Determining the phase shift of quasiharmonic signals through envelope analysis

The paper presents a new technique for the accurate measurement of the phase difference between two quasi-harmonic optical signals through analyzing and processing their envelope values obeying the Rice statistical distribution. With this technique, the envelope values of three signals are measured: two initial quasi-harmonic signals for which the phase difference is measured and a third signal formed as superposition of the first two. The phase shift under measurement is calculated from simple geometrical considerations as the angle of a triangle formed by the amplitude values of the reconstructed undistorted signals. The fundamental distinction of the proposed technique consists in the fact that the phase characteristics are derived from the amplitude measurements alone, thus significantly mitigating the requirements imposed on the equipment and simplifying the practical implementation of the method. It is proposed that the undistorted amplitudes should be estimated using methods of the Rician data analysis. The paper provides a strict mathematical analysis of the problem and computer simulation results. The ability to conduct accurate phase shift measurements based on the proposed method is useful for a wide range of applied tasks solved in numerous ranging and communication systems.