# An Optical Interference Suppression Scheme for TCSPC Flash LiDAR Imagers
## 5 Interference Suppression  
The FLISS technique allows a TCSPC LiDAR to operate safely and free from optical interference in the presence of an arbitrary number of aggressors without requiring any central coordination or communication between devices. Optical interference suppression is achieved by the addition of discrete random delays to the generation of the laser pulse of the victim. The interval between two laser pulses of the victim then becomes  
\[\Delta T_{p,p}=\mathrm{T}+T_{\mathrm{md}}=\frac{1}{\mathrm{PRF}}+T_{\mathrm{md}}, \tag{3}\]  
where \(\Delta T_{p,p}\) is the interval between two consecutive laser pulses of the victim, PRF is the nominal pulse repetition frequency of the victim, \(\mathrm{T}\) is the period of laser repetition at the nominal PRF, and  
Figure 3: Illustrative example of optical interference. The victim imager emits and detects reflected laser pulses along the blue arrows. The emission of a second camera active in the same environment (the aggressor) is also detected by the victim. If the two trains of pulses are sufficiently similar in timing, duration, and repetition frequency, then the victim would have no way of distinguishing the origin of each individual pulse, the time-of-flight (ToF) to the target object being unknown. In this case, the victim will construct a histogram containing two peaks, which is a source of potential ambiguity. is a discrete random variable describing a positive delay with a different value for every generated laser pulse. Under this definition, the victim implementing FLISS will operate at an effective average PRF that is lower than the nominal PRF and is defined as  
\[\text{PRF}_{\text{eff}}=\frac{1}{\text{T}+E(T_{\text{rmd}})}, \tag{4}\]  
where \(E(T_{\text{rmd}})\) represents the expected value of the random variable \(T_{\text{rmd}}\). The next laser pulse is therefore fired at \(T_{p,v}=T_{0}+T_{\text{rmd}}\), where \(T_{0}\) is the time at which the laser would normally have fired according to its nominal PRF. Due to the delay in the firing of the laser, all signal-related pixel activity will also be delayed by an equal amount (\(T_{\text{pixel}}=T_{\text{ToF}}+T_{\text{rmd}}\)). The statistics of events induced by ambient light and noise won't change as a consequence of the introduction of \(T_{\text{rmd}}\). The final timestamp is calculated as the difference of the previous quantities, therefore  
\[T_{\text{ts}}=T_{\text{pixel}}-T_{p,v}=T_{\text{ToF}}+T_{\text{rmd}}-T_{0}-T_{ \text{rmd}}=T_{\text{ToF}}-T_{0}. \tag{5}\]  
It is shown that the victim is in principle not affected by \(T_{\text{rmd}}\), regardless of its value and temporal evolution. The delay \(T_{\text{rmd}}\) is chosen randomly in a bounded interval \((0,T_{\text{MAX}}]\), where \(T_{\text{MAX}}\) is finite. The absolute timing of the laser pulses generated by the aggressor is not influenced by the random delay \(T_{\text{rmd}}\), therefore the timestamps generated by the victim from aggressor activity can be defined as  
\[T_{\text{ts,a}}=T_{\text{ToF},\mu}-T_{0}-T_{\text{rmd}}, \tag{6}\]  
where \(T_{\text{ToF},\mu}\) is the ToF from the aggressor to the victim, passing by the target object. It is shown that each aggressor timestamp is shifted in the victim's reference frame by an amount equal to the variable quantity \(T_{\text{rmd}}\), which is not canceled out for the aggressor. Thanks to the variable nature of \(T_{\text{rmd}}\), aggressor timestamps can be distributed across the entire measurement range of the victim, effectively decorrelating the aggressor signal. The quality and performance of the decorrelation depend on the statistical properties of the temporal evolution of \(T_{\text{rmd}}\). The random delay \(T_{\text{rmd}}\) can be generated in a variety of ways.