Analyzing the effect of shot noise in indirect Time-of-Flight cameras

Continuous wave indirect Time-of-Flight cameras obtain depth images by emitting a modulated continuous light wave and measuring the delay of the received signal. In this paper we generalize the estimation of the effect of the shot noise when obtaining the phase delay with an arbitrary number of points in the Discrete Fourier Transform, extending and generalizing the analysis done in previous works for the case of four points. For that particular case, we compare our analysis with the state of art. Moreover, we extend the error model using a second order approximation in the error propagation analysis, which provides more accurate estimations according to the Montecarlo simulation experiments. The analysis, based on both analytical and numerical methods, shows that the phase error is, in general, related to the exposure time and weakly to the number of points in the Discrete Fourier Transform. It also depends on the background illumination level, on the amplitude of the received signal, and, when using a three point DFT, on the distance to the objects.