# An Overview of Lidar Imaging Systems for Autonomous Vehicles
## 2 Basics of Lidar Imaging
### Measurement Principles
#### 2.1.2 Continuous Wave Amplitude Modulated (AMCW) Approach  
The AMCW approach consists of using the intensity modulation of a continuous lightwave instead of the laser pulses mentioned before. This principle is known as CW modulation, phase-measurement, or amplitude-modulated continuous-wave (AMCW). It uses the phase-shift induced in an intensity-modulated periodic signal in its round-trip to the target in order to obtain the range value. The optical power is modulated with a constant frequency \(f_{M}\), typically of some tenths of MHz, so the emitted beam is a sinusoidal or square wave of frequency \(f_{M}\). After reflection from the target, a detector collects the received light signal. Measurement of the distance \(R\) is deduced from the phase shift \(\Delta\Phi\) occurring between the reflected and the emitted signal [18; 26; 27]:  
\[\Delta\Phi=k_{M}d=\frac{2\pi f_{M}}{c}2R\Rightarrow R=\frac{c}{2}\frac{\Delta \Phi}{2\pi f_{M}}, \tag{2}\]  
where \(R\) and \(c\) are, again, the range to the target and the speed of light in free space; \(k_{M}\) is the wavenumber associated to the modulation frequency, \(d\) is the total distance travelled and \(f_{M}\) is the modulation frequency of the amplitude of the signal. Figure 2 shows the schematics of a conventional AMCW sensor. There are a number of techniques that may be used to demodulate the received signal and to extract the phase information from it. For the sake of brevity, they will only be cited so the reader is referred to the linked references. For example, phase measurement may be obtained via signal processing techniques using mixers and low-pass filters [28], or, more generally, by cross-correlation of the sampled signal backscattered at the target with the original modulated signal shifted by a number (typically four) of fixed phase offsets [13; 19; 29; 30]. Another common approach is to sample the received modulated signal and mix it with the reference signal, to then sample the resultant signal at four different phases [31]. The different types of phase meters are usually implemented as electronic circuitry of variable complexity. In the AMCW approach, the resolution is determined by the frequency \(f_{M}\) of the actual ranging signal (which may be adjusted) and the resolution of the phase meter fixed by the electronics. By increasing \(f_{M}\), the resolution is also increased if the resolution in the phase meter is fixed. However, larger \(f_{M}\) frequencies bring on shorter unambiguous range measurements, meaning the phase value of the return signal at different range values starts to repeat itself after a 2 \(\pi\) phase displacement. Thus, a significant trade-off appears between the maximum non-ambiguous range and the resolution of the measurement. Typical modulation frequencies are generally in the few tenths of MHz range. Approaches using advanced modulated-intensity systems have been proposed, which deploy multi-frequency techniques to extend the ambiguity distance without reducing the modulation frequency [23]. Further, even though phase measurement may be coherent in some domains, the sensitivity of the technique remains limited because of the reduced sensitivity of direct detection in the optical domain. From the point of view of the SNR, which is also related to the depth accuracy, a relatively long integration time is required over several time periods to obtain an acceptable signal rate. In turn, this introduces motion blur in the presence of moving objects. Due to the need for these long integration times, fast shutter speeds or frame rates are difficult to obtain [24; 27]. AMCW cameras have, however, been commercialized since the 90s [32], and are often referred to as TOF cameras. They are usually implemented as parallel arrays of emitters and detectors, as discussed in Section 2.2.2, being limited by the range-ambiguity trade-off, and the limited physical integration capability of the phase-meter electronics, which is done pixel by pixel or for a group of pixels in the camera.