Where \(E\) is the total electric field entering the detector, \(E_1\) and \(E_2\) are the amplitudes of electric fields of signal light and reference light, \(f_1\) is the frequency of the signal, which is the sum of AOM modulation frequency, the laser frequency and the Doppler shift caused by the movement of the surface. \(f_2\) is the frequency of the reference, which equals the laser frequency. Therefore \(f_1-f_2=f_{AOM}+f_{Doppler}\). \(φ_1\) is the phase of the signal, and \(φ_2 (x,y)\) is the phase of the reference. The spatial dependence of \(φ_2 (x,y) \) is related to the roughness of the measured surface. Because \(f_1\) and \(f_2\) are at optical frequency band and beyond the detector’s response, only the cross-term is detected. The output of the detector has the following expression
\[S(t)=kI(t)=kE^2∝∬E_1E_2\cos[2\pi(f_s1-f_s2)t+φ_1-φ_2(x,y)]dxdy\]