Problem Of Light Transport Research Articles

Inverse Rendering for Tomographic Volumetric Additive Manufacturing

Tomographic Volumetric Additive Manufacturing (TVAM) is an emerging 3D printing technology that can create complex objects in under a minute. The key idea is to project intense light patterns onto a rotating vial of photo-sensitive resin, causing polymerization where the cumulative dose of these patterns reaches the polymerization threshold. We formulate the pattern calculation as an inverse light transport problem and solve it via physically based differentiable rendering. In doing so, we address longstanding limitations of prior work by accurately modeling and correcting for scattering in composite resins, printing in non-symmetric vials, and supporting unusual printing geometries. We also introduce an improved discretization scheme that exploits the ray tracing operation to mitigate resolution-related artifacts in prints. We demonstrate the benefits of our method in real-world experiments, where our computed patterns produce prints with an improved fidelity.

Exact analytical solution of the one-dimensional time-dependent radiative transfer equation with linear scattering

The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its importance, an exact analytical solution to the RTE has remained elusive, necessitating the use of numerical approximations such as Monte Carlo, discrete ordinate, and spherical harmonics methods. In this paper, we present an exact solution to the one-dimensional time-dependent RTE. We delve into the moments of the photon distribution, providing a clear view of the transition to the diffusion regime. This analysis offers a deeper understanding of light propagation in the medium. Furthermore, we demonstrate that the one-dimensional RTE is equivalent to the Klein-Gordon equation with an imaginary mass term determined by the inverse reduced scattering length. Contrary to naive expectations of superluminal solutions, we find that our solution is strictly causal under appropriate boundary conditions, determined by the light transport problem. We validate the found solution using Monte Carlo simulations and benchmark the performance of the latter. Our analysis reveals that even for highly forward scattering, dozens of random light scatterings are required for an accurate estimate, underscoring the complexity of the problem. Moreover, we propose a method for faster convergence by adjusting the parameters of Monte Carlo sampling. We show that a Monte Carlo method sampling photon scatterings with input parameters (μs,g), where μs is the inverse scattering length and g is the scattering anisotropy parameter, is equivalent to that with (μs(1−g)/2,−1). This equivalence leads to a significantly faster convergence to the exact solution, offering a substantial improvement of the Monte Carlo method for the one-dimensional RTE. Our findings not only contribute to the theoretical understanding of the RTE but also have potential implications for improving the numerical methods used to approximate it.

Exact analytical solutions and corresponding Monte Carlo models for the problem of light transport in turbid media with continuous absorption and discrete scattering at the single scattering approximation

Although the radiative transport theory is widely used in various biomedical, ocean, and atmospheric optic problems, there are few light transport problems that can be solved analytically. Therefore, Monte Carlo (MC) numerical simulations are used in most practical applications. In this study, light transport problems in continuously absorbing and discretely scattering media for pencil-like incident beams were considered theoretically using the single scattering approximation. Strict and closed-form analytical solutions to these problems were derived and compared with МС numerical results. Two sets of probabilistic parameters for the MC algorithm were explored. The first was the classical set for media with continuous absorption and smooth scattering, while the second was the newly substantiated set for media with continuous absorption and discrete scattering corresponding to the analytical medium's model. It was shown that if the same model was used in MC simulations and the analytical approach, all of the results were identical. A divergence up to 10% between the obtained analytics and MC results in the case of continuous absorption and smooth scattering was observed.

Physically meaningful Monte Carlo approach to the four-flux solution of a dense multilayered system.

Due to the complexity of the radiative transfer equation, light transport problems are commonly solved using either models under restrictive assumptions, e.g., N-flux models where infinite lateral extension is assumed, or numerical methods. While the latter can be applied to more general cases, it is difficult to relate their parameters to the physical properties of the systems under study. Hence in this contribution we present, first, a review of a four-flux formalism to study the light transport problem in a plane-parallel system together with a derivation of equations to evaluate the different contributions to the total absorptance and, second, as a complementary tool, a Monte Carlo algorithm with a direct correspondence between its inputs and the properties of the system. The combination of the four-flux model and the Monte Carlo approach provides (i) all convergence warranties since the formalism has been established as a limit and (ii) new added capabilities, i.e., both temporal (transient states) and spatial (arbitrarily inhomogeneous media) resolution. The support between the theoretical model and the numerical tool is reciprocal since the model is utilized to set a Monte Carlo discretization criterion, while the Monte Carlo approach is used to validate the aforementioned model. This reinforces the parallel approach used in this work. Furthermore, we provide some examples to show its capabilities and potential, e.g., the study of the temporal distribution of a delta-like pulse of light.

Transient imaging with a time-of-flight camera and its applications

Transient imaging is a technique in photography that records the process of light propagation before it reaches a stationary state such that events at the light speed level can be observed. In this review we introduce three main models for transient imaging with a time-of-flight (ToF) camera: correlation model, frequency-domain model, and compressive sensing model. Transient imaging applications usually involve resolving the problem of light transport and separating the light rays arriving along different paths. We discuss two of the applications: imaging objects inside scattering media and recovering both the shape and texture of an object around a corner.

Gradient-Domain Photon Density Estimation

The most common solutions to the light transport problem rely on either Monte Carlo MC integration or density estimation methods, such as uni- & bi-directional path tracing or photon mapping. Recent gradient-domain extensions of MC approaches show great promise; here, gradients of the final image are estimated numerically instead of the image intensities themselves with coherent paths generated from a deterministic shift mapping. We extend gradient-domain approaches to light transport simulation based on density estimation. As with previous gradient-domain methods, we detail important considerations that arise when moving from a primal- to gradient-domain estimator. We provide an efficient and straightforward solution to these problems. Our solution supports stochastic progressive density estimation, so it is robust to complex transport effects. We show that gradient-domain photon density estimation converges faster than its primal-domain counterpart, as well as being generally more robust than gradient-domain uni- & bi-directional path tracing for scenes dominated by complex transport.

Asymptotic solution of light transport problems in optically thick luminescent media

We study light transport in optically thick luminescent random media. Using radiative transport theory for luminescent media and applying asymptotic and computational methods, a corrected diffusion approximation is derived with the associated boundary conditions and boundary layer solution. The accuracy of this approach is verified for a plane-parallel slab problem. In particular, the reduced system models accurately the effect of reabsorption. The impacts of varying the Stokes shift and using experimentally measured luminescence data are explored in detail. The results of this study have application to the design of luminescent solar concentrators, fluorescence medical imaging, and optical cooling using anti-Stokes fluorescence.

Perturbation Monte Carlo methods for tissue structure alterations

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.

Radiative transport produced by oblique illumination of turbid media with collimated beams.

We examine the general problem of light transport initiated by oblique illumination of a turbid medium with a collimated beam. This situation has direct relevance to the analysis of cloudy atmospheres, terrestrial surfaces, soft condensed matter, and biological tissues. We introduce a solution approach to the equation of radiative transfer that governs this problem, and develop a comprehensive spherical harmonics expansion method utilizing Fourier decomposition (SHEF(N)). The SHEF(N) approach enables the solution of problems lacking azimuthal symmetry and provides both the spatial and directional dependence of the radiance. We also introduce the method of sequential-order smoothing that enables the calculation of accurate solutions from the results of two sequential low-order approximations. We apply the SHEF(N) approach to determine the spatial and angular dependence of both internal and boundary radiances from strongly and weakly scattering turbid media. These solutions are validated using more costly Monte Carlo simulations and reveal important insights regarding the evolution of the radiant field generated by oblique collimated beams spanning ballistic and diffusely scattering regimes.

Light transport simulation with vertex connection and merging

Developing robust light transport simulation algorithms that are capable of dealing with arbitrary input scenes remains an elusive challenge. Although efficient global illumination algorithms exist, an acceptable approximation error in a reasonable amount of time is usually only achieved for specific types of input scenes. To address this problem, we present a reformulation of photon mapping as a bidirectional path sampling technique for Monte Carlo light transport simulation. The benefit of our new formulation is twofold. First, it makes it possible, for the first time, to explain in a formal manner the relative efficiency of photon mapping and bidirectional path tracing, which have so far been considered conceptually incompatible solutions to the light transport problem. Second, it allows for a seamless integration of the two methods into a more robust combined rendering algorithm via multiple importance sampling. A progressive version of this algorithm is consistent and efficiently handles a wide variety of lighting conditions, ranging from direct illumination, diffuse and glossy inter-reflections, to specular-diffuse-specular light transport. Our analysis shows that this algorithm inherits the high asymptotic performance from bidirectional path tracing for most light path types, while benefiting from the efficiency of photon mapping for specular-diffuse-specular lighting effects.

The magic lens

We present an automatic approach to design and manufacture passive display devices based on optical hidden image decoding. Motivated by classical steganography techniques we construct Magic Lenses , composed of refractive lenslet arrays, to reveal hidden images when placed over potentially unstructured printed or displayed source images. We determine the refractive geometry of these surfaces by formulating and efficiently solving an inverse light transport problem, taking into account additional constraints imposed by the physical manufacturing processes. We fabricate several variants on the basic magic lens idea including using a single source image to encode several hidden images which are only revealed when the lens is placed at prescribed orientations on the source image or viewed from different angles. We also present an important special case, the universal lens , that forms an injection mapping from the lens surface to the source image grid, allowing it to be used with arbitrary source images. We use this type of lens to generate hidden animation sequences. We validate our simulation results with many real-world manufactured magic lenses, and experiment with two separate manufacturing processes.

Mode analysis for periodically modulated metal slits

We investigate light transport in metal slits filled with a one-dimensional periodic stack of low- and high-index dielectric media. We have analytically extracted an exact independent-mode model where each transverse eigenmode is subject to its own Bragg scattering and dispersion modulation. The analytical model allows for easy analysis of the complex band structures calculated by means of the finite-difference time-domain method, where the physical origin of each band can be identified and assigned to a certain eigenmode of a metal slit. The analytical model is also very efficient and convenient to analyze the optical transmission spectra for these metal slits. The origin of all subtle spectral features can be discerned from the band diagram analysis of the relevant independent eigenmodes. A comparative study shows that the simple analytical independent-mode theory is powerful in handling the intrinsic light transport problems for periodically modulated metal slits and analyzing their complicated spectrum responses.

Transverse Electromagnetic Modes in Aperture Waveguides Containing a Metamaterial with Extreme Anisotropy

We use metamaterials with extreme anisotropy to solve the fundamental problem of light transport in deep subwavelength apertures. By filling a simply connected aperture with an anisotropic medium, we decouple the cutoff frequency and the group velocity of modes inside apertures. In the limit of extreme anisotropy, all modes become purely transverse electromagnetic modes, free from geometrical dispersion, propagate with a velocity controlled by the transverse permittivity and permeability, and have zero cutoff frequency. We analyze physically realizable cases for a circular aperture and show a metamaterial design using existing materials.

Analytical single-mode model for subwavelength metallic Bragg waveguides

We develop a theoretical formalism that incorporates the method of moment with the analytical eigenmode expansion to investigate the dispersion relation of light transport in subwavelength metallic Bragg waveguide (WG) with each unit cell composed of a wide and a narrow segment of metallic gap. The approach fully accounts for the light scattering at the interface between two consecutive discontinuous segments. A simple single-mode analytical model is derived for both the fundamental even and odd guided modes. The model shows that the band structure of light transport in the structure resembles that of an ordinary dielectric one-dimensional photonic crystal with appropriate physical and geometric parameters that can be analytically derived. Numerical simulations by the finite-difference time-domain method on the optical transmission spectra and band diagrams for these metallic Bragg WGs agree well with the analytical results of band diagrams. In addition, the analytical model can handle structures working in both the microwave and infrared regimes. This indicates that the simple analytical model is effective and efficient in handling various light transport problems for subwavelength metallic Bragg WGs.

Guest Editor's Introduction: Special Section on the Eurographics Symposium on Parallel Graphics and Visualization (EGPGV)

THIS special section on Parallel Graphics and Visualization features extended versions of three selected papers from the Eurographics Symposium on Parallel Graphics and Visualization (EGPGV) in 2009. EGPGV 2009 was held in Munich, Germany, from 29-30 March 2009. It was the ninth event of this successful series of symposia, and was colocated with the Eurographics Annual Conference, which took place from 30 March to 3 April 2009. More information on EGPGV and its supporting Eurographics Working Group on Parallel Graphics can be found at http:// www.egpgv.org. EGPGV 2009 received 27 full paper submissions, which were reviewed by an International Program Committee with 23 members and by the three editors of the symposium proceedings (the symposium chair and the two paper cochairs). Each submission received three or more reviews, culminating with a final program that contained 14 papers, for an acceptance rate just short of 52 percent. Accepted papers for EGPGV 2009 covered a healthy range of topics from the fields of both computer graphics and visualization. The topics included simulation, global illumination, rendering, visualization, and general purpose computing on graphics processing units (GPUs), covering a wide variety of parallel computing platforms ranging from multicore to grid computing. Based on the reviewers’ comments and scoring as well as the quality of the oral presentations at EGPGV 2009, a committee that consisted of the proceedings editors and additional members selected three papers to be invited for submission to this special section of the IEEE Transactions on Visualization and Computer Graphics (TVCG). The authors extended their papers to include new additional material. The extended paper then underwent a full journal review process, including multiple cycles of editing and reviewing. The paper “GPU-Based Multilevel Clustering” by Iurie Chiosa and Andreas Kolb addresses the problem of mesh and data clustering. They present an efficient parallel algorithm for multilevel clustering, specifically designed for fast execution on GPUs. They demonstrate that their clustering method is useful for mesh clustering and general data clustering alike. “Parallel Iteration to the Radiative Transport in Inhomogeneous Media with Bootstrapping” by Laszlo SzirmayKalos, Gabor Liktor, Tamas Umenhoffer, Balazs Toth, Shree Kumar, and Glenn Lupton presents a method to solve the radiative transport equation in inhomogeneous participating media. The proposed solution involves running a multiple-scattering solver in parallel on the GPU or across different nodes in a cluster. “Efficient Rasterization for Outdoor Radio Wave Propagation” by Arne Schmitz, Tobias Rick, Thomas Karolski, Torsten Kuhlen, and Leif Kobbelt considers the problem of simulating and propagating radio waves, which is more complex than the analogous light transport problem due to the fact that waves bend around corners because of diffraction. In this work, the authors present a parallel beam tracing solution to this problem. We would like to thank all members of the International Program Committee of EGPGV 2009, the external reviewers for EGPGV 2009, and the reviewers for the extended papers for TVCG for their help. We would also like to take this opportunity to thank Kurt Debattista for his great work as symposium chair and his support and help during the reviewing process of EGPGV 2009, as well as all of the people from the University of Warwick who designed and hosted the symposium Web pages. Finally, we thank the local organizers of the Eurographics Conference, Rudiger Westermann and Joachim Georgii, who were very supportive of local arrangements for EGPGV 2009.

Efficient Rasterization for Outdoor Radio Wave Propagation

Conventional beam tracing can be used for solving global illumination problems. It is an efficient algorithm and performs very well when implemented on the GPU. This allows us to apply the algorithm in a novel way to the problem of radio wave propagation. The simulation of radio waves is conceptually analogous to the problem of light transport. We use a custom, parallel rasterization pipeline for creation and evaluation of the beams. We implement a subset of a standard 3D rasterization pipeline entirely on the GPU, supporting 2D and 3D frame buffers for output. Our algorithm can provide a detailed description of complex radio channel characteristics like propagation losses and the spread of arriving signals over time (delay spread). Those are essential for the planning of communication systems required by mobile network operators. For validation, we compare our simulation results with measurements from a real-world network. Furthermore, we account for characteristics of different propagation environments and estimate the influence of unknown components like traffic or vegetation by adapting model parameters to measurements.

Replica Exchange Light Transport

Abstract We solve the light transport problem by introducing a novel unbiased Monte Carlo algorithm called replica exchange light transport, inspired by the replica exchange Monte Carlo method in the fields of computational physics and statistical information processing. The replica exchange Monte Carlo method is a sampling technique whose operation resembles simulated annealing in optimization algorithms using a set of sampling distributions. We apply it to the solution of light transport integration by extending the probability density function of an integrand of the integration to a set of distributions. That set of distributions is composed of combinations of the path densities of different path generation types: uniform distributions in the integral domain, explicit and implicit paths in light (particle/photon) tracing, indirect paths in bidirectional path tracing, explicit and implicit paths in path tracing, and implicit caustics paths seen through specular surfaces including the delta function in path tracing. The replica‐exchange light transport algorithm generates a sequence of path samples from each distribution and samples the simultaneous distribution of those distributions as a stationary distribution by using the Markov chain Monte Carlo method. Then the algorithm combines the obtained path samples from each distribution using multiple importance sampling. We compare the images generated with our algorithm to those generated with bidirectional path tracing and Metropolis light transport based on the primary sample space. Our proposing algorithm has better convergence property than bidirectional path tracing and the Metropolis light transport, and it is easy to implement by extending the Metropolis light transport.

A meshless hierarchical representation for light transport

We introduce a meshless hierarchical representation for solving light transport problems. Precomputed radiance transfer (PRT) and finite elements require a discrete representation of illumination over the scene. Non-hierarchical approaches such as per-vertex values are simple to implement, but lead to long precomputation. Hierarchical bases like wavelets lead to dramatic acceleration, but in their basic form they work well only on flat or smooth surfaces. We introduce a hierarchical function basis induced by scattered data approximation. It is decoupled from the geometric representation, allowing the hierarchical representation of illumination on complex objects. We present simple data structures and algorithms for constructing and evaluating the basis functions. Due to its hierarchical nature, our representation adapts to the complexity of the illumination, and can be queried at different scales. We demonstrate the power of the new basis in a novel precomputed direct-to-indirect light transport algorithm that greatly increases the complexity of scenes that can be handled by PRT approaches.

Metropolis Instant Radiosity

Abstract We present Metropolis Instant Radiosity (MIR), an unbiased algorithm to solve the Light Transport problem. MIR is a hybrid technique which consists in representing the incoming radiance field by a set of Virtual Point Lights (V PLs) and in computing the response of all sensors in the scene (i.e. camera captors) by accumulating their contributions. In contrast to other similar approaches, we propose to sample the VPLs with an innovative Multiple‐try Metropolis‐Hastings (MTMH) Algorithm: the goal is to build an efficient, aggressive, and unconditionally robust variance reduction method that works well regardless of the scene layout. Finally, we present a fast ray tracing implementation using MIR and show how our complete rendering pipeline can produce high‐quality and high‐resolution pictures in a few seconds.

Simultaneous integrated diffuse optical tomography and functional magnetic resonance imaging of the human brain.

A complete methodology has been developed to integrate simultaneous diffuse optical tomography (DOT) and functional magnetic resonance imaging (MRI) measurements. This includes development of an MRI-compatible optical probe and a method for accurate estimation of the positions of the source and detector optodes in the presence of subject-specific geometric deformations of the optical probe. Subject-specific head models are generated by segmentation of structural MR images. DOT image reconstruction involves solution of the forward problem of light transport in the head using Monte Carlo simulations, and inversion of the linearized problem for small perturbations of the absorption coefficient. Initial results show good co-localization between the DOT images of changes in oxy- and deoxyhemoglobin concentration and functional MRI data.