# An Overview of Lidar Imaging Systems for Autonomous Vehicles
## 3 Sources and Detectors for Lidar Imaging Systems in Autonomous Vehicles
### Photodetectors
#### 3.2.1 Gain and Noise  
As described above, the gain is a critical ability of a photodetector in low SNR conditions as it enables us to increase the available signal from an equivalent input. Gain increases the power or amplitude of a signal from the input (in lidar, the initial number of photoelectrons generated by the incoming photons which are absorbed) to the output (the final number of photoelectrons sent to digitization) by adding energy to the signal. It is usually defined as the mean ratio of the output power to the input signal, so a gain greater than 1 indicates amplification. On the other hand, noise includes all the unwanted, irregular fluctuations introduced by the signal itself, the detector and the associated electronics which accompany the signal and perturb its detection by obscuring it. Photodetection noise may be due to different parameters well described in [127].  
Gain is a relevant feature of any photodetector in low SNR applications. Conventionally, a photon striking the detector surface has some probability of producing a photoelectron, which in turn produces a current within the detector which usually is converted to voltage and digitized after some amplification circuitry. The gain of the photodetector dictates how many electrons are produced by each photon that is successfully converted into a useful signal. The effect of these detectors in the signal-to-noise ratio of the system is to add a gain factor G to both the signal and certain noise terms, which may also be amplified by the gain.  
Noise is, in fact, a deviation of the response to the ideal signal; so, it is represented by a standard deviation (\(\sigma_{noise}\)). A combination of independent noise sources is then the accumulation of its standard deviations, which means that a dominant noise term is likely to appear:  
\[\sigma_{noise}=\sqrt{\sigma_{shot}^{2}+\sigma_{th}^{2}+\sigma_{back}^{2}+ \sigma_{read}^{2}+...} \tag{8}\]  
Thermal noise \(\sigma_{th}\) and shot noise \(\sigma_{shot}\) are considered fixed system noise sources. The first is due to the thermal motion of the electrons inside the semiconductor, which adds electrons to the output current which are not related to the incident optical power. Shot noise is related to the statistical fluctuations in the optical signal itself and the statistical interaction process with the detector. Shot noise is relevant only in very low light applications, where the statistics of photon arrival become observable. Other noise sources are considered as external, such as background noise \(\sigma_{back}\), readout noise \(\sigma_{read}\), or speckle noise \(\sigma_{speckle}\). They respectively appear as a consequence of the existence of background illumination in the same wavelength of the laser pulses, fluctuations in the generation of photoelectrons or its amplification, or the presence of speckle fluctuations in the received laser signal. While fixed system noise will not be affected by the gain of the detector, background, readout and speckle noise will also be amplified by the gain, which may become counter-productive for detection. When either thermal or shot noise are the dominant noise source, we are said to be in the thermal or shot noise regimes of a detector, and the existence of gain significantly improves the SNR value.  
The SNR for a detector with gain may then be written as:  
\[SNR_{Gain}\approx\frac{G\cdot N_{signal}}{\sqrt{\sigma_{shot}^{2}+\sigma_{th }^{2}+G^{2}\cdot\sigma_{back}^{2}+G^{2}\cdot\sigma_{read}^{2}+...}}. \tag{9}\]  
where \(N_{signal}\) is the number of photoelectrons generated by real incoming photons. Equation (9) shows the advantage to work in thermal or shot regime regarding gain.