Multi-depth photon-counting imaging based on polarisation modulation

We present a method for multi-depth imaging that uses polarisation modulation to reconstruct multiple depths from photon-counting observations. The echo photon signals of the scene with multiple targets are modelled under the low-flux condition based on a confocal scanning system. We establish a computational method by constructing the relationship between the received photon rate after polarisation modulation and several variables described for multi-echo signals: the detected average number of photons before polarisation modulation and the flight time corresponding to phase shift based on polarisation modulation. The photon rate is directly calculated from the photon-counting value received by a photon-counting detector based on the Poisson negative log-likelihood function. We suggest solving the abovementioned relationship by changing the waveform of the operating voltage applied to the modulator to derive analytic forms of the detected average number of photons and the flight time. We experimentally demonstrate that the proposed method can accurately reconstruct the reflectivity and depth images of two targets in a 3D scene with a significant improvement beyond what the polarisation modulation imaging method for single-depth can achieve. Moreover, we demonstrate the effectiveness of the proposed method by varying the reflection properties of the targets, the number of echo photons (e.g. less than one photon in a pulse) and the background noise. We exhibit a fast imaging capability with the imaging frequency of one pixel at 8 kHz and the root mean-square error of depth smaller than 6 cm.