accuracy of the measuring system.

Ray tracing model for long-range acoustic vortex wave propagation underwater

The use of vortex waves in multiple environments is of increasing interest for numerous applications including underwater acoustic communications, particle manipulations, and sonothrombolysis. Finite element methods are limited in the range for which the propagation of these vortex beams may be simulated. On the other hand, ray tracing programs simulate well over long ranges, though are generally limited in their ability to resolve the features of a propagating vortex. Methods for overcoming these difficulties in simulating the long-range propagation of such waves in inhomogeneous environments have been developed and employed, though their specific implementation has not been thoroughly discussed. This manuscript provides the methods by which existing ray tracing programs may be used to approximate the long-range propagation of acoustic vortex beams in complex environments.

Research on Stellar Occultation Detection with Bandpass Filtering for Oxygen Density Retrieval

Stellar occultation instruments detect the transmission of stellar spectra through the planetary atmosphere to retrieve densities of various atmospheric components. This paper introduces an idea of using instruments with bandpass filters for stellar occultation detection. According to the characteristics of the occultation technique for oxygen density measurement, a full-link forward model is established, and the average transmission under a typical nocturnal atmosphere is calculated with the help of the HITRAN database, occultation simulation and a 3D ray-tracing program. The central wavelength and bandwidth suitable for 760 nm oxygen A-band absorption measurement are discussed. This paper also compares the results of the forward model with GOMOS spectrometer data under this band, calculates the observation signal-to-noise ratio corresponding to different instrument parameters, and target star magnitudes. The results of this paper provide a theoretical basis for the development of a stellar occultation technique with a bandpass filter and guidance on the instrument design.

Optical performance of a new design of a trifocal intraocular lens based on the Devil's diffractive lens.

In this work, we propose a new diffractive trifocal intraocular lens design with focus extension, conceived to provide a high visual performance at intermediate distances. This design is based on a fractal structure known as the "Devil's staircase". To assess its optical performance, numerical simulations have been performed with a ray tracing program using the Liou-Brennan model eye under polychromatic illumination. The simulated through the focus visual acuity was the merit function employed to test its pupil-dependence and its behavior against decentering. A qualitative assessment of the multifocal intraocular lens (MIOL) was also performed experimentally with an adaptive optics visual simulator. The experimental results confirm our numerical predictions. We found that our MIOL design has a trifocal profile, which is very robust to decentration and has low degree of pupil dependence. It performs better at intermediate distances than at near distances and, for a pupil diameter of 3 mm, it works like an EDoF lens over almost the entire defocus range.

Numerical feasibility study on signal discrimination in reflective environment of tungsten PFC

In the reflective environments of tungsten plasma facing components (PFCs), diagnostics of tokamaks will suffer from signal distortions since the reflectivity of tungsten PFCs are not negligible especially in the infrared (IR) range [1,2]. However, considering that most optical reflective systems are linear, it might be possible to eliminate the reflections if all ray information is provided. So, the possibility depends on the ray information of the system, and it can be derived using ray tracing simulations. For the feasibility study, the own ray tracing program of KFE has to be built since the conventional ray tracing programs have a limitation in providing full ray information. Among diagnostics, temperature measurement of PFCs is an issue for tungsten PFCs since it is a fundamental measurement for machine safety. So, as a feasibility study of signal discriminations, the emitted radiance was examined, and it has shown to be quite successful. This paper shows the possibility of reflection discrimination using ray path information.

A New Two-Foci V-Trough Concentrator for Small-Scale Linear Fresnel Reflectors

We present the design of an original secondary cavity for use in Small-Scale Fresnel Reflectors in photovoltaic applications. The cavity is similar to the classical V-trough, but the primary reflector system is configured so that there are two focal points on the aperture. The rays coming from each side of the primary system reach the opposite side of the cavity, producing a non-symmetrical distribution of the irradiance. This modifies the acceptance half-angle and allows us to break the maximum limit for the concentration ratio of ideal symmetric concentrators. Our study is analytic, and we provide formulas for any number of reflections. Numerical simulations with a ray-tracing program based on MATLAB are included. We provide a comparison of optical concentration ratio, height and cost parameter between our system and two classical designs with a single focal point: the V-trough and the Compound Parabolic concentrators. This way, we verify that our design yields better concentration ratios while keeping the ray acceptance rate at one. Our solution proves to be better than both the classical one-focus V-trough and the Compound Parabolic concentrator. Specifically, the proposed solution is significantly better than the classical one-focus V-trough in optical concentration ratio, with an increase between 15.02 and 35.95%. As regards the compound parabolic concentrator, the optical concentration ratio is always slightly better (around 4%). The height of the cavity, however, is notably less in this design (around 54.33%).

The Rules of 4-Dimensional Perspective: How to Implement Lorentz Transformations in Relativistic Visualization

This paper presents a pedagogical introduction to the issue of how to implement Lorentz transformations in relativistic visualization. The most efficient approach is to use the even geometric algebra in 3+1 spacetime dimensions, or equivalently complex quaternions, which are fast, compact, and robust, and straightforward to compose, interpolate, and spline. The approach has been incorporated into the Black Hole Flight Simulator, an interactive general relativistic ray-tracing program developed by the author.

Advanced Modeling and Simulation Methods for Evaluation of Thermal Neutron Scattering Materials

With the rise of interest in thermal neutron scattering data for advanced reactor, criticality safety, and shielding applications, new experimental data are required for evaluation of new materials or for re-evaluation (or validations) of previously evaluated materials. New experimental data are evaluated in a three-step process: (1) computing the phonon characteristics, (2) computing the dynamic structure factor (DSF) from the data, and (3) using the experimental setup to simulate the experimental data. All three steps have challenges, ranging from the need for a suffciently general material simulation code—a processing code that can compute the corresponding DSF—to having a detailed layout of the instrument/beamline/facility where the data were measured. Whereas phonon characteristics of materials can be computed using various methods (molecular dynamics, density functional theory, etc.), a high-fidelity computation of the DSF and the simulation of the experiment based on the DSF is vital to the accuracy of the evaluation. The latter two steps can be achieved by using the two corresponding code systems developed by instrument scientists at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory: (1) OCLIMAX, a program that calculates the dynamic structure factor from DFT and MD simulation results, and (2) MCViNE, a Monte Carlo neutron ray-tracing program designed to simulate neutron scattering experiments. Recently, polyethylene and yttrium hydride were measured at the Wide Angular-Range Chopper (ARCS) and SEQUOIA instrument stations of the SNS. These experiments are simulated using the density functional theory code, the Cambridge Serial Total Energy Package (CASTEP), to compute its phonon characteristics (eigenvalues/vectors and PDOS), which is then processed using OCLIMAX to yield the DSF, and finally the data at each instrument station are simulated by the MCViNE for comparison to the measured data for evaluation. For comparison to conventional evaluation methods, the scattering data processed from OCLIMAX are compared against those processed from the LEAPR module of NJOY, and the results from MCViNE simulations are compared against previously used simplified beamline models implemented in the Monte Carlo N-Particle (MCNP) code.

Statistical and simulation study on the separation in junction frequencies between ordinary (O) and extraordinary (X) wave in oblique ionograms

The most important aim in interpreting an oblique ionogram is to obtain the accurate Junction Frequencies (JFs) of the ordinary (O) and extraordinary (X) mode. This requires the correct identification of O- and X-mode traces, so it is very helpful and worthy to grasp the relative position between the two modes. This paper presents a statistical and simulation study of the separation in JFs between O- and X-waves based on observed oblique ionograms over three mid-latitude paths within China and a 3D ray-tracing program. The dependence on local time, season, geomagnetic activity, O-wave JF and group path, solar activity, direction, and length of propagation is investigated. The main conclusions are as follows: (a) the separation on east–west path is susceptible to ionospheric variability, while the separation on north–south path does not show a significant correlation with local time and season; (b) a general diurnal tendency and a summer anomaly on east–west propagation are first proposed and discussed, which may be related to the diurnal variation of hmF2 above the reflection point and the strong lower layers below the reflection point; (c) the separation varies approximately as a cosine function with the propagation direction owning two maxima in the north–south direction and two minima in the east–west direction; (d) the variation patterns of the separation with the propagation length are obviously not the same in different directions. In the case of east–west propagation, the separation decreases to a minimum near ground range of 2000 km and then increases very slowly with increasing ground range, while it monotonically increases for the north–south propagation path.Graphical

Phase sensitivity in single-shot speckle interferometry using a custom integrating glass-sphere for the measurement of femtometric wavelength change

Phase sensitivity single-shot speckle interferometry for detection of wavelength changes in the femtometric scale depends on the optical path differences (OPDs) produced by the multiple reflections inside an integrating sphere. In this work the OPDs are calculated using a ray-tracing program of a glass sphere coated with white paint, which shows that the resulting OPDs are distributed randomly over the speckle field-of-view but with a characteristic curve that depends strongly on the dimensions of the optical setup, the internal reflection coefficient, and the diameter of the integrating sphere that combined produce the final phase sensitivity of the optical setup. It is also shown that singularities removal of vortices is necessary for the phase-change calculation. The ray-tracing simulations of the proposed optical setup are confirmed by the experimental results of the optical implementation.

Extension of a fifth-order intrinsic aberration for a soft x-ray and vacuum ultraviolet optical system from a one- to two-dimension field light source.

Based on the fifth-order intrinsic aberration of a soft x-ray and vacuum ultraviolet (XUV) optical system with a one-dimension field light source, it is extended to the case of two-dimension in this paper, and the corresponding aberration calculation method is studied. Firstly, we derived sixth-order intrinsic wave aberration expressions of these kinds of optical systems with the aperture-ray coordinates on the reference exit wavefront; and then, derived the calculation expressions for fifth-order intrinsic aberration on the image plane caused by the contributions of wave aberration and defocus, respectively. Finally, the aberration expressions derived in this paper are applied to calculate the aberration distributions of two design examples of these kinds of optical systems, and these calculation results are compared with the ray-tracing program Shadow to validate the aberration expressions. The study shows that the calculation accuracy of aberration expressions is very satisfactory.

Numerical Tool for Calculating Birefringence in Mirror-Substrates for Gravitational-Wave Detectors

The influence of birefringence on rays entering and exiting a non-isotropic medium is a complex process that depends on its dielectric tensor, the orientation and geometry of the medium, the surrounding material, and the inclination of the incident ray. Thus, when aiming for a calculation of the effects, many parameters need to be taken into account while simplifications are generally not applicable. Moreover, the complexity of the general issue makes it almost impossible to find an analytical solution for backward calculations of stress-birefringence from polarization measurements. In this paper, a report is given on the formulation of a birefringence ray-tracing program in Python for the convenient evaluation of optical effects inside uniaxial crystals under stress. The aim thereby is to have an easily applicable tool that can be used in interferometer commissioning for current and future gravitational-wave detectors. Results from test simulations using realistic parameters for a sapphire mirror as used in the gravitational-wave detector KAGRA are implemented and show the capabilities of this tool.

Using a ray tracing program to calculate sunrise times over a digital terrain model based visible horizon using a simplified atmospheric model, part II

In a previous paper we compared observations to calculated values of the sunrise times for one place in Jerusalem. It was shown that the sunrise over the actual physical horizon could be modeled to an accuracy of about ±15 s for most of the year. Success of those calculations suggested that terrain modeling was the most important factor in obtaining this result. To investigate this point, we repeated our calculations using the ray tracing method and simplified atmosphere developed by Siebren Van der Werf, whose atmospheric model is easily applied to other places in the world. Our results show that the new calculation method maintained our requirement of ±15 s accuracy (required for publication of sunrise time tables, critical for daily Jewish observances worldwide). Standard formulas for atmospheric refraction produce approximately the same results even for near horizon zenith angles. For portions of the year where low altitude inversions are especially important, e.g., during those days associated with maximum radiative cooling, these additional atmospheric effects can be effectively modeled in a very simple way.

Design and optimization of transparent scattering solar concentrator based on SiO<sub>2</sub> aerogel

Scattering solar concentrators (SSCs), an important component of transparent/translucent photovoltaic devices, can concentrate large-area sunlight on small-area solar cells while allowing some sunlight to pass through the devices. However, owing to the lack of suitable scattering materials, there have been few reports on SSCs in recent years. In this study, we fabricated SiO<sub>2</sub> aerogel-based SSCs and tested their performances. The photoelectric performance was found to be moderate. Additionally, the results demonstrated excellent transmittance and color rendering index, which meet the lighting requirements of the windows. A Monte Carlo ray tracing program was developed to simulate an SSC and analyze the fate of all photons. We also analyzed the multiple scattering mechanism in SSCs that damages the photoelectric efficiency of a device via theoretical simulation. Finally, we proposed an anisotropic scattering device that can increase the primary scattering and suppress multiple scattering, resulting in excellent photoelectric efficiency.

Computational vector fiducial for deflectometry system alignment.

One of deflectometry's cardinal strengths is its ability to measure highly dynamically sloped optics without needing physical null references. Accurate surface measurements using deflectometry, however, require precise calibration processes. In this Letter, we introduce an alignment technique using a computational fiducial to align a deflectometry system without additional hardware equipment (i.e., algorithmic innovation). Using the ray tracing program, we build relationships between the plane of the screen and detector and algorithmically generate a fiducial pattern for the deflectometry configuration. Since the fiducial pattern is based on ideal system geometry, misalignment of the unit under test with its target position causes a discrepancy between the actual image on the camera detector and the ideal fiducial image. We leverage G and C vector polynomials to quantify misalignment and estimate the alignment status through a reverse optimization method. Simulation and experimental results demonstrate that the proposed algorithm can align the 195mm×80mm of a rectangular aperture freeform optic within 10 µm of peak-to-valley accuracy. The computational fiducial-based alignment algorithm is simple to apply and can be an essential procedure for conventional methods of deflectometry system alignment.

Teaching underwater acoustics and sonar during the COVID pandemic

USNA’s Underwater Acoustics and Sonar (SP411) course, taught in a studio classroom, can seat 36 students with 5 experimental/computer workstations on each side of the classroom. This non-laboratory course relies on hands-on demos and in-class mini-laboratory experiences bringing theoretical concepts and experimental aspects of sound propagation and detection theory to life. Experiments include: (a) sound speed versus temperature in water, (b) beam pattern functions versus angle for multi-element arrays, (c) Fourier analysis of periodic waveforms including rectangular pulses, and (d) square law detection of signals plus noise—generating receiving operating characteristic ROC curves. Computer visualizations using Mathematica included phasor addition of signals, N-element array superposition for directivity analysis and a user friendly ray tracing program implementing any sound speed versus depth profile. On 20 March, 2020, the USNA entered the pandemic era by requiring remote learning for all 4100 midshipman, commencing shortly after spring break. Remote learning in SP411 was asynchronous, devoid of lectures, including handouts and videos of wave effects and worked examples. Mathematica visualizations replaced experiments and extra instruction (in different time zones) was always available. Co-author LEB’s photoacoustic imaging experiments, done remotely, used homemade electronics (pulsed LED driver and low-noise amplifiers)—keeping future midshipmen research going.

Comparison of spherical and aspherical intraocular lenses with decentration and tilt error using a physical model of human contrast vision and an image quality metric

PurposeIn this study, two intraocular lenses (spherical IOL SA60AT and aspherical IOL SN60WF) are examined in an eye model under conditions of misalignment (defocus, decentration and tilt). The lenses are rated using the contrast sensitivity function (CSF) based on Barten's physical model. The square root integral (SQRI) method is used as a quality criterion comparable to the subjective image quality assessment of the human eye. MethodsThe IOLs to be tested are decentered from 0 to 1mm and tilted from −5 to +5 degrees in the Navarro eye model (optimized for far-point 6m and pupil aperture 3mm). The defocus of the IOLs is ±0.1mm at the anterior chamber depth (ACD). The optical modulation transfer function (MTF) is simulated with a ray tracing program. The SQRI is calculated using this MTF and the Barten CSF model (for in-focus at aperture 3 and 4.5mm and for defocus at 3mm). ResultsWith increasing decentration, the spherical IOL shows a significantly smaller loss of quality for both apertures compared to the aspherical lens. With an aperture of 4.5mm, the image quality of the aspherical IOL is better for small decentration and tilt. The loss of quality of the spherical IOL increases with increasing tilt in both directions. In contrast, the image quality of the aspherical IOL is reduced under decentration for certain tilt values. For ACD−0.1mm, both IOLs behave similarly to the in-focus situation. For ACD+0.1mm, the influence of tilt without decentration is small for both IOLs. With increasing decentration, the quality loss of the aspherical IOL is similar to that in-focus and greater than that of the spherical lens. ConclusionIn general, under the same conditions the spherical SA60AT displays a lower tolerance in loss of quality of subjective vision with lens alignment errors, in comparison to the aspherical SN60WF, limited by certain combinations of decentration and tilt according to this study. This study shows a way to evaluate IOLs based on the subjective visual performance of the eye.

Non-null interferometers for irregular surface measurement with system modeling

A design method of non-null interferometers is proposed in this paper for measuring irregular surfaces such as optical aspherics, freeform surfaces and droplet surfaces. With system modeling and raytracing, the improved reverse optimization reconstruction method is employed to correct the retrace error and obtain the accurate shape of the test part with all frequency information. To simplify the model in the raytracing program, an imaging lens images the desired interferogram at a certain plane on the detector and, therefore, only the test arm needs to be modeled. The imaging error of an interferogram, which can be reduced by the partial compensation system (PCS), is analyzed, and the design of the PCS is also demonstrated. Two cases with different optical layouts show the feasibility and the versatility of our method.

Rate maximizing OFDM parameter optimization on HF channels

In this work, we propose an algorithm which maximizes the bit rate of a given wideband OFDM (Orthogonal Frequency-Division Multiplexing) system operating in the HF (High Frequency) band. The proposed algorithm is built on the work given in the literature for estimating the electron densities in the ionosphere and estimating the propagation path of signals throughout the ionosphere. Algorithm uses the outputs of the ray tracing programs in order to calculate the channel parameters for using to optimize the parameters of the HF communication system. Proposed algorithm helps to determine the capacity of the subchannels, transmitter power, number of subchannels, carrier frequency, subchannel bandwidth and cyclic prefix for the OFDM in order to maximize the bit rate. Carrier frequencies produced by the proposed algorithm are compared with the frequencies suggested by the VOACAP (Voice of America Coverage Analysis Program) program.

Optical analysis of a multi-aperture solar central receiver system for high-temperature concentrating solar applications.

A multi-aperture solar central receiver system is optically analyzed for increasing the net power to the receiver in a wide temperature range of 600-1800 K. A model system comprises a tower, a multi-aperture receiver with compound parabolic concentrators, and heliostat sub-fields. Optical modeling is performed using in-house developed Monte-Carlo ray-tracing programs. The heliostat sub-field geometrical configuration, the number of receiver apertures and optical properties of reflective surfaces are varied in the parametric study. Increasing the number of apertures from one to four increases the maximum net receiver power from 116 MW to 332 MW. The use of more than four apertures results in only limited further gain of the net receiver power but significantly decreases the overall optical efficiency and the solar-to-thermal efficiency. The optimal temperature for the maximized annual solar-to-exergy efficiency is found in the range of 1100-1200 K. This optimal temperature decreases slightly with an increasing number of apertures.