Refractive Boundary Research Articles

Efficient Path‐Space Differentiable Volume Rendering With Respect To Shapes

AbstractDifferentiable rendering of translucent objects with respect to their shapes has been a long‐standing problem. State‐of‐the‐art methods require detecting object silhouettes or specifying change rates inside translucent objects—both of which can be expensive for translucent objects with complex shapes.In this paper, we address this problem for translucent objects with no refractive or reflective boundaries. By reparameterizing interior components of differential path integrals, our new formulation does not require change rates to be specified in the interior of objects. Further, we introduce new Monte Carlo estimators based on this formulation that do not require explicit detection of object silhouettes.

Super-dispersive demultiplexer design using positive–negative refraction boundary and hetero-photonic crystals

Super-dispersive demultiplexer design using positive–negative refraction boundary and hetero-photonic crystals

Establishment of Personalized Finite Element Model of Crystalline Lens Based on Sweep-Source Optical Coherence Tomography

The virtual lens model has important value in ophthalmic research, clinical diagnosis, and treatment. However, the establishment of personalized lens models and the verification of accommodation accuracy have not been paid much attention. We proposed a personalized lens model establishment and the accommodation accuracy evaluation method based on sweep-source optical coherence tomography (SS-OCT). Firstly, SS-OCT is used to obtain a single lens image in the maximum accommodation state. After refraction correction, boundary detection, and curve fitting, the central curvature radius, thickness, and lens nucleus contour of the anterior and posterior surfaces of the lens were obtained. Secondly, a personalized finite element model improved from Burd’s model was established using these individual parameters, and the adaptation process of the lens model was simulated by pulling the suspensory ligament. Finally, the shape and refractive power changes of the real human lens under different accommodation stimuli were collected and compared with the accommodation process of the finite element model. The results show that the accommodation process of the finite element model is highly consistent with that of the real lens. From the un-accommodation state to the maximum-accommodation state, the difference rate of all geometric and refractive parameters between the two is less than 5%. Thus, the personalized lens finite element model obtained by the calibration and correction of the existing model can accurately simulate the regulation process of a specific human lens. This work helps to provide a valuable theoretical basis and research ideas for the study of clinical diagnosis and treatment of related diseases.

The factorization method for the scattering by a mixed inhomogeneous medium

Abstract We use the classical factorization method proposed firstly by Kirsch to reconstruct the support of the mixed inhomogeneous medium associated with complex valued refractive indexes and different transmission boundary conditions. We will show that for well-chosen inhomogeneous backgrounds, one obtains a necessary and sufficient condition characterizing the support of the medium via the eigensystem of a self-adjoint operator, which is related to the far field operator. Moreover, for completeness of our problem, the variational method is applied to solve the direct scattering problem. And, we present a variant of numerical examples in 2D to verify the effectiveness and robustness of the proposed inverse algorithms.

SEISMIC MODEL OF THE UPPER EARTH`s CRUST ON NORTH-EAST PART OF TRAVERSE 3-DV BASED ON RESULTS OF HEAD WAVES DIGITAL PROCESSING

Digital processing of refracted waves data, which are registered on North-East part of profile3-DV, is done. Time sections and velocity model are formed. It is proved, that refraction horizons on depth interval of 0-1.5 km are geologic boundaries in sedimentary cover on Ayan-Yuryakh tectonic block. Refraction boundary on depth of ~1.0 km is not lithologic border on Inyaly-Debin block. Layers, which are potentially productive for ore mineral resources, are substracted by low values of V/V (1.66-1.70) on depth below 1.0 km, on Inyaly-Debin block and Orotukan-Balygychan elevation.

A practical path guiding method for participating media

Rendering translucent materials is costly: light transport algorithms need to simulate a large number of scattering events inside the material before reaching convergence. The cost is especially high for materials with a large albedo or a small mean-free-path, where higher-order scattering effects dominate. In simple terms, the paths get lost in the medium. Path guiding has been proposed for surface rendering to make convergence faster by guiding the sampling process. In this paper, we introduce a path guiding solution for translucent materials. We learn an adaptive approximate representation of the radiance distribution in the volume and use it to sample the scattering direction, combining it with phase function sampling by resampled importance sampling. The proposed method significantly improves the performance of light transport simulation in participating media, especially for small lights and media with refractive boundaries. Our method can handle any homogeneous participating medium, with high or low scattering, with high or low absorption, and from isotropic to highly anisotropic.

Analysis of two transmission eigenvalue problems with a coated boundary condition

In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown that the eigenvalues can be recovered from the scattering data and hold information about the material properties of the media one wishes to determine. Motivated by recent works we will study the electromagnetic transmission eigenvalue problem and scalar ‘zero-index’ transmission eigenvalue problem for a media with a coated boundary. Existence of infinitely many real eigenvalues will be proven as well as showing that the eigenvalues depend monotonically on the refractive index and boundary parameter. Numerical examples in two spatial dimensions are presented for the scalar ‘zero-index’ transmission eigenvalue problem. Also, in our investigation we prove that as the boundary parameter tends to zero and infinity we recover the classical eigenvalue problems.

Overcoming the penetration depth limit in optical microscopy: Adaptive optics and wavefront shaping

Despite the unique advantages of optical microscopy for molecular specific high resolution imaging of living structure in both space and time, current applications are mostly limited to research settings. This is due to the aberrations and multiple scattering that is induced by the inhomogeneous refractive boundaries that are inherent to biological systems. However, recent developments in adaptive optics and wavefront shaping have shown that high resolution optical imaging is not fundamentally limited only to the observation of single cells, but can be significantly enhanced to realize deep tissue imaging. To provide insight into how these two closely related fields can expand the limits of bio imaging, we review the recent progresses in their performance and applicable range of studies as well as potential future research directions to push the limits of deep tissue imaging.

Fast Computation of Single Scattering in Participating Media with Refractive Boundaries Using Frequency Analysis.

Many materials combine a refractive boundary and a participating media on the interior. If the material has a low opacity, single scattering effects dominate in its appearance. Refraction at the boundary concentrates the incoming light, resulting in an important phenomenon called volume caustics. This phenomenon is hard to simulate. Previous methods used point-based light transport, but attributed point samples inefficiently, resulting in long computation time. In this paper, we use frequency analysis of light transport to allocate point samples efficiently. Our method works in two steps: in the first step, we compute volume samples along with their covariance matrices, encoding the illumination frequency content in a compact way. In the rendering step, we use the covariance matrices to compute the kernel size for each volume sample: small kernel for high-frequency single scattering, large kernel for lower frequencies. Our algorithm computes volume caustics with fewer volume samples, with no loss of quality. Our method is both faster and uses less memory than the original method. It is roughly twice as fast and uses one fifth of the memory. The extra cost of computing covariance matrices for frequency information is negligible.

Shallow seismic sounding based on ellipticity analysis of microtremor

A brief review is carried out of the previous study about the spectral ratios of horizontal and vertical components of microseismic oscillations displacement. The basic principles of resonant boundaries allocation and the construction of deep sections based on the H/V relations (ellipticity) are considered. A description of the equipment used, the method of recording and processing microseismic noise are presented. The main goal of the research work is to clarify the nature of the connection between the ellipticity of microseisms with geological features and the correctness of constructing deep sections based on them. The initial data are the amplitude spectra of the components of microseismic signal, obtained using the fast Fourier transformation. In the course of experimental work it was found that the spectral relations retain their characteristic features regardless of the azimuth of observations. A number of practical examples compare microseismic sections with results from other geophysical methods and drilling information. The results obtained indicate the complex nature of the ellipticity of microseismic noise under different conditions, however, they make it possible to determine the main interfaces between the upper part of the geological section. Resonant boundaries emitted by microtremor are often located near refractive seismic boundaries. This is consistent with the theory that resonance effects occur at the interface between two media with a high contrast of acoustic impedance.

The Hidden Depths of Planetary Atmospheres

Abstract Atmospheric regions below a refractive boundary are hidden in limb observations. Refraction thus creates a gray continuum in the planet’s transmission spectrum, which can hide spectral features associated with sources of atmospheric opacity. We combine refractive theory with recent analytical advances describing the effects of surfaces and clouds on transmission spectra, to express the location of this boundary in atmospheric opacity space, for both atomic and molecular extinction, as well as collision-induced absorption. This allows one to quickly estimate how refraction affects spectral features in well-mixed atmospheres. We show that differences in the geometry of limb observations between solar system planets and exoplanets lead to different locations of this boundary, and that more than four extra scale heights of atmosphere are hidden in exoplanet transits compared to solar system observations of cold gas giants. We explore how the location of this refractive boundary in exoplanet transits changes in a well-mixed isothermal atmosphere with its temperature and composition, the spectral type of the planet’s host star, and the size of the planet. We demonstrate that five extra scale heights of atmosphere are hidden in a terrestrial planet with a CO2 atmosphere compared to a helium atmosphere, resulting in a flatter spectrum than from its smaller scale height alone. We provide results for a few exoplanets, notably those in the TRAPPIST-1 system, to help the scientific community estimate the impact of refraction on the size of spectral features without radiative transfer calculations, and thus help refine planned James Web Space Telescope observations.

Physically-Based Rendering of Particle-Based Fluids with Light Transport Effects

Recent interactive rendering approaches aim to efficiently produce images. However, time constraints deeply affect their output accuracy and realism (many light phenomena are poorly or not supported at all). To remedy this issue, in this paper, we propose a physically-based fluid rendering approach. First, while state-of-the-art methods focus on isosurface rendering with only two refractions, our proposal (1) considers the fluid as a heterogeneous participating medium with refractive boundaries, and (2) supports both multiple refractions and scattering. Second, the proposed solution is fully particle-based in the sense that no particles transformation into a grid is required. This interesting feature makes it able to handle many particle types (water, bubble, foam, and sand). On top of that, a medium with different fluids (color, phase function, etc.) can also be rendered.

Analytic Scattering and Refraction Models for Exoplanet Transit Spectra

Abstract Observations of exoplanet transit spectra are essential to understanding the physics and chemistry of distant worlds. The effects of opacity sources and many physical processes combine to set the shape of a transit spectrum. Two such key processes—refraction and cloud and/or haze forward-scattering—have seen substantial recent study. However, models of these processes are typically complex, which prevents their incorporation into observational analyses and standard transit spectrum tools. In this work, we develop analytic expressions that allow for the efficient parameterization of forward-scattering and refraction effects in transit spectra. We derive an effective slant optical depth that includes a correction for forward-scattered light, and present an analytic form of this correction. We validate our correction against a full-physics transit spectrum model that includes scattering, and we explore the extent to which the omission of forward-scattering effects may bias models. Also, we verify a common analytic expression for the location of a refractive boundary, which we express in terms of the maximum pressure probed in a transit spectrum. This expression is designed to be easily incorporated into existing tools, and we discuss how the detection of a refractive boundary could help indicate the background atmospheric composition by constraining the bulk refractivity of the atmosphere. Finally, we show that opacity from Rayleigh scattering and collision-induced absorption will outweigh the effects of refraction for Jupiter-like atmospheres whose equilibrium temperatures are above 400–500 K.

Point-Based Rendering for Homogeneous Participating Media with Refractive Boundaries.

Illumination effects in translucent materials are a combination of several physical phenomena: refraction at the surface, absorption and scattering inside the material. Because refraction can focus light deep inside the material, where it will be scattered, practical illumination simulation inside translucent materials is difficult. In this paper, we present an a Point-Based Global Illumination method for light transport on homogeneous translucent materials with refractive boundaries. We start by placing light samples inside the translucent material and organizing them into a spatial hierarchy. At rendering, we gather light from these samples for each camera ray. We compute separately the sample contributions for single, double and multiple scattering, and add them. We present two implementations of our algorithm: an offline version for high-quality rendering and an interactive GPU implementation. The offline version provides significant speed-ups and reduced memory footprints compared to state-of-the-art algorithms, with no visible impact on quality. The GPU version yields interactive frame rates: 30fps when moving the viewpoint, 25fps when editing the light position or the material parameters.

An analytical formalism accounting for clouds and other ‘surfaces’ for exoplanet transmission spectroscopy

Although the formalism of Lecavelier des Etangs et al. is extremely useful to understand what shapes transmission spectra of exoplanets, it does not include the effects of a sharp change in flux with altitude generally associated with surfaces and optically thick clouds. Recent advances in understanding the effects of refraction in exoplanet transmission spectra have, however, demonstrated that even clear thick atmospheres have such a sharp change in flux due to a refractive boundary. We derive a more widely applicable analytical formalism by including first-order effects from all these ‘surfaces’ to compute an exoplanet's effective radius, effective atmospheric thickness and spectral modulation for an atmosphere with a constant scaleheight. We show that the effective radius cannot be located below these ‘surfaces’ and that our formalism matches the formalism of Lecavelier des Etangs et al. in the case of a clear atmosphere. Our formalism explains why clouds and refraction reduce the contrast of spectral features, and why refraction decreases the Rayleigh scattering slope as wavelength increases, but also shows that these are common effects of all ‘surfaces’. We introduce the concept of a ‘surface’ cross-section, the minimum mean cross-section that can be observed, as an index to characterize the location of ‘surfaces’ and provide a simple method to estimate their effects on the spectral modulation of homogeneous atmospheres. We finally devise a numerical recipe that extends our formalism to atmospheres with a non-constant scaleheight and arbitrary sources of opacity, a potentially necessary step to interpret observations.

Microtremor response of the Cheongcheon dam in Korea

Microtremors were analysed using the reference-dependent horizontal spectral (H/H) method and the horizontal-to-vertical spectral ratio (H/V) method to estimate site effects of the Cheongcheon earthen dam in Korea. Seismic vibrations were recorded on the dam’s crest, at the toe of the dam, and in a downstream borehole using three-component accelerometers. The H/H peaks for crest versus toe-of-dam accelerations occurred at 3.1, 6.7 and 13.1 Hz with ratios of 6.9, 11.4 and 8.9, respectively. The H/V peaks for the crest of the dam occurred at 3.0, 7.0 and 13.4 Hz with ratios of 6.7, 7.8 and 5.6, respectively. The peak near 3 Hz may correspond to depth to bedrock, whereas the other peaks at higher frequencies may reflect the geometrical effect of the dam or overtone responses to the thickness of dam fill overlying the clay core. For the toe data, from the H/V spectral ratio method, the basement boundary appeared as double peaks near 8 and 10 Hz with corresponding amplification factors of 5.2 and 6.2. These may indicate a gradual change in velocity across the basement boundary at ~10 m depth. The third resonance, which occurred at 15 Hz, may correlate with the refraction boundary at 5–6 m depth in the overburden layer. Both the frequencies and magnitudes of resonance derived from the H/H and H/V methods are reasonably well matched to the theoretical response curves computed by the reflection and transmission matrix and the two-dimensional finite difference methods.

Refraction in planetary atmospheres: improved analytical expressions and comparison with a new ray-tracing algorithm

Atmospheric refraction affects to various degrees exoplanet transit, lunar eclipse, as well as stellar occultation observations. Exoplanet retrieval algorithms often use analytical expressions for the column abundance along a ray traversing the atmosphere as well as for the deflection of that ray, which are first-order approximations valid for low densities in a spherically symmetric homogeneous isothermal atmosphere. We derive new analytical formulae for both of these quantities, which are valid for higher densities, and use them to refine and validate a new ray-tracing algorithm which can be used for arbitrary atmospheric temperature–pressure profiles. We illustrate with simple isothermal atmospheric profiles the consequences of our model for different planets: temperate Earth-like and Jovian-like planets, as well as HD 189733b, and GJ1214b. We find that, for both hot exoplanets, our treatment of refraction does not make much of a difference to pressures as high as 10 atm, but that it is important to consider the variation of gravity with altitude for GJ1214b. However, we find that the temperate atmospheres have an apparent scaleheight significantly smaller than their actual density scaleheight at densities larger than 1 amagat, thus increasing the difficulty of detecting spectral features originating in these regions. These denser atmospheric regions form a refractive boundary layer where column abundances and ray deflection increases dramatically with decreasing impact parameter. This refractive boundary layer mimics a surface, and none of the techniques mentioned above can probe atmospheric regions denser than about 4 amagat on these temperate planets.

Accurate Computation of Single Scattering in Participating Media with Refractive Boundaries

AbstractVolume caustics are high‐frequency effects appearing in participating media with low opacity, when refractive interfaces are focusing the light rays. Refractions make them hard to compute, since screen locality does not correlate with spatial locality in the medium. In this paper, we give a new method for accurate computation of single scattering effects in a participating media enclosed by refractive interfaces. Our algorithm is based on the observation that although radiance along each camera ray is irregular, contributions from individual triangles are smooth. Our method gives more accurate results than existing methods, faster. It uses minimal information and requires no pre‐computation or additional data structures.

청천댐 주변의 천부 P파 및 S파 속도구조

높이 23 m인 보령시 청천댐 상부와 인근에서 5 kg 해머를 이용하여 소규모 굴절법 및 표면파 탐사를 실시하였다. 인공 지진파의 수직 및 수평성분을 초동주시 토모그래피 및 레일리파 분산곡선 역산을 통하여 천부 P파속도(<TEX>${\nu}_p$</TEX>)와 S파속도(<TEX>${\nu}_s$</TEX>) 구조를 파악하였다. 중생대 퇴적암질 기반암의 평균 <TEX>${\nu}_p$</TEX>와 <TEX>${\nu}_s$</TEX>는 댐마루 30 m 깊이에서 각각 1650 m/s와 950 m/s, 하류쪽 댐체 끝 지점 10 m 깊이에서 각각 1650 m/s와 940 m/s로 분석된다. 이 층들의 동포아송비는 0.24 ~ 0.25의 범위로, 고화된 퇴적층의 값과 일치한다. 댐체로부터 152 m 하류지점의 깊이 45 m 시추공 부근에서의 SH파 굴절법 토모그램은 10 ~ 12 m 깊이에 평균 vs가 870 m/s인 임계굴절면이 존재함을 보여준다. 이 지역에서는 덮개층의 <TEX>${\nu}_p$</TEX>와 <TEX>${\nu}_s$</TEX>가 각각 500 m/s와 200 m/s인 상부층과 깊이에 따라 속도가 거의 선형으로 증가하는 하부층으로 구성되어 있다. On and near the 23-m high earthen Cheongcheon dam in Boryeong City, Korea, short seismic refraction and surface-wave profiles were conducted using a 5-kg sledgehammer. From vertical and horizontal components of the seismic waves, near-surface P-wave velocities (<TEX>${\nu}_p$</TEX>) and S-wave velocities (<TEX>${\nu}_s$</TEX>) were derived by inverting first-arrival refraction times and dispersion curves of Rayleigh waves. Average <TEX>${\nu}_p$</TEX> and <TEX>${\nu}_s$</TEX> for the Jurassic sedimentary basement were determined to be 1650 and 950 m/s at a depth of 30 m directly beneath the dam and 1650 m/s and 940 m/s at a depth of 10 m at the toe of the dam, respectively. The dynamic Poisson's ratio for these strata were therefore in the range of 0.24 to 0.25, which is consistent with ratios for consolidated sedimentary strata. Near a 45-m borehole 152 m downstream from the dam crest, an SH tomogram indicates a refraction boundary with an average <TEX>${\nu}_s$</TEX> of 870 m/s at depths of 10 ~ 12 m. At this site, the overburden comprises the upper layer with relatively constant <TEX>${\nu}_p$</TEX> and <TEX>${\nu}_s$</TEX> around 500 and 200 m/s, respectively, and the lower layer in which both <TEX>${\nu}_p$</TEX> and <TEX>${\nu}_s$</TEX> increase with depth almost linearly. The dynamic Poisson's ratios for the overburden were in the range of 0.30 to 0.43.

Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces

The least-squares natural element method (LSNEM) is employed for solving radiative heat transfer problem in two-dimensional semitransparent graded index medium with semitransparent and diffusely reflecting surfaces. LSNEM is an extension of natural element method (NEM). Unlike the NEM based on Galerkin discretization, the least-squares weighted residuals approach is employed to spatially discretize the radiative heat transfer equations in LSNEM. Radiative heat transfer problem in rectangular enclosure filled with graded index medium having opaque surfaces is examined to verify the LSNEM. Afterwards, radiative heat transfer in the semicircular enclosure with an inner circle filled with graded index medium is studied. Two kinds of refractive index distributions are considered. The studies show that the refractive index distributions and optical boundary conditions of the surfaces greatly influence the radiative transfer. Effects of the extinction coefficient are investigated on the temperature distributions and radiative heat fluxes.