# An Overview of Lidar Imaging Systems for Autonomous Vehicles
## 2 Basics of Lidar Imaging
### Measurement Principles  
#### 2.1.1 Pulsed Approach  
Pulsed TOF techniques are based on the simplest modulation principle of the illumination beam: distance is determined by multiplying the speed of light in a medium by the time a light pulse takes to travel the distance to the target. Since the speed of light is a given constant while we stay within the same optical medium, the distance to the object is directly proportional to the traveled time. The measured time is obviously representative of twice the distance to the object, as light travels to the target forth and back, and, therefore, must be halved to give the actual range value to the target [13; 18; 19]:  
\[R=\frac{c}{2}t_{\mathrm{oF}}, \tag{1}\]  
where \(R\) is the range to the target, \(c\) is the speed of light (\(c=3\times 10^{8}\) m/s) in free space and \(t_{\mathrm{oF}}\) is the time it takes for the pulse of energy to travel from its emitter to the observed object and then back to the receiver. Figure 1 shows a simplified diagram of a typical implementation. Further technical details of measuring \(t_{\mathrm{OF}}\) can be found in references like [18; 20]. The attainable resolution in range (\(\Delta R_{min}\)) is directly proportional to the resolution in time counting available (\(\Delta t_{min}\)). As a consequence, the resolution in depth measurement is dependent on the resolution in the time counting electronics. A typical resolution value of the time interval measurement can be assumed to be in the 0.1 ns range, resulting in a resolution in depth of 1.5 cm. Such values may be considered as the current reference, limited by jitter and noise in the time-counting electronics. Significant improvements in resolution may be obtained by using statistics [21], but this requires several pulses per data point, degrading sensor performance in key aspects like frame rate or spatial resolution. Figure 1: Pulsed time-of-flight (TOF) measurement principle. Theoretically speaking, the maximum attainable range (\(R_{max}\)) is only limited by the maximum time interval (\(t_{max}\)) which can be measured by the time counter. In practice, this time interval is large enough so the maximum range becomes limited by other factors. In particular, the laser energy losses during travel (especially in diffusing targets) combined with the high bandwidth of the detection circuit (which brings on larger noise and jitter) creates a competition between the weak returning signal and the electronic noise, making the signal-to-noise ratio (SNR) the actual range limiting factor in pulsed lidars [22; 23]. Another aspect to be considered concerning maximum range is the ambiguity distance (the maximum range which may be measured unambiguously), which in the pulsed approach is limited by the presence of more than one simultaneous pulse in flight, and thus is related to the pulse repetition rate of the laser. As an example, this ambiguity value ranges to 150 m at repetition rates of the laser close to the MHz range using Equation (1). The pulsed principle directly measures the round trip time between light pulse emission and the return of the pulse-echo resulting from its backscattering from a target object. Thus, pulses need to be as short as possible (usually a few nanoseconds) with fast rise and fall times and large optical power. Because the pulse irradiance power is much higher than the background (ambient) irradiance power, this type of method performs well outdoors (although it is also suitable for indoor applications, where the absence of solar background will reduce the requirements on emitted power), under adverse environmental conditions, and can work for long-distance measurements (from a few meters up to several kilometers). However, once a light pulse is emitted by a laser and reflected onto an object, only a fraction of the optical energy may be received back at the detector. Assuming the target is an optical diffuser (which is the most usual situation), this energy is further divided among multiple scattering directions.