# An Optical Interference Suppression Scheme for TCSPC Flash LiDAR Imagers
## 2 TCSPC LiDAR  
A TCSPC LiDAR is a type of direct time-of-flight (d-ToF) sensor. In direct time-of-flight (d-ToF), the distance \(z\) to an object is estimated by measuring the round trip time \(T_{\text{ToF}}\) of an electromagnetic pulse (usually infrared light) from a suitable emitter contiguous to the detector to the object, according to the d-ToF relation  
\[z=\frac{c\cdot T_{ToF}}{2}, \tag{1}\]  
where \(c\) is the travel speed of the chosen electromagnetic wave in the propagation medium (Figure 1).  
In optical TCSPC imaging (especially 3D range finding) emitters are usually chosen among Q-switched lasers [8] or vertical-cavity surface-emitting laser (VCSEL) arrays [9], due to their fast switching speeds.  
Figure 1: Schematic representation of a time-correlated single-photon counting (TCSPC) imager. A dedicated digital block generates the control signal for a pulsed laser. The same control signal is used by the time-to-digital converter to start measuring time synchronously to the generation of the laser pulse. The laser pulse travels to the object to be imaged, and it is diffused back to the sensor. On the sensor, it is detected by suitable pixels capable of discriminating the time of arrival of the pulse. The time of arrival event is sent to the time-to-digital converter to produce a digital representation of the duration of the time interval between laser emission and photon detection.  
Single-photon detectors such as single-photon avalanche diodes (SPADs) are used on the receiver side to detect the time of arrival of individual photons. Photoelectrons generated by the absorption of individual photons are accelerated by the strong electric field in the diode and undergo an avalanche multiplication process that produces a macroscopic, measurable current through the device [10]. Events detected by the SPAD pixels are often timed on-chip using combinations of time-to-analog converters (TACs) and analog-to-digital converters (ADCs) [11; 12], or time-to-digital converters (TDCs) [13; 14; 15], to produce a digital representation of the time of arrival of each detected photon, called a timestamp. Each timestamp \(T_{\text{ts}}\) is a measure of the time of arrival of a photon detected by the pixel \(T_{\text{pixel}}\) relative to the generation time of the laser pulse \(T_{0}\), according to the relation  
\[T_{\text{ts}}=T_{\text{pixel}}-T_{0}=T_{\text{ToF}}-T_{0}. \tag{2}\]  
Given it is impossible to discriminate between the possible origins of each individual event produced by a SPAD pixel (thermal noise, ambient light, and active signal being the most prominent sources), TCSPC LiDAR imagers often repeat the same timestamp measurement 10-10,000 times. All measured timestamps undergo simple statistical processing to extract the relevant features of the useful signal. Ambient photon detections and dark counts (including thermally induced events and trap-assisted tunneling) occur at random times and are not correlated to the active signal. Active signal photons, on the other hand, are emitted synchronously to the activation instant of the TDC, and therefore, their time of arrival at the sensor is correlated and dependent on their time-of-flight (ToF). If plotted in a histogram, all detected timestamps will produce a noisy plateau representing uncorrelated events (ambient light and internal detector noise) and a peak constituted by the time of arrival of signal photons. A typical TCSPC histogram is shown in Figure 2.