Where \(U\) is APD output voltage, \(e\) is elementary charge, \(η\) is the quantum efficiency of APD, \(M\) is the gain of the APD, \(h\) is the Planck constant, \(v\) is the photon frequency, \(\frac{P_0}{r^2}\) is the received laser power when the surface is static, \(R\) is the TIA load resistance, and \(r\) is the distance between REAL and the speaker, \(Δr\) is surface displacement. We could use constant  \(A=\frac{eη}{hv}P_0MR\) to simplify the equation. \(A\) is 2.48 Vm2 when the emitted laser power is 9 mW in our setup.
We use the root mean square \(σ\) to quantify noise amplitude. REAL signal \(ΔU\) is affected by laser power fluctuation \(σ_l\), optical shot noise \(σ_s\), electronic noise \(σ_e\), target movement noise \(σ_m\) and laser pointing noise \(σ_p\). Total noise is expressed as
\[σ=\sqrt{σ_l^2+σ_s^2+σ_e^2+σ_m^2+σ_p^2}\]