## 2 FMCW LiDAR
### FMCW LiDAR Key Parameters
#### 2.3.5 FM Linearity  
Frequency-modulation linearity is crucial in FMCW LiDAR systems, referring to the uniformity and consistency of frequency changes during signal transmission. A lack of high linearity in the frequency-modulation process can significantly impair measurement accuracy and resolution. Non-linear frequency-modulation can lead to a broadened spectrum of the detected beat signal, complicating the identification of effective frequency peaks, which, in turn, impacts the accuracy of frequency estimations. The linearity of frequency modulation is directly and critically related to the performance of the laser source. The performance parameters of the light source in FMCW LiDAR impose stringent requirements on the laser linewidth and modulation bandwidth, and these factors collectively determine the performance and application range of the FMCW LiDAR system [21]. In an FMCW LiDAR system, the modulation of the laser frequency causes its wavelength to change in the opposite direction:  
\[\lambda=\frac{c}{f}, \tag{14}\]  
where \(\lambda\) is the wavelength, \(f\) is the frequency, and \(c\) is the speed of light. When the laser frequency is modulated by a triangular waveform, the wavelength changes. The receiver measures this wavelength change by analyzing the received optical signal spectrum and calculates the distance to the target. Coherent demodulation technology is used to detect these wavelength changes. Specifically, the wavelength change is inferred by comparing the frequency difference between the transmitted signal and the returned signal. A high-bandwidth coherent receiver can accurately measure these frequency changes and infer the distance to the target. This method also applies to sawtooth modulation  
Figure 7: Schematic power spectrum of a differential frequency signal. waveforms because the basic principle of wavelength change is the same under different modulation waveforms. In FMCW LiDAR systems, modulation depth is usually measured using modulation frequency. This is because the modulation frequency is in the GHz range, and the distance resolution is directly related to the frequency, while the modulation wavelength is in the picometer range, so frequency modulation is more suitable for adjustment in practical applications. In fact, as indicated by Equation (10), when the laser frequency is modulated, the wavelength will correspondingly change. Therefore, although the focus of discussion is on the modulation frequency, this does not imply that the laser wavelength remains unchanged. The receiver detects these wavelength changes by analyzing the frequency spectrum of the optical signal, enabling precise measurement. FMCW LiDAR systems utilize three principal laser source types: internally modulated laser sources, externally modulated laser sources, and chirped-pulse laser sources [22]. The predominant modulation methods in FMCW LiDAR involve internal and external modulation. Internally modulated laser sources offer precision in controlling laser frequency and intensity by adjusting the resonant parameters of the laser cavity during the laser oscillation's formation phase. This technique commonly employs distributed-feedback semiconductor lasers, which depend on thermo-optic effects and carrier dispersion effect for modulation. Advantages of internally modulated laser sources include their structural simplicity, the capability to deliver high-power laser signals, and suitability for long-range detection applications [23]. An externally modulated laser transmission system comprises a single-frequency laser and an optical modulator. The laser generated by the single-frequency laser is modulated by the optical modulator to achieve linear modulation of the frequency of the output. This is achieved by externally realizing the modulation process, which reduces the complexity of the system and effectively avoids non-linear effects due to the increase in the modulation bandwidth. This is due to the excellent linearity of the optical modulator.