A Monte Carlo rendering framework for simulating optical heterodyne detection

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2025
SIGGRAPH 2025 Best Paper Award (Honorable Mention); 2nd Prize Neukom Institute Outstanding Graduate Research in Computational Science

We propose a ray-tracing based Monte Carlo rendering framework for simulating optical heterodyne detection (OHD). (A) OHD is a technique that measures the frequency modulation of light using optical interferometry. Through spectral analysis of the photon-induced current on the photodetector, we can obtain useful information such as object velocity/distance or Doppler spectra. (B) Our MC simulation is based on the OHD path integral that resembles radiometric path integral [Veach 1997], but is resolved by the path frequency which depends on the path length and velocity. (C) Using our simulator, one can simulate various OHD scenarios, such as coherent lidar used in autonomous vehicles, non-invasive blood flow measurement, and atmospheric Doppler sensing.

Abstract

Optical heterodyne detection (OHD) employs coherent light and optical interference techniques 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. 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.

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Acknowledgements

We thank the anonymous reviewers for their feedback. We also thank the authors of Hu et al. [2022] for helpful discussions regarding Doppler effects in AMCW cameras. This work is supported by NSF awards 2403122, 2326904, and 1844538.

Cite

@article{kim25ohd,
    author  = {Kim, Juhyeon and Benko, Craig and Wrenninge, Magnus and Villemin, Ryusuke and Barber, Zeb and Jarosz,
               Wojciech and Pediredla, Adithya},
    title   = {A {Monte} {Carlo} Rendering Framework for Simulating Optical Heterodyne Detection},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
    year    = {2025},
    month   = aug,
    volume  = {44},
    number  = {4},
    doi     = {10.1145/3731150}
}

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