## 2 Principle  
A schematic of the coherent ranging system, which is phase-modulated by a pseudo-random binary code, is illustrated in Figure 1a. Fiber optic coupler 1 (FOC1) divides the laser into two parts: the signal \(E_{\mathrm{S}}\) and the local oscillator \(E_{\mathrm{L}}\). The signal \(E_{\mathrm{S}}\) is phase-modulated with the pseudo-random code \(b_{5}\) using an electro-optic phase modulator (EOPM). An acousto-optic modulator (AOM) is used to shift the frequency of the signal by a specified amount \(f_{1}\). Finally, the frequency-shifted signal \(E_{\mathrm{SI}}\) is transmitted through a variable optical attenuator (VOA) and a collimator. The backscattered signal \(E_{\mathrm{R}}\) from the target and local oscillator \(E_{\mathrm{L}}\) are optically mixed using a 2 \(\times\) 2 fiber optic coupler 2 (FOC2), leading the coherent light to a balanced detector, where it is converted into an electrical signal \(U\) of intermediate frequency (IF). The pseudo-random code \(b_{4}\) is generated by an arbitrary waveform generator (AWG), which produces a pseudo-random code synchro nization pulse (PCSP) at the beginning of each pseudo-random code sequence to be fed into the acquisition module. The acquisition module is a digital storage oscilloscope (DSO), which samples the IF electrical signal triggered by the PCSP. Subsequently, the sampled data are processed on a computer to determine the distance and velocity of the target. The reference output clock (REF-Clock) of the DSO serves as the reference clock for the AWG to ensure that the transmission and reception of the system are synchronized. The two output signals of FOC1 with a splitting ratio of \(r_{1}\) are expressed as [20]  
\[E_{\text{S}}(t)=\sqrt{r_{1}}E_{0}e^{i(2\pi f_{0}t+\phi_{0})}, \tag{1}\]  
\[E_{\text{L}}(t)=\sqrt{1-r_{1}}E_{0}e^{i(2\pi f_{0}t+\phi_{0}-\frac{\pi}{2})}, \tag{2}\]  
where \(f_{0}\), \(E_{0}\), and \(\phi_{0}\) denote the frequency, amplitude, and initial phase of the laser, respectively. \[b_{4}(t)=\sum_{i=0}^{N_{1}-1}a_{i}g(t-iT_{\text{C}})\ \ \ [i(\text{modulo }N_{1})], \tag{3}\]  
Here, \(a_{i}\) is a pseudo-random code composed of \(-1\) and \(+1\), \(g(t)\) is the gate function, \(T_{\text{C}}\) denotes the chip duration, \(N_{1}\) denotes the length of the pseudo-random code, \(b_{5}(t)=\int_{-\infty}^{+\infty}b_{4}(t)h_{1}(t-\tau_{1})d\tau_{1}\), and \(h_{1}(t)\) represents the impulse response of the low-pass filter (LPF). The signal \(E_{\text{S1}}\) is expressed as  
\[E_{\text{S1}}(t)=\sqrt{r_{1}}\cdot E_{0}e^{i[2\pi(f_{0}+f_{1})t+\phi_{0}]}e^{ i\pi\frac{\pi}{2}b_{5}(t)}, \tag{4}\]  
Figure 1: Schematic of distance measurement and flowchart of traditional and proposed distance measurement methods. (**a**) Schematic of distance measurement. (**b**) Traditional ranging flowchart. (**c**) Proposed ranging flowchart. where \(\alpha\) is the phase modulation depth factor, and \(f_{1}\) is the frequency shift caused by the AOM. The expression for the backscattered light \(E_{\text{R}}\) from the target is  
\[E_{\text{R}}(t)=\sqrt{r_{1}}\beta E_{0}e^{i[2\pi(f_{0}+f_{1})(t-\tau_{0})+\theta _{0}]}e^{i[2\pi f_{0}t}e^{i[\alpha\frac{\pi}{2}b_{5}(t-\tau_{0})]}, \tag{5}\]  
where \(f_{\text{D}}\) is the Doppler shift generated by the target velocity, \(\tau_{0}\) is the time delay of light to and from the target, and \(\beta\) is the amplitude attenuation coefficient. The backscattered light \(E_{\text{R}}\) is mixed with the local oscillation light \(E_{\text{L}}\) by FOC2 with a splitting ratio of \(r_{2}\).