Single-photon lidar (SPL) can achieve high-accuracy, lowlight ranging; however, velocity estimation typically requires regression over multiple distance measurements. Here, we introduce Doppler SPL, which enables joint instantaneous velocity and range estimation. First, we derive a measurement model for SPL, showing that a target moving at a constant velocity introduces a Doppler shift into the sequence of photon detection times. We then introduce estimators for range and velocity based on Fourier analysis of the detection time sequence. Simulations show improved accuracy of our method over baseline approaches, and we further validate our approach on experimental SPL data for a moving target.

Remote temperature sensing of volumetric flows has a variety of applications, such as promoting thermal comfort, heat dissipation, or data center cooling. The emergence of background-oriented schlieren (BOS) imaging in recent years has enabled transparent flow visualization at minor costs. In this paper, we develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using BOS measurements and physics-informed reconstruction. Our framework utilizes a light projector that projects a pattern onto a target back wall and a camera that observes small distortions in the light pattern due to the change in the refractive index of the air as a result of the temperature variation. While the single-view BOS tomography problem is severely ill-posed, we regularize the reconstruction using a physics-informed neural network (PINN) that ensures that the reconstructed airflow is consistent with the coupled Boussinesq approximation of the incompressible Navier– Stokes and the heat transfer equations.

Conventional wisdom suggests that single-photon lidar (SPL) should operate in low-light conditions to minimize dead-time effects. Many methods have been developed to mitigate these effects in synchronous SPL systems. However, solutions for free-running SPL remain limited despite the advantage of reduced histogram distortion from dead times. To improve the accuracy of free-running SPL, we propose a computationally efficient joint maximum likelihood estimator of the signal flux, the background flux, and the depth using only histograms, along with a complementary regularization framework that incorporates a learned point cloud score model as a prior. Simulations and experiments demonstrate that free-running SPL yields lower estimation errors than its synchronous counterpart under identical conditions, with our regularization further improving accuracy.

In single photon lidar (SPL), the laser repetition rate sets the maximum distance that can be recovered unambiguously. Conventional SPL extends this maximum recordable depth by reducing the repetition rate; however, the slower acquisition speed limits the number of received photons, which may be insufficient to track fast-moving objects. Inspired by recent successes in modulo sensing, we leverage the smoothness of typical trajectories to achieve long-range tracking beyond the unambiguous range. Although SPL naturally acquires modulo time-of-flight measurements, it introduces several challenges—including random sampling times, multiple noise sources, and absolute distance uncertainty—that are not addressed by the current modulo sensing literature. Hence, we propose an interpolation and denoising method that operates directly over the modulo samples. We further disambiguate the absolute distance based on the changing reflectivity fall-off. Monte Carlo simulations considering realistic trajectories under practical conditions show that, when properly unwrapped, the normalized mean squared error of our depth estimate decreases by over 20 dB with respect to a lidar setup whose repetition period leads to no ambiguity.

Single-pixel imaging is an efficient image acquisition process where light from a target scene is passed through a spatial light modulator and then projected onto a single photodiode with a high temporal acquisition rate. The scene reconstruction is achieved using computational methods that leverage prior assumptions on the scene structure. In this paper, we propose to model the structure of a dynamic spatio-temporal scene using a reduced-order model that is learned from training data examples. Specifically, by combining single-pixel imaging methods with a reduced-order model prior implemented as a neural ordinary differential equation, image sequence reconstruction can be accomplished with significantly reduced data requirements while maintaining performance levels on par with leading methods. We demonstrate superior reconstruction at low sampling rates for simulated trajectories governed by Burgers’ equation and turbulent plumes emulating gas leaks.

In frequency-modulated continuous-wave (FMCW) lidar, the distance to an illuminated target is proportional to the beat frequency of the interference signal. Laser phase noise often limits the range accuracy of FMCW lidar, and existing frequency estimation methods make overly simplistic assumptions about the noise model. In this work, we propose an algorithm that performs frequency estimation via phase unwrapping by explicitly accounting for correlations in the phase noise. Given a candidate frequency, we approximately recover the maximum likelihood unwrapping sequence using the Viterbi algorithm and the phase noise statistics. The algorithm then alternates between unwrapping and frequency estimate refinement until convergence. Compared to state-of-the-art alternatives, our algorithm consistently achieves superior performance at long range or with large-linewidth lasers when the signal-to-noise ratio is sufficiently high.

Optical coherence tomography (OCT) using Fourier domain processing can resolve micrometer-scale depth information. However, the conventional volumetric reconstruction approach is unnecessary for opaque samples with only one reflector per lateral position, and the required sample interpolation degrades performance. In this paper, we show that surface depth profilometery with a Fourier-domain OCT system simplifies to a sinusoidal parameter estimation problem. We derive approximate maximum likelihood estimators for the sample depth and reflectivity, which can easily be computed by backprojecting the data without interpolating. Iterative refinement further improves results at high signal-to-noise ratio (SNR). We demonstrate the performance of the technique compared to the conventional Fourier transform approach on both simulated and experimental data collected with a spectral-domain OCT system. Our results show that maximum likelihood profilometry is fast and more robust to noise than the Fourier approaches at moderate SNR.

Edge-resolved transient imaging (ERTI) is a method for non-line-of-sight imaging that combines the use of direct time of flight for measuring distances with the azimuthal angular resolution afforded by a vertical edge occluder. Recently conceived and demonstrated for the first time, no performance analyses or optimizations of ERTI have appeared in published papers. This paper explains how the difficulty of detection of hidden scene objects with ERTI depends on a variety of parameters, including illumination power, acquisition time, ambient light, visible-side reflectivity, hidden-side reflectivity, target range, and target azimuthal angular position. Based on this analysis, optimization of the acquisition process is introduced whereby the illumination dwell times are varied to counteract decreasing signal-to-noise ratio at deeper angles into the hidden volume. Inaccuracy caused by a coaxial approximation is also analyzed and simulated.

Time-correlated single photon counting (TCSPC) is a powerful technique for lidar depth imaging, allowing for accurate range measurements from very low light levels. However, single-photon detectors used in TCSPC have a dead time after each photon detection, which blocks registration of subsequent photons arriving within that dead time, causing a distortion of the detection time distribution. The most common approach to avoiding dead time distortion is to optically reduce the photon arrival rate such that with high probability no photons arrive during the dead time. However, this prevents the high photon flux acquisition necessary for real-time applications such as autonomous navigation. In this paper, we propose a dead time compensation method that enables fast data acquisition with dead time-limited detectors. Specifically, we model dead time-affected detection times as a Markov chain, present a simple method for approximating the stationary distribution, and estimate depths using a log-matched filter matched to that distribution. Our method applies to multimodal imaging systems where a standard camera is used in conjunction with lidar to provide information about scene reflectivity. Simulation results for real 3D scenes show that our method reduces the root mean squared error by several orders of magnitude for the same acquisition time.

Using detector arrays can speed up lidar systems by parallelizing acquisition. However, current SPAD arrays have time bins longer than typical laser pulse durations, resulting in measurement errors dominated by quantization. We propose an optical time-of-flight system that uses subtractive dither to improve image depth resolution. Modeling the measurement noise with a generalized Gaussian distribution further improves estimation error in simulations, although model mismatch prevents the same advantage for our experimental data. Experimental results with the ratio of laser pulse standard deviation to quantization bin duration equal to 0.15 and using an average of 267 photons per pixel show a reduction in RMS error as large as 9-fold over estimates from coarsely quantized data.