J. Eur. Opt. Society-Rapid Publ. 22, 40( 2026) 399
Figure 8. Simulated localization errors for different laser pulse widths at 12,500 measurements using different filter combinations.
flattened, which disadvantages precise edge detection, although the increased SNR enables coarse localization at lower statistics( green, dashed outline, Fig. 7a). For the statistics of 12,500 measurements used in Figure 7c, Gaussian filtering( green dots) promotes edge detection near the actual target position, while the temporally unfiltered reconstruction appears to perform worse( purple dots). In fact, the temporally unfiltered result has a comparable RMSE but shows larger offsets for outliers. This bare edge detection without temporal filtering( purple dots Fig. 7c) shows binary localization behavior and yields either the correct target position or an uncorrelated false position. Matched filtering combined with edge detection results in a systematic error, since the temporal filter is not designed to retain rising edges for edge detection but is included for completeness. The extracted positions are thus shifted towards the relay wall( blue dots, Fig. 7c).
The filter analysis shows, that a combination of temporal and spatial filtering can decrease the localization error best for the smallest statistics of 1,250 measurements( green, dashed outline, Fig. 7a), by denoising the risingedge in the temporal regime and thus increasing the contrast of the feasible target region for better spatial edge detection. For higher statistics, the exclusive use of a temporal matched filter performs better, that is then outperformed by an exclusive spatial edge filter for the highest statistics. Nevertheless, the latter relies on very steep rising-edges of the pulse form, that is guaranteed for the simulation but not necessarily given by a physical setup due to temporal jitters and limited pulse form qualities.
For the determination of the best filter combination for extended pulse widths in general, the pulse-width-dependent localization performance is examined for a fixed measurement statistic of 12,500 measurements, corresponding to reasonable data acquisition of 1 fps. While shorter pulse widths generally allow for higher laser peak powers, this would increase the SNR in a way that is comparable to increasing the measurement statistics. In order to compare filter performance only, a fixed laser power is used in
Figure
8 for each pulse width ranging from twice the value of the temporal detector resolution to a 12-fold pulse width. The direct link between pulse width and high intensity area in the reconstruction is evident for maximum detection of the unfiltered reconstruction, represented by the increasing localization error with increasing pulse width( purple, solid outline, Fig. 8). Besides matched temporal filtering without edge detection, all filter combinations show pulse width dependent localization errors. These either originate from detecting different edges of the enlarged overlapping area or from the formation of a displaced global maximum due to the reshaped laser profile. This maximum formation causes a decreased standard deviation of the localization result and introduces a systematic offset that depends on the laser pulse width( green, solid outline, Fig. 8). The exclusive spatial edge detection in the reconstruction volume( purple, dashed outline) shows best performance for the shortest pulse width. That stands to reason, since it is comparable to the standard FBP scenario where this filtering is commonly used. There the pulse width, the temporal detector resolution and the reconstruction resolution are matched, eliminating uncertainties based on temporal pulse width. For any larger pulse widths, the spatial edge detection faces the extended feasible target region that bares the risk of detecting any part of its edge, increasing the error with increasing feasible target region.
In summary, the target location using long laser pulses is best determined using edge detection as is common in FBP imaging. The condition for this is sufficient measurement statistics and a steep rising edge of the pulse form so that the reconstruction resembles the model given in Figure 2c. Nevertheless, systematic but position dependent localization errors occur due to edge detections along the pulse width induced feasibly target region. Matched filtering offers pulse width independent performance for localization of single targets in a NLOS scenarios. By incorporating all photons received in the pulse form used, this filtering is particularly suitable for eye-safe systems with limited emission and repetition rates.
4 Conclusion and outlook
Aiming for a compact NLOS localization system, applicable to scenarios outside the laboratory, illumination schemes for limited laser emission and compensation for the compact but long-pulse laser diodes have been examined. Since the reconstruction resolution of NLOS systems depends heavily on temporal detection resolution, the demonstrator presented, which is based on LiDAR hardware with comparatively low-resolution, cannot compete with state-of-the-art systems. However, this platform offers a photon-efficient and eye-safe solution to localization problems outside the direct field of view when exact scene replication is not required.
It was shown that multiple illumination positions can improve NLOS localization performance in two ways of systems that compile with eye-safety restrictions. First, separated laser sources allow for multiplication of emitted signal that can be distributed more equally across the