What is Phase Coherence?

Phase Coherence is a phenomenon where a constant phase difference exists between any two signals or waves of the same frequency. For instance, when two sinusoidal signals or sine waves are resonating at the same frequency and are time-shifted relative to each other, their relative phase does not change with respect to time. This means that the two waves are perfectly coherent in phase with changes in time.

In the above figure, two sinusoidal waves of the same frequency, wavelength, and amplitude are generated and time-shifted with respect to each other. However, the phase of orange wave relative to the black wave (or vice-versa) does not change as a function of time and they produce crests and troughs at the same time. Thus, it can be concluded that there exists a constant phase difference and hence a perfect phase coherence between the two waves. Phase coherent waves are particularly useful in producing stable interference patterns.

In practical situations, waves (e.g., electromagnetic waves, acoustic waves) may face disturbances due to the surrounding environments (e.g., reflection, refraction, scattering, diffraction etc.,) and may lead to a change in phase. In such scenarios, the relative phase or phase difference is not constant and hence the incident and disturbed waves are no longer coherent in phase – or become phase incoherent. The figure below shows the scenario where the relative phases are not constant, or phase incoherent with respect to each other.

Situations may exist where the relative phase between the two waves may constantly vary with time. Therefore, in such cases, the segments of time where the phase difference is constant are referred to as phase coherent segments. The figure below presents an illustration of the concept.