Dead Time Compensation for High-Flux Ranging

Abstract

Dead time effects have been considered a major limitation for fast data acquisition in various time-correlated single photon counting applications, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. Through the application of lidar ranging, this work explores the empirical distribution of detection times in the presence of dead time and demonstrates that an accurate statistical model can result in reduced ranging error with shorter data acquisition time when operating in the high-flux regime. Specifically, we show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain. Depth estimation can then be performed by passing the empirical distribution through a filter matched to the stationary distribution. Moreover, based on the Markov chain model, we formulate the recovery of arrival distribution from detection distribution as a nonlinear inverse problem and solve it via provably convergent mathematical optimization. By comparing per-detection Fisher information for depth estimation from high-and low-flux detection time distributions, we provide an analytical basis for possible improvement of ranging performance resulting from the presence of dead time. Finally, we demonstrate the effectiveness of our formulation and algorithm via simulations of lidar ranging.Index Terms-Dead time, high-flux ranging, lidar, Markov chain, nonlinear inverse, single-photon detection.J. Rapp and Y. Ma contributed equally to this work.

Asynchronous Single-Photon 3D Imaging

“…This non-linear distortion, known as photon pileup [14,25,17] makes it challenging to reliably locate the laser pulse, resulting in large depth errors. Although there has been a lot of research toward correcting these distortions in post-processing [14,9,23,25,28], strong pileup due to ambient light continues to limit the scope of this otherwise exciting technology.…”

“…In contrast, we use shifting to mitigate pileup and present a theoretically optimal method for choosing the sequence of shifts and durations of the SPAD measurement gates without any prior knowledge of scene depths. Photon-driven acquisition: The photon-driven (or freerunning) mode of operation has been analyzed for FLIM [16,9,1], and recently for LiDAR [28] where a Markov chain model-based iterative optimization algorithm is proposed to recover the incident waveform from the distorted histogram. The focus of these approaches is on designing efficient waveform estimation algorithms.…”

“…However, due to the large variance in the arrival time of the first photon in each cycle, a fixed m cannot achieve both these goals on a per-photon basis. It is possible to achieve photon-adaptive active time durations using the free-running mode [28] where the SPAD is always active, except after a photon detection when it enters a dead time.…”

Photon-Flooded Single-Photon 3D Cameras

“…Multi-photon SPAD LiDAR: With recent improvements in detector technology, SPADs with lower dead times (tens of ns) can be realized, which enable capturing more than one photon per laser cycle. This includes multi-stop TC-SPC electronics and SPADs that can be operated in the freerunning mode, for which imaging models and estimators have been proposed recently [31,15]. An interesting future direction is to derive optimal flux criterion for such multiphoton SPAD-based LiDARs.…”

Fast Online 3D Reconstruction of Dynamic Scenes From Individual Single-Photon Detection Events

“…Yet, robust, automated and scalable methods allowing for fast analysis of single-photon data are still required. One of the main bottlenecks of most stateof-the-art 3D reconstruction methods [15], [23]- [27] is that they rely on the construction of histograms of photon times of arrival (ToA) (or batches of detection events), which, when synchronised with a pulsed laser (time correlated singlephoton counting, TCSPC) correspond to photon times of flight (ToF), used to infer object ranges. One important exception is the so-called "first-photon" imaging approach [28] whereby the reflectivity and 3D profiles of the scene can be recovered using a single photon per pixel.…”