JEOS RP ISSN03 | Page 399

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J. Eur. Opt. Society-Rapid Publ. 22, 40( 2026)

gather sufficient statistical information and recover the required transients for NLOS reconstruction. The pixelspecific bin widths of these histograms are approximately 400 ps, as given by the integrated TDC circuits. The detector has a microlens-enhanced fill factor of 26.8 % and a quantum efficiency of 2 % at 905 nm [ 16 ]. The FoV covers a2m 2 m. rectangular region on the relay wall. The soft-gated detector precludes direct illumination within the FoV because the direct reflection of the laser pulse would saturate the detector. To mitigate the resulting illumination inhomogeneity, two illumination points are placed at opposite edges of the FoV, as shown in Figure 1b.

The laser sources are pulsed laser diodes operating at 905 nm, this mitigating eye-safety conditions and optical pollution due to their non-visibility to the human eye. They generate pulses with 2.4 ns temporal width( full width at half maximum) and a nearly top-hat temporal beam profile. Each diode generates 30 W peak optical, resulting in an average power below 1 mW at the repetition rate of 12.5 kHz. Their pulse-on-demand capabilities are used to emit laser pulses synchronized with the detector. Because each pulse emission can only generate one timestamp per pixel, the measurement statistics scale with the number of emitted pulses. Given the fixed repetition rate, the achievable frame rate is inversely proportional to the number of pulses per acquisition. The alternating emission of the laser sources is necessary to assign the measured timestamps to an illumination position, which is essential for valid reconstruction. With a doubled detector frame rate, the two alternating 12.5 kHz emissions can be captured, resulting in the same measurement frame rate for the single and dual illumination scheme.

2.2 Simulation and calibration

For a controlled, calibration-independent assessment of system performance, simulated measurements are used in addition to proof-of-concept measurements with the physical setup. However, certain experimental conditions, such as specific pulse lengths and a central illumination scheme, cannot be achieved with the physical setup that has been developed. Spatially and temporally resolved transients of scattering light at the relay wall are therefore simulated while incorporating first-photon detector behavior. Because a photon can be detected only if the SPAD has not already fired, the first-detection probability decays exponentially with time ataratesetbythebackgroundlightlevelr B. Impinging photon rates r L of the three-bounce laser pulses are calculated using view factors, which yield the fractions of Lambertian scattering into a specified solid angle. These rates and their corresponding ToF define the photon detection probability density function( PDF) of each detector pixel:

Here, t P is the temporal width of a rectangular laser pulse and t ToF is the time of flight determined by the distances between the illumination position, target position and the imaged pixel position on the relay wall. Synthetic histograms are generated using the inverse transfer method by sampling arrival times from the PDF( 1). Subtracting the exponentially decaying background component induced by a constant background rate r B mitigates intensity gradients in the reconstruction.

The simulation assumes only Lambertian surfaces. Specular and retroreflective targets would naturally lead to alternative distributions of the receivable light, as described in Section 3.1. Nevertheless, the extensive area of detection increases the probability of receiving specular components of the target reflections, especially given the changing angle of incidence of the target illumination due to the dual illumination scheme. Retroreflective targets, which are best detected by confocal measurements, can also be detected, because the illumination positions are placed close to the edge of the detection area.

While the simulation covers the entire light transfer function from laser emission to detection via triple reflection, the original data of the measurement setup must be further calibrated in order to extract the relevant parts of the transient histograms. The line-of-sight( LOS) propagation of the laser pulse from the system to the relay wall and the LOS observation of the relay wall must be subtracted to obtain the light transmission relevant for NLOS reconstruction. Theoretically, the propagation times between the detector and the detection point on the relay wall could be extracted from a LiDAR measurement of the relay wall. To rule out errors from such additional measurements, the spatial alignment between the system and the relay wall is measured manually. For this purpose, the intensity-based photon-counting mode of the system is used to map the relay wall equipped with retroreflector landmarks. The virtual start time of the pulse propagation originating from the relay wall is calibrated using the high-intensity peak of the primary reflection of the laser pulse on the relay wall within the measured histograms. The pixel-dependent propagation times between the detection point on the relay wall and actual detection at the system are compensated using the geometrical model of the measurement setup, yielding the required light transfer function between relay wall and target for the reconstruction procedure. Pixel-dependent temporal bin widths and periodic bin width variations are compensated prior to reconstruction using individual TDC calibration data provided by the system. This interpolates all measured histograms to a uniform temporal grid with 400 ps steps.

Multipath clutter of light paths with more than three bounces are ignored, as signal intensities decrease drastically with each diffusive reflection. Nevertheless, vertical walls adjacent to the relay wall have a significant impact on the transient data, requiring subtraction of an otherwise empty scene to extract the target positions as described below. The simulations therefore omit additional walls, but the physical measurement includes a parallel surface( the floor) at a distance of 3 m from the relay wall. Its additional NLOS contribution within the transient data is