Single-Photon Radar

Updated 5 July 2026

Single-photon radar is an active ranging system that uses individual photon detection and time-of-flight measurements to infer distance.
It integrates photon-counting LiDAR with multimodal fusion techniques, often combining optical and millimeter-wave data to enhance 3D imaging accuracy.
Quantum variants employ entangled-photon detection to improve sensitivity and robustness, enabling precise range estimation even in low-SNR conditions.

Single-photon radar denotes a family of active ranging and imaging systems that operate in a regime where individual detected photons carry the measurement. In the literature, the term is used for photon-counting optical time-of-flight LiDAR, for multimodal systems that fuse a single-photon temporal channel with millimeter-wave radar, and for quantum radar architectures that employ single-photon or entangled-photon detection. Across these variants, the central observable is a time-resolved return, and range is inferred from round-trip delay through relations such as $R = c t / 2$ or $d = c \Delta t / 2$ ; performance is then set by photon statistics, instrument response, background counts, receiver technology, and the inverse mapping from sparse temporal data to depth, trajectory, or detection decisions (Wang et al., 2024, Chan et al., 2018, Allahverdi et al., 9 Jun 2026).

1. Terminological scope and conceptual identity

In optical work, single-photon radar is often effectively synonymous with photon-counting LiDAR: a pulsed source illuminates a scene, a single-photon-sensitive detector records returns, and time-correlated single-photon counting or gated acquisition converts photon arrivals into depth information. This usage appears explicitly in long-range 3D imaging, free-space-coupled superconducting detector systems, and space-debris ranging, where the emphasis is on single-photon sensitivity, picosecond-scale timing, and photon-efficient reconstruction (Li et al., 2019, Wang et al., 2024, Liu et al., 2024).

A distinct but related usage treats single-photon radar as a multimodal fusion paradigm. In "Single-pixel 3D imaging based on fusion temporal data of single photon detector and millimeter-wave radar" (Lai et al., 2023), the optical single-photon channel and the mmWave channel are both treated as temporal sensors, and the fused system is described as realizing a Single-Photon Radar: a data-driven 3D imager that uses single-photon time-of-flight augmented with radar cues to achieve robust, ambiguity-free reconstructions.

A third usage arises in quantum radar. Here the receiver may employ a single microwave-photon detector, a quantum transducer followed by a single optical-photon detector, or coincidence measurements on entangled photon pairs. The detection problem is then framed not only in terms of return intensity but also in terms of joint statistics, correlation functions, or quantum hypothesis testing (Allahverdi et al., 9 Jun 2026, Zhao et al., 2021).

This diversity of usage is accompanied by an important boundary condition. In the Gaussian-beam quantum radar protocol, the $N=1$ case reduces to conventional single-photon time-of-flight radar or LiDAR, with no entanglement advantage; the range precision is then $\Delta R_1 = (c/2)\Delta \tau$ , set by source bandwidth and detector timing (Maccone et al., 2023).

2. Measurement physics and forward models

The basic optical model is a photon-counting time-of-flight measurement. In single-pixel temporal imaging, photon arrivals in time bin $t$ are modeled as Poisson,

$k_t \sim \mathrm{Poisson}(\lambda_t),$

with forward model

$\lambda_t = \sum_i \rho_i s(\tau_i) h(t-\tau_i) + b,\qquad \tau_i = \frac{2\|r_i\|}{c}.$

Here $\rho_i$ is voxel reflectivity, $s(\tau_i)$ encodes illumination and geometric fall-off, $h(\cdot)$ is the instrument response function, and $d = c \Delta t / 2$ 0 is background or ambient count contribution. The resulting histogram is a one-dimensional temporal encoding of depth and reflectivity convolved with the IRF, and a distance estimate follows from a peak lag by $d = c \Delta t / 2$ 1 (Lai et al., 2023).

Single-photon ranging papers use the same time-of-flight relation in different instrumental forms. In TCSPC-based systems, the histogram peak position gives range, while the full width at half maximum of the timing response determines range resolution through $d = c \Delta t / 2$ 2. In gated systems, each pixel’s temporal response versus gate index is modeled as a step-like function convolved with the instrument response, often fitted by an error-function form to obtain sub-sample depth estimates (Wang et al., 2024, Chan et al., 2018).

For obscured or non-line-of-sight geometries, the propagation model is modified but remains time-of-flight based. In the confocal three-bounce geometry,

$d = c \Delta t / 2$ 3

after compensating the transceiver–wall path for wall pixel $d = c \Delta t / 2$ 4. Picosecond gating suppresses out-of-window multipath and early wall scatter, thereby isolating the desired triple-bounce returns (Zhu et al., 2021).

When a radar channel is added, the optical histogram is paired with a microwave range profile. The mmWave side is described by the monostatic radar equation

$d = c \Delta t / 2$ 5

with FMCW or LFM range processing governed by

$d = c \Delta t / 2$ 6

In the fusion formulation,

$d = c \Delta t / 2$ 7

and the inverse map $d = c \Delta t / 2$ 8 is learned from data (Lai et al., 2023).

Photon statistics remain central throughout. Optical single-photon measurements, background counts, and dark counts are consistently modeled as Poisson processes. This matters not only for reconstruction fidelity but also for false-alarm behavior, coincidence estimation, and low-SNR detection in both classical and quantum variants (Chan et al., 2018, Zhao et al., 2021, Liu et al., 2024).

3. Architectures and detector technologies

Single-photon radar architectures span a wide range of transmitter–receiver implementations. A representative fusion system combines a 1550 ± 25 nm supercontinuum laser with pulse width about 6 ps, a superconducting nanowire single-photon detector with about 50 ps jitter, a measured system IRF of about 200 ps, a Swabian Time Tagger Ultra, and a TI IWR6843 mmWave radar at about 60 GHz. The optical, radar, and depth camera streams are synchronized every 3 s, and absolute range is calibrated by setting the measured peak from a reflector at 1 m to 1 m (Lai et al., 2023).

Picosecond-gated optical systems use a different architecture. Around-the-corner sensing with nonlinear gated single-photon detection employs a mode-locked laser at 50 MHz, signal pulses centered near 1545–1554 nm with FWHM about 6.1 ps, pump pulses centered at 1565.5 nm with FWHM about 6.6 ps, a periodically poled lithium niobate waveguide for quantum frequency conversion, and a free-running silicon SPAD with about 70% efficiency at about 780 nm. The measured IRF is about 10 ps FWHM, the effective gate width is about 10 ps, and external ASE or background rejection is about 36 dB better than a 1 ns-gated InGaAs detector (Zhu et al., 2021).

Array-based quantum LiDAR uses widefield coincidence detection rather than a single detector. One implementation employs a 355 nm pulsed pump laser at 20 MHz and 27 mW, a 1-mm-thick type-I BBO crystal generating SPDC pairs filtered around 710 nm, and a SwissSPAD2 camera with 512 × 512 pixels, pixel pitch 16.38 μm, native fill factor 10.5%, and photon detection probability about 25% at 700 nm. Time gating uses a gate width of about 15 ns scanned in 18 ps steps (Zhao et al., 2021).

Detector engineering is itself a major subtopic. A free-space-coupled superconducting microstrip single-photon detector has been reported with a 260 μm-diameter active area, a dark count rate of about 5 kcps at the chosen imaging operating point, and system timing jitter of 171 ps FWHM at 1550 nm. The same work reports a practical dead time set by a recovery time of about 360 ns and a free-space imaging configuration based on a galvanometer scanner and a Becker & Hickl SPC-150NX TCSPC module (Wang et al., 2024).

At extra-long optical ranges, a confocal 1550 nm single-photon LiDAR architecture has been demonstrated with an Er-doped near-IR fiber laser, pulse width about 500 ps, repetition rate 100 kHz, average power up to 120 mW, a 280 mm Cassegrain telescope, polarization filtering, narrowband spectral filtering, multimode-fiber coupling, and a free-running InGaAs/InP SPAD. The system is scanned by a piezo-driven tip-tilt mirror and a two-axis telescope rotation stage (Li et al., 2019).

In microwave quantum direct-detection radar, the receive front end is instead based on a single microwave-photon detector or a quantum microwave-to-optical transducer followed by a single optical-photon detector. The analytical performance study identifies the transducer-plus-SOPD configuration as the optimal detection method and states that conventional antennas limit the potential benefits of quantum-entangled noise radar systems (Allahverdi et al., 9 Jun 2026).

4. Reconstruction, fusion, and target inference

A large part of single-photon radar research concerns the inverse problem. In single-pixel temporal imaging, one-dimensional measurements are severely ambiguous because a single viewpoint produces radially symmetric histograms. Scene points on the same iso-range sphere contribute at approximately the same arrival time, so left–right or more general azimuthal symmetries relative to the detector yield identical histograms. This produces the symmetry blur or “mirror ghost” phenomenon in recovered 3D images (Lai et al., 2023).

The multimodal fusion solution is to add a second temporal measurement from a displaced radar origin. The optical histogram $d = c \Delta t / 2$ 9 and radar range profile $N=1$ 0 are concatenated as

$N=1$ 1

and a multilayer perceptron maps the fused vector to a depth map. In the reported implementation, supervised pairs $N=1$ 2 are formed using an Orbbec Gemini 2 depth camera, and structural similarity is used for evaluation. The method does not require a fixed asymmetric background, because the nonzero baseline between the single-photon detector and the radar breaks the lateral symmetry responsible for blur (Lai et al., 2023).

Long-range computational imaging addresses a different failure mode: extremely weak echoes mixed with strong noise and multiple depths inside a single field of view due to diffraction or turbulence. At 45 km, the forward model is written as a 3D convolution,

$N=1$ 3

and reconstruction proceeds by global histogram-based gating followed by 3D deconvolution with a Poisson negative log-likelihood and a spatial total-variation penalty. The unknown volume $N=1$ 4 jointly encodes reflectivity and depth, which allows recovery when one-depth-per-pixel assumptions fail (Li et al., 2019).

At 150 m, sparse gated SPAD-array data have been combined with an aligned optical image through non-local data fusion. The measurement model uses a cumulative Gaussian-IR step,

$N=1$ 5

with pixelwise depth and intensity recovered under a Poisson model and then regularized by RGB-guided non-local weights over 15 × 15 neighborhoods. This formulation is designed for low-signature regions where sparse LiDAR sampling alone is insufficient (Chan et al., 2018).

Target inference can also exploit motion rather than spatial regularity. In space-debris ranging, velocity-based sparse photon clustering maps each detected photon to a distance–time point and computes pairwise implied velocities and accelerations. Photons with consistent kinematics are clustered under a quadratic track model,

$N=1$ 6

which enables trajectory extraction from sparse photon data in low-SNR conditions (Liu et al., 2024).

Quantum LiDAR introduces yet another inversion mode: coincidence estimation. The joint-probability estimator

$N=1$ 7

subtracts accidentals by frame differencing, and the spatially averaged correlation image $N=1$ 8 yields a depth-dependent correlation peak that isolates genuine entangled-pair returns from spurious light (Zhao et al., 2021).

Quantum variants of single-photon radar are not a single model. One line of work studies frequency-entangled Gaussian beams. In that protocol, the round-trip travel time is measured as in conventional radar, but the beam is composed of $N=1$ 9 photons entangled in the frequency degree of freedom. The estimator based on the average arrival time $\Delta R_1 = (c/2)\Delta \tau$ 0 has uncertainty $\Delta R_1 = (c/2)\Delta \tau$ 1, whereas $\Delta R_1 = (c/2)\Delta \tau$ 2 independent photons yield $\Delta R_1 = (c/2)\Delta \tau$ 3. The reported consequence is a $\Delta R_1 = (c/2)\Delta \tau$ 4 quantum enhancement over the unentangled case in the ideal noiseless regime; at $\Delta R_1 = (c/2)\Delta \tau$ 5, the protocol reduces to standard time-of-flight ranging (Maccone et al., 2023).

Another line emphasizes robustness rather than Heisenberg scaling. In "Quantum Light Detection and Ranging" (Zhao et al., 2021), entangled photon pairs generated by SPDC are used with time-resolved coincidence measurements to reject synchronous spoofing and asynchronous interference. The relevant observables are spatiotemporal correlations rather than singles counts, and the effective return is the true coincidence rate

$\Delta R_1 = (c/2)\Delta \tau$ 6

contrasted with accidentals scaling as

$\Delta R_1 = (c/2)\Delta \tau$ 7

This architecture treats the correlation peak as a physically distinctive signature of the source.

Quantum direct-detection and noise-radar analyses recast the same problem in terms of receiver thresholds. For single-photon radar in the microwave sense, the maximum detection range of a direct-detection radar is written in Lambert- $\Delta R_1 = (c/2)\Delta \tau$ 8 form, with reliable detection when $\Delta R_1 = (c/2)\Delta \tau$ 9. The same framework shows that a quantum-entangled noise radar can be regarded as an enhanced direct-detection radar with an effective threshold signal-to-noise ratio, and introduces the range enhancement factor for comparison with classical-correlated noise radars (Allahverdi et al., 9 Jun 2026).

Partially postselected filtering adds a distinct non-Gaussian receiver strategy. The filter

$t$ 0

is applied through joint measurements on entangled photons, photon catalysis, or zero-photon heralding. In the low-transmission regime, the amplification ratio approaches $t$ 1, Monte Carlo simulations under Gaussian white noise show a remarkable enhancement in imaging SNR, and the reported trade-off is an increase in mean-squared error due to postselection (Li et al., 2024).

Not all entanglement claims point in the same direction. For quantum radar cross section, signal–idler entanglement does not provide any enhancement of the QRCS, whereas signal–signal entanglement can enhance biphoton QRCS over both single-photon QRCS and two-photon separable QRCS. For two-dimensional target geometries in monostatic and bistatic configurations, the effect appears as an entanglement-induced reshaping of the scattering pattern, including side-lobe enhancement, and the double-Gaussian model permits arbitrary entanglement strength through the Schmidt number

$t$ 2

This result is one of the clearest objective corrections to the common assumption that any signal–idler entanglement automatically enhances every radar observable (Kang et al., 4 Jun 2026).

6. Performance regimes, applications, and limitations

Reported performance spans from room-scale 3D imaging to kilometer-scale detection. In the fusion single-photon/mmWave system, a dataset of 4000 fused histogram plus depth-map pairs was collected in a 6 m × 6 m open room, with 90% training and 10% testing. Average SSIM over 400 test samples was 0.6576 for fusion, 0.6389 for SPAD-only, and 0.5266 for radar-only. Fusion reconstructions of humans were reported as clear, while SPAD-only suffered lateral ambiguity without background and radar-only lost shape because of coarse resolution (Lai et al., 2023).

Picosecond-gated NLOS sensing reported an effective gate width of about 10 ps, a range resolution of about 1.5 mm per two-way segment, lateral resolution of about 1.1 cm for the stated geometry, and detection of hidden-object profiles with only about $t$ 3 detected information-carrying photons per pulse per pixel at the histogram peak. The same apparatus resolved two obscured bars vibrating at about 250 Hz and about 420 Hz through time-gated single-photon vibrometry (Zhu et al., 2021).

At 150 m, a time-gated 240 × 320 SPAD array combined with non-local data fusion achieved sub-centimeter precision in all three spatial dimensions. Standard deviations over 25 × 25-pixel depth-board patches were 0.96 cm, 0.82 cm, 0.89 cm, and 0.59 cm, while mean inter-panel differences of 9.26 cm, 8.79 cm, 11.05 cm, and 29.10 cm were recovered against ground truth offsets of 10, 10, 10, and 30 cm (Chan et al., 2018).

At 45 km, confocal single-photon computational 3D imaging was demonstrated in an urban environment with approximately 1 photon per pixel return level. The reported operating points included about 2.59 photons per pixel at 45 km with SNR about 0.03 and about 1.20 photons per pixel at 21.6 km with SNR about 0.11 in daylight and 0.15 at night. The recovered transverse resolution at 45 km was about 0.6 m, surpassing the system’s about 1.0 m transverse diffraction limit (Li et al., 2019).

Detector-limited performance remains decisive. The free-space-coupled SMSPD achieved 171 ps FWHM timing jitter at 1550 nm, corresponding to a FWHM range resolution of about 25.6 mm and Gaussian-equivalent $t$ 4 of about 10.9 mm. In a 0.5 m stand-off imaging experiment, the same system used 151 × 151 and 101 × 101 scan grids, 100 ms per pixel, detected echo rates of 10–100 kcps, and signal-to-background ratio above 80 in bright pixels (Wang et al., 2024).

Sparse-photon motion processing can operate far below imaging-style SNR regimes. The velocity-based sparse photon clustering algorithm extracted a quadratic track with over 99 percent accuracy in only tens of milliseconds at a 5 percent signal photon counting rate and -20 dB SNR, with averaged metrics of recall 0.85, accuracy 0.97, precision 0.96, and time about 5 ms in the reported comparison (Liu et al., 2024).

Quantum systems bring distinct gains and distinct constraints. The coincidence-based quantum LiDAR reported correlation-peak SNR of about 30 with $t$ 5 8-bit frames per gate and about 6 with $t$ 6 frames, while the analytical microwave framework stated that a quantum-entangled noise radar with current technology can reach maximum detection ranges on the order of a few kilometers. A representative parameter set yielded about 1.56 km in search mode and about 1.19 km in track mode for $t$ 7, while also showing that conventional antennas can clip the entanglement-enabled range unless a quantum transducer plus single optical-photon detector is used (Zhao et al., 2021, Allahverdi et al., 9 Jun 2026).

Several limitations recur across the literature. In single-pixel temporal imaging, very small baselines weaken parallax cues and very large baselines can create blind spots; in NLOS systems, acquisition time and depth scanning are major bottlenecks; in long-range optical systems, atmospheric attenuation, turbulence, and background photons dominate the link budget; and in quantum radar, loss, noise, detector inefficiency, and receiver technology can reduce or nullify idealized advantages (Lai et al., 2023, Zhu et al., 2021, Li et al., 2019, Maccone et al., 2023). These constraints suggest that single-photon radar is best understood not as a single device class but as a measurement regime in which photon-counting hardware, temporal inference, and—where applicable—multimodal or quantum correlations are combined to extract range or structure from extremely weak returns.