Direct Time-of-Flight Measurement Accuracy Improvement With Perimeter-Gated SPADs
Authors: Md Sakibur Sajal, Hunter Guthrie, Zexi Liu, Marc Dandin
Organizations: Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213, USA
Abstract
Direct time of flight (dToF) measurements are susceptible to errors because of system-level and circuit-level timing jitters. In addition, device-level uncertainty stemming from the dark noise of single-photon avalanche diode (SPAD) contributes to the aggregated error. We demonstrate that perimeter gating can help reduce the device-level detection inaccuracy for SPAD devices by reducing the dark noise probability. Specifically, in this work, we developed a general framework to accurately estimate the dToF jitters stemming from different source levels and analyzed a counter-based time to digital converter (TDC) circuit that are commonly used in such systems. We have also measured dToFs using a perimeter-gated SPAD (pg-SPAD) detector fabricated in a 0.35 μm standard CMOS process. Experimental results show that pg-SPADs can improve measurement accuracy in both free-running and time-gated operations.
Single-photon avalanche diode (SPAD) cameras are promising for low-light and high-dynamic-range intensity imaging, but their practical use is limited by complex sensor-specific noise. Unlike time-correlated single-photon counting (TCSPC) systems, SPAD cameras record whether at least one detection occurred in each gate without photon timestamps in intensity imaging mode, making explicit noise decomposition difficult. We present a practical noise modeling and calibration framework for SPAD intensity denoising. Our forward model describes binary-frame accumulation with a Binomial observation process, models signal-independent dark noise as an exposure-dependent pure dark count term plus an exposure-independent dark-frame bias term, and incorporates pixel-wise response non-uniformity. We design a dedicated calibration procedure for the proposed model and use it to build a count-domain noise-synthesis pipeline for network training. For denoising, we further design a SPAD-specific dark-shading correction (SPAD-DSC) to remove most systematic noise before network training. We construct a real-world SPAD intensity dataset for testing. Experimental results demonstrate the superiority of the proposed noise model.
Direct Time-of-Flight (dToF) sensors provide highly accurate metric depth and are more robust than indirect ToF systems in challenging real-world conditions. However, their high manufacturing cost and limited photodiode array size produce depth maps that are extremely sparse, low-resolution, and noisy, making them unsuitable for VR/XR, robotics, and 3D perception tasks that require dense metric depth. Existing monocular and depth completion methods struggle to handle the unique sampling patterns and hardware artifacts of dToF devices, and their performance often deteriorates significantly under severe sparsity or noise. We present a generalizable framework for dense metric depth completion from sparse dToF measurements, capable of operating across diverse sensor types, sparsity levels, and noise conditions. Our model employs a depth-guided dual-branch Vision Transformer encoder that processes RGB images and sparse dToF measurements separately, while a masked joint attention module allows depth tokens to reliably guide image features without being overwritten by them. A lightweight decoder reconstructs dense metric depth efficiently, without diffusion-based or refinement-heavy post-processing. To address the scarcity of paired training data, we introduce a comprehensive dToF simulation pipeline that reproduces the characteristics of flash, sub-VGA flash, and rotating sensors, including hardware-induced degradation, irregular sparsity, and realistic noise distributions. Trained entirely on synthetic data, our model achieves strong zero-shot generalization across 6 datasets and 3 real dToF devices, outperforming state-of-the-art approaches in both accuracy and computational efficiency. This establishes a robust and practical solution for dense metric depth completion from sparse direct ToF sensors. Our code and models are open-sourced. See https://vclab.kaist.ac.kr/cvpr2026p3.
Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.