where we assumed these noises are independent. In noise analysis, the emitted laser power \(P\) is proportional to the collected laser power \(P_c \)  given that r is fixed. The collected laser power is \(P_c=\frac{(1+n)P_0}{r^2}\), where \(n\) represents the power fluctuation ratio and is much smaller than one. Therefore, the laser fluctuation is proportional to laser power: \(σ_l^2∝P^2\). The shot noise \(σ_s\) is determined by the Poisson process and goes as squared root of laser power: \(σ_s^2∝P\). The electronic noise \(σ_e\) is mainly determined by the electronic thermal noise and can be assumed as a constant. The target movement noise \(σ_m\) is caused by the target movement. Our simulated \(σ_m^2\) is 3.1265×10-12 Vin audio frequency range, which is caused by a movement ( \(Δr\) ) with a moving speed of 0.1 m/s, when laser power is 9 mW and distance ( \(r\)) is 10 m. Since this noise is relatively small and different each time, we do not introduce \(σ_m\) in the total noise model. The laser pointing noise \(σ_p\) is usually caused by the unstable lasing mode change within the laser cavity and can be ignored from a stable laser. Therefore, the relationship between noise and laser power is as follows
\[σ^2=σ_l^2+σ_s^2+σ_e^2=aP^2+bP+c\]