## 2 FMCW LiDAR
### FMCW LiDAR Key Parameters
#### 2.3.1 Detection Distance and Accuracy  
Detection range stands as a crucial parameter for evaluating LiDAR system's performance. Figure 5 shows the FMCW ranging method. First, the transmitter sends out a set of frequency ft that linearly varies with the time laser signal. The modulation bandwidth for \(B\) and modulation time for \(t_{s}\) will be adjusted after the laser beam beams for the local oscillation beam and the detection of the beam. Then, the detection of the beam after experiencing a detection distance of \(d\) after the echo beam produced by the detection system to receive--due to the existence of flight delay \(t_{E}\)--the received echo beam frequency \(f_{F}\) and the frequency of the local oscillation beam \(f_{t}\) differ with the frequency of the beam \(\mathrm{f_{b}}\), as shown in the image below [9]. \[f_{b}=\frac{2\cdot R\cdot B}{c\cdot t_{s}} \tag{8}\]  
The equation governing this process incorporates several variables: \(c\) is the speed of light; \(t_{s}\) is modulation time; \(R\) is the detection distance; \(f_{b}\) is the frequency difference between the echo beam and the local oscillation beam at the same moment; and \(B\) signifies the laser's frequency-modulation range. Figure 5: FMCW ranging method. Due to the limitations of the detector devices, the high-frequency component cannot be detected, so the light intensity expression for the received mixed frequency beam:  
\[\text{I}(\text{t})=A\cdot B\cos\left[(\omega_{A}(t)-\omega_{B}(t))t+(\varphi_{A} -\varphi_{B})\right]=A\cdot B\cos[2\pi f_{b}t+(\varphi_{A}-\varphi_{B})]. \tag{9}\]  
In the equation, \(I(t)\) is the light intensity of a mixed-frequency beam; \(A\) and B are the electric field amplitudes of the local oscillator beam and the probe beam; \(\omega_{A}(t)\) and \(\omega_{B}(t)\) are the electric field frequencies that change linearly with time; and \(\varphi_{A}\) and \(\varphi_{B}\) are the electric field phases of the local oscillator beam and the probe beam. The frequency of the resulting mixing signal is the desired frequency difference \(f_{b}\), which can be combined with Equation (8) to find the detection distance \(R\). In FMCW LiDAR, the maximum detection range is a crucial indicator influenced by several factors. This range is determined by the repetition period of the transmitted signal, where only return signals received within this period or sooner can be accurately interpreted as distance information. Returns arriving after this period risk being misinterpreted as signals from subsequent signals, creating potential ambiguity [10]. Moreover, the maximum detection range is contingent on the coherence length of the optical wave signal. When the target's echo exceeds this length, beat frequency signal might significantly diminish, resulting in a lower signal-to-noise ratio (SNR) and preventing effective detection. The SNR is further influenced by the transmitted light power, receiver's bandwidth and sensitivity, and the level of environmental noise. Notably, FMCW LiDAR has the advantages of high precision and large data volume compared with microwave radar; however, the detection ability of FMCW LiDAR is affected by the atmospheric environment (including very large rain, snow, haze, and other factors). The impact of atmospheric transmission on LIDAR is primarily reflected in the atmospheric absorption, atmospheric scattering, and atmospheric turbulence. When the FMCW LiDAR is utilized in medium- and short-range detection, the impact of atmospheric turbulence is less than that of atmospheric absorption and atmospheric scattering. As FMCW LiDAR technology advances, its application scope broadens, promoting an escalation in performance requirements. Current research efforts aim to improve detection accuracy and performance through such as balanced detectors, PIN photodiode (PIN-PD), and optical phased array (OPA) to satisfy the growing need for high-performance detection systems.