Single-photon laser ranging based on amplitude-modulated continuous-wave scheme

ObjectiveSingle-photon lidar has attracted increasing attention for long-range, high-sensitivity, and eye-safe active imaging, especially under low-light conditions and in scenarios where the received optical power is extremely weak. Compared with conventional linear-mode detection, single-photon detection can provide a significantly improved detection capability at the photon-counting level. However, the performance of single-photon lidar is strongly affected by ambient background noise, detector dark counts, and the temporal statistical fluctuation of photon arrivals. These factors can severely degrade ranging accuracy and stability, particularly when the target distance is long and the signal-to-noise ratio (SNR) becomes low. Therefore, developing a robust and high-precision ranging scheme that can operate reliably under photon-limited and noise-dominated conditions remains an important challenge. We derives the probability density function (PDF) of photon detection distribution under amplitude-modulated continuous-wave (AMCW) signals, and establishes a chirped and sinusoidal lidar system operating at the single-photon level. Simulation and experimental results demonstrate that our system simultaneously achieves 150 km non-ambiguity range and resolution less than 15 cm, together with differential ranging precision below 1mm and accuracy better than 1.6 mm.MethodsA probabilistic framework was established to describe single-photon AMCW (amplitude-modulated continuous-wave) ranging in the presence of noise, based on the detection characteristics of a single-photon avalanche diode (SPAD). Specifically, the photon-detection process was modeled as a stochastic point process, where the detected counts in each sampling bin are governed by the combined contributions from the target return and the noise component. The model explicitly accounts for the photon-counting nature of SPAD detection and forms the basis for subsequent parameter estimation. Following the derivations in Eqs.(1)-(12), the likelihood function of the measured photon-counting sequence was formulated with the unknown range (or time delay) as the target parameter, enabling quantitative performance analysis under controlled signal and noise conditions. To evaluate the proposed AMCW ranging strategy under long-distance conditions, numerical simulations were performed using a Monte Carlo procedure. The coarse ranging stage employed chirp-modulated AMCW signals to produce an initial distance estimate over the full unambiguous range, while the fine ranging stage used sinusoidal modulation to refine the distance within the local interval determined by the coarse result. Accumulation time was treated as a key controllable parameter in both stages, allowing the ranging resolution and accuracy to be assessed under practical integration-time constraints. In addition to simulation, an all-fiber experimental setup was built to validate the ranging model and the corresponding estimation procedure. The experiment implemented the sinusoidal-signal AMCW ranging configuration and used an electrical delay line to controllably adjust the effective time delay, thereby emulating distance variations without physically translating a target over large distances. This experimental design provides a practical and repeatable way to test the ranging algorithm and the underlying probabilistic model in a stable laboratory environment.Results and DiscussionsThe simulation results indicate that at photon rates of 1000, 2000, and 3000 counts per second, the coarse distance measurement using chirp signals can achieve a resolution of 15 cm over a 100 km range within 1-second accumulation time. The chirp-modulated stage first provides a coarse distance estimate over a 100 km span, which constrains the fine-ranging search interval and resolves range ambiguity. Based on the coarse distance, the precise distance measurement with sinusoidal signals achieves differential range precision better than 0.4 mm and accuracy of 0.8 mm within a 3-second accumulation time (Fig.5, Tab.1). According to the simulation parameter settings, under the condition of 400 noise counts per second, all-fiber experiment setup achieved a ranging precision of 0.9 mm and 1.6 mm accuracy using sinusoidal signal (Fig.8, Tab.2), validating the model's performance.ConclusionsWe proposes a chirp-sine modulated single-photon long-range differential ranging technique based on the AMCW (Amplitude Modulated Continuous Wave) scheme. It establishes a photon detection event probability model under chirp signals and employs Monte Carlo simulations to numerically analyze the impact of different photon levels on ranging results over a 100 km distance. The study demonstrates the feasibility of extending the unambiguous range to over 100 kilometers while achieving sub-millimeter differential ranging accuracy. An indoor fiber-optic experimental system was constructed for validation. Both simulation and experimental results indicate that the AMCW-based single-photon lidar holds potential for applications in extremely low-light scenarios.