Search for: All records

Abstract We present a wave‐optics‐based BSDF for simulating the corona effect observed when viewing strong light sources through materials such as certain fabrics or glass surfaces with condensation. These visual phenomena arise from the interference of diffraction patterns caused by correlated, disordered arrangements of droplets or pores. Our method leverages the pair correlation function (PCF) to decouple the spatial relationships between scatterers from the diffraction behavior of individual scatterers. This two‐level decomposition allows us to derive a physically based BSDF that provides explicit control over both scatterer shape and spatial correlation. We also introduce a practical importance sampling strategy for integrating our BSDF within a Monte Carlo renderer. Our simulation results and real‐world comparisons demonstrate that the method can reliably reproduce the characteristics of the corona effects in various real‐world diffractive materials. 

This 3 hour course provides a detailed overview of grid-free Monte Carlo methods for solving partial differential equations (PDEs) based on the walk on spheres (WoS) algorithm, with a special emphasis on problems with high geometric complexity. PDEs are a basic building block of models and algorithms used throughout science, engineering and visual computing. Yet despite decades of research, conventional PDE solvers struggle to capture the immense geometric complexity of the natural world. A perennial challenge is spatial discretization: traditionally, one must partition the domain into a high-quality volumetric mesh—a process that can be brittle, memory intensive, and difficult to parallelize. WoS makes a radical departure from this approach, by reformulating the problem in terms of recursive integral equations that can be estimated using the Monte Carlo method, eliminating the need for spatial discretization. Since these equations strongly resemble those found in light transport theory, one can leverage deep knowledge from Monte Carlo rendering to develop new PDE solvers that share many of its advantages: no meshing, trivial parallelism, and the ability to evaluate the solution at any point without solving a global system of equations. The course is divided into two parts. Part I will cover the basics of using WoS to solve fundamental PDEs like the Poisson equation. Topics include formulating the solution as an integral equation, generating samples via recursive random walks, and employing accelerated distance and ray intersection queries to efficiently handle complex geometries. Participants will also gain experience setting up demo applications involving data interpolation, heat transfer, and geometric optimization using the open-source “Zombie” library, which implements various grid-free Monte Carlo PDE solvers. Part II will feature a mini-panel of academic and industry contributors covering advanced topics including variance reduction, differentiable and multi-physics simulation, and applications in industrial design and robust geometry processing. 

Optical heterodyne detection (OHD) employs coherent light and optical interference techniques (Fig. 1-(A)) to extract physical parameters, such as velocity or distance, which are encoded in the frequency modulation of the light. With its superior signal-to-noise ratio compared to incoherent detection methods, such as time-of-flight lidar, OHD has become integral to applications requiring high sensitivity, including autonomous navigation, atmospheric sensing, and biomedical velocimetry. However, current simulation tools for OHD focus narrowly on specific applications, relying on domain-specific settings like restricted reflection functions, scene configurations, or single-bounce assumptions, which limit their applicability. In this work, we introduce a flexible and general framework for spectral-domain simulation of OHD. We demonstrate that classical radiometry-based path integral formulation can be adapted and extended to simulate the OHD measurements in the spectral domain. This enables us to leverage the rich modeling and sampling capabilities of existing Monte Carlo path tracing techniques. Our formulation shares structural similarities with transient rendering but operates in the spectral domain and accounts for the Doppler effect (Fig. 1-(B)). While simulators for the Doppler effect in incoherent (intensity) detection methods exist, they are largely not suitable to simulate OHD. We use a microsurface interpretation to show that these two Doppler imaging techniques capture different physical quantities and thus need different simulation frameworks. We validate the correctness and predictive power of our simulation framework by qualitatively comparing the simulations with real-world captured data for three different OHD applications—FMCW lidar, blood flow velocimetry, and wind Doppler lidar (Fig. 1-(C)). 

Transient absorption spectroscopy (TAS) is a field of study that investigates the dynamic process of chemical compounds. Thanks to the recent emergence of ultrafast pulsed lasers, TAS now extends its reach to studying photochemical reactions occurring within few femtosecond to nanosecond timescales. With ultrafast TAS, changes in sample absorbance or transmittance over time following excitation by pulsed light can be measured at a high temporal resolution -tens of femtoseconds. An application of ultrafast TAS is lifetime measurement for fluorescence decay. However, due to various noise sources (sensor noise, shot noise, unintended photochemical reactions, etc.) during measurement, obtaining a reliable lifetime value often necessitates extensive repetition resulting in experiments lasting several hours. In this paper, we introduce an effective time sampling strategy tailored for lifetime measurement from noisy transient signals. We start with a well-established non-linear curve fitting algorithm and demonstrate that sampling time shifts that maximize the signal derivative (t=τ) will minimize the variance in lifetime estimation. Additionally, we reduce the number of parameters by normalization to ensures the correctness of our algorithm. We demonstrate using simulation that our proposed method outperforms conventional time sampling or normalization methods across various conditions. Especially, we found that proposed method gives same error with 5.5 x less samples compared to the common TAS measurement strategy that uses exponential time sampling with full parameter curve-fitting. Moreover, through real-world TAS measurements, we show that our technique results in 2 - 8 x less standard deviation compared to baseline methods. We expect that our algorithm will be valuable not only for researchers who use TAS but also for researchers across various fields who use time-gated transient cameras for lifetime analysis.