Single-Photon LiDARs: Advances & Applications

Updated 19 October 2025

Single-Photon LiDAR is an optical remote sensing system that uses SPAD detectors to capture individual photon time-of-flight data for high-precision 3D imaging.
The technology integrates quantum-enhanced protocols and classical correlation methods to surpass traditional range and velocity measurement limits while reducing noise.
Innovative computational imaging and compressive sensing algorithms enable super-resolution reconstruction and uncertainty quantification in photon-starved scenarios.

Single-photon LiDARs are optical remote sensing systems that utilize single-photon detectors—most notably, single-photon avalanche diodes (SPADs)—to capture time-of-flight (ToF) information at the granularity of individual photons. By leveraging extreme sensitivity and picosecond-scale timing resolution, single-photon LiDARs enable high-precision three-dimensional (3D) imaging in low-photon-flux scenarios, supporting applications from long-range terrestrial and airborne imaging to safety-critical autonomous navigation. The interplay between photon efficiency, spatiotemporal resolution, data processing, and quantum enhancement strategies defines the current state and ongoing evolution of single-photon LiDAR technology.

1. Physical Principles and Noise Statistics

Single-photon LiDAR relies on pulsed laser illumination and time-correlated single-photon detection. The illumination pulse is scattered or reflected by the scene, and returning photons are detected with timing resolution typically in the tens-of-picoseconds regime. Photon arrivals for each detector pixel are accurately modeled as an inhomogeneous Poisson process with rate

$\lambda(t) = \alpha\, s(t-\tau) + \lambda_b,$

where $\alpha$ is the reflectivity, $s(t)$ is the normalized system impulse response (pulse shape), $\tau$ encodes the target depth via $\tau = 2z/c$ , and $\lambda_b$ accounts for the background flux from ambient light and dark counts (Chan et al., 25 Mar 2024).

The task of depth reconstruction is to estimate $\tau$ for each pixel based on observed photon timestamps. In the single-photon regime, photon detection noise, dead time, and background counts play a central role; the time-of-arrival statistics underpin the estimator variance and the limits of achievable spatial and temporal resolution.

2. Quantum-Enhanced and Correlation-Based Architectures

Quantum techniques exploit photonic entanglement or time-frequency correlations to exceed classical limits for simultaneous range and velocity measurements. Entanglement-enhanced LiDAR protocols employ pairs of entangled photons: one "signal" photon is transmitted to the target, while the "idler" photon is retained. After interaction with the target (which imprints both a time delay and a Doppler shift), a joint measurement is performed on the returned signal and the stored idler via a unitary transformation of the form

$\hat{B}_{SI} = \int d\omega_S \int d\omega_I \left|\frac{\omega_S+\omega_I}{2}\right\rangle_S \left|\omega_S-\omega_I\right\rangle_I \langle \omega_S|_S \langle\omega_I|_I,$

allowing separate extraction of range and radial velocity observables that do not commute classically (Zhuang et al., 2017). This design not only bypasses the Arthurs–Kelly uncertainty bound—reaching Cramér–Rao bounds $\delta t_S = (2W)^{-1}$ and $\delta\omega_S = (2T)^{-1}$ for bandwidth $W$ and duration $T$ —but, in lossless, noiseless regimes with $M$ entangled pairs, achieves Heisenberg scaling $\delta t_S,\, \delta\omega_S \propto M^{-1}$ .

Coherent LiDAR analogs also exploit classical time-frequency correlations between broadband probe and reference beams, enabling sum frequency generation (SFG) detection that achieves "single-photon sensitivity" with $>100$ dB in-band noise rejection. The signal, appearing as a spectrally narrow peak due to phase conjugate probe/reference correlations, is easily separated from the broad i-SFG noise background by narrowband filtering (Liu et al., 2023).

Intensity interferometry-based approaches leverage classical second-order correlations $g^{(2)}(\tau)$ inherent in thermal light to determine depth, providing robustness to atmospheric scattering and enabling potentially passive 3D imaging using ambient light sources (Wagner et al., 2020).

3. System Design: Sensing Arrays, Data Acquisition, and High-Flux Effects

Modern single-photon LiDARs deploy large-format SPAD arrays fabricated in CMOS, attaining high spatial resolution and fast parallel data acquisition (Chan et al., 2018, Gyongy et al., 2022). Photon arrivals are resolved into temporal histograms or timestamp streams, with each SPAD acting as a binary detector contributing to bit-plane accumulation.

High-flux operation introduces nonlinearity due to SPAD dead time: after each photon detection the detector is inactive for a fixed period, resulting in "pile-up" distortion of the timing histogram (i.e., an over-representation of early arrivals, suppression of later bins). The optimal incident photon flux that minimizes depth estimation error is given by

$\Upsilon^{\text{opt}} = \frac{c \Delta}{2 d_{\max} \Phi_{\text{bkg}}},$

where $c$ is the speed of light, $\Delta$ is time-bin width, $d_{\max}$ is the maximum unambiguous depth, and $\Phi_{\text{bkg}}$ is the ambient background flux per bin (Gupta et al., 2019). Adapting attenuation on a per-pixel basis ensures robust operation even under highly variable background illumination.

In free-running (event-driven) SPL systems, detectors reactivate immediately after dead time, reducing histogram distortion and yielding lower estimation error for both depth and flux at high signal rates compared to synchronous (clocked) SPL, which restricts to one detection per cycle and is sensitive to pile-up and depth-induced bias (Kitichotkul et al., 12 Jul 2025). Joint maximum likelihood estimators that simultaneously fit signal flux $S$ , background $B$ , and depth $z$ —augmented with plug-and-play score-based regularization using learned point cloud priors—substantially improve reconstruction in the high-flux regime.

4. Computational Imaging, Compression, and Super-Resolution

Photon-efficient computational algorithms are crucial for 3D reconstruction, especially in ultra-long-range, photon-starved conditions. Forward models for time-binned photon counts are Poisson: $Y \sim \text{Poisson}(g \ast RD + B),$ where $RD$ is a 3D matrix encoding reflectivity and depth, $g$ is the spatiotemporal kernel, and $B$ is background (Li et al., 2020, Li et al., 2019). Inverse problems are solved by optimizing negative log-likelihoods regularized with, e.g., total variation,

$\min_{RD} L_{RD}(RD; Y, g, B) + \beta \cdot \text{penalty}(RD), \quad \text{subject to } RD \geq 0,$

enabling super-resolution reconstruction with only $\sim$ 1 photon per pixel.

Data reduction is enabled by compressive "sketching," in which the characteristic function (CF) of the ToF photon distribution is sampled at a small set of frequencies. Each pixel's empirical sketch is

$z_n = \frac{1}{n} \sum_{j=1}^n \Phi(x_j),$

with $\Phi(x)$ Fourier features and compression rates up to 150 $\times$ shown to retain near-optimal depth inference accuracy (Sheehan et al., 2021). Foveated SPAD sensing policies further exploit external depth priors to restrict histogram sampling to expected signal windows, yielding up to $1/1548$ of the original memory footprint without degrading depth resolution (Folden et al., 3 Dec 2024).

For small-format SPAD arrays or low-lateral-resolution sensors, deep 3D convolutional networks enable joint temporal denoising and upscaling (e.g., $4\times$ ) of ToF sequences, extracting sharp, high-resolution depth maps from noisy, undersampled data (Martín et al., 2022). Center-of-mass computations on binned photon histograms facilitate "sub-bin" depth resolution, with frame rates up to 100 kFPS for direct output in dToF sensors with embedded peak tracking (Gyongy et al., 2022).

5. Materials Classification, Uncertainty Quantification, and Scene Understanding

Hierarchical Bayesian models, often with coordinate gradient descent solvers, permit joint estimation of surfaces, reflectivities, and class labels from multispectral single-photon LiDAR data (Belmekki et al., 2023). Surface returns are detected using multiscale saliency in space-time data cubes, while priors over reflectivity and class assignments (e.g., gamma MRF and Potts models) enforce spatial and spectral coherence. These models robustly separate background and layout surfaces, perform spectral classification, and quantify uncertainty.

A simple, lightweight representation called "Probabilistic Point Cloud" (PPC, Editor's term) captures measurement uncertainty by augmenting each 3D point with a probability attribute, derived as

$Pr(p^{ij}) = \frac{h_{i,j}[m]}{\sum_{n=1}^{N} h_{i,j}[n]}, \quad m = \arg\max_n h_{i,j}[n]$

from the raw histogram. PPCs are used for denoising (Neighbor Probability Density filtering), robust keypoint sampling (Farthest Probable Point Sampling), and as point-wise features in neural object detection pipelines, yielding improved mAP and AP across challenging low-SNR conditions (Goyal et al., 31 Jul 2025).

Joint estimation of depth and reflectivity becomes statistically beneficial as background noise increases; under a Poisson model, the variance of reflectivity estimation decreases when conditioned on known depth, and vice versa. The SPLiDER network jointly estimates both modalities from misaligned timestamp frames, thereby improving reconstruction accuracy and eliminating the need for long histogram integration even for fast-moving scenes (Weerasooriya et al., 19 May 2025).

6. Implementation Limits, Trade-offs, and Future Directions

The fundamental "resolution limit" of single-photon LiDAR is set by the total photon flux and the trade-off between spatial resolution and per-pixel SNR. The analytical framework yields a minimum mean squared error (MSE) for the ML depth estimator,

$\mathbb{E}[(\hat{\tau}-\tau_0)^2] = \left[\int_{-T}^T \frac{(\alpha\,\dot{s}(t))^2}{\alpha\,s(t)+\lambda_b}\,dt\right]^{-1}$

for a pixel with pulse $s(t)$ and background $\lambda_b$ (Chan et al., 25 Mar 2024). For $N$ pixels in a fixed-illumination scene, the spatial MSE is

$\text{MSE} = \frac{c^2}{12N^2} + \frac{N}{\alpha_0} \left( c^2 \sigma_x^2 + \sigma_t^2 \right),$

where $\sigma_x$ (effective pixel size) and $\sigma_t$ (pulse width) govern spatial and timing uncertainties. There exists an optimal $N$ that balances discretization bias and photon-noise variance.

Simulation under high-flux and hardware dead time is computationally demanding. Learning-based emulators utilizing autoencoder neural networks directly map flux input to the registered photon PDF $f_r(t)$ , allowing rapid, accurate simulation of photon statistics under arbitrarily complex physical regimes (Zhang et al., 29 May 2025).

Possible future directions include: real-time adaptive foveation across space and time, advanced quantum-enhanced architectures for robust operation in high-background or jamming scenarios, integration of high-dimensional quantum information methods (e.g., chaotic quantum frequency conversion (Liu et al., 2023)) into classical LiDAR, and further fusion of photon-efficient computation with learned priors and uncertainty modeling.

Key Equations and Algorithmic Summaries

Aspect	Key Equation/Algorithm	Reference(s)
Photon arrival PDF	$\lambda(t) = \alpha\, s(t-\tau) + \lambda_b$	(Chan et al., 25 Mar 2024, Zhang et al., 29 May 2025)
CF-based sketch	$z_n = \frac{1}{n} \sum_{j=1}^n \Phi(x_j)$	(Sheehan et al., 2021)
Foveated bin width	$\Delta t_{\rm depth} = (M\cdot T) / N^2$	(Folden et al., 3 Dec 2024)
PPC probability	$Pr(p^{ij}) = h_{i,j}[m] / \sum_n h_{i,j}[n]$	(Goyal et al., 31 Jul 2025)
ML depth MSE	$\mathbb{E}[(\hat{\tau}-\tau_0)^2] = \left[\int_{-T}^T \frac{(\alpha\,\dot{s}(t))^2}{\alpha\,s(t)+\lambda_b}\,dt\right]^{-1}$	(Chan et al., 25 Mar 2024)
Flux attenuation	$\Upsilon^{\text{opt}} = \frac{c\Delta}{2 d_{\max} \Phi_{\text{bkg}}}$	(Gupta et al., 2019)

Single-photon LiDAR continues to advance through the co-evolution of quantum-enhanced measurement protocols, optical and SPAD hardware, photon-efficient and compressive computational imaging, and sophisticated models for data representation and uncertainty. These developments collectively drive improvements in spatial resolution, depth accuracy, range, robustness under strong background or high flux, and overall system scalability.