# Temporal and Spatial Coherence

1. Apr 12, 2013

### elemis

What is the difference between the two in simple terms ?

2. Apr 12, 2013

### Claude Bile

The thing to keep in mind is that coherence is a statistical measure of phase. Specifically, if I know the phase at some point in space-time, coherence determines how precisely the phase at some other point in space-time is known. For example;

If I know the phase of a wave at time, t1 and position x1;
- if the wave is perfectly temporally coherent then I can precisely determine the phase of a wave at time t2 and position x1.
- if the wave is perfectly spatially coherent then I can precisely determine the phase of a wave at time t1 and position x2.
- For a perfectly incoherent wave, the phase at t1 and x1 tells me nothing about the phase at different times and in different points in space.
- For partially coherent waves, I can determine the phase at different times and positions within a precision determined by the degree of (temporal and spatial) coherence.

Note too that;
- If the x-direction is parallel to the direction of wave propagation then temporal and spatial coherence are linked via c = x/t.
- If the x-direction is perpendicular to the direction of wave propagation then the temporal and spatial coherence are independent. That is, a wave can be simultaneously spatially coherent and temporally incoherent (and vice-versa).

Claude.