# Can a spatially coherent light source be monochromatic but not temporally coherent?

Someone told me monochromatic light can be temporally incoherent. If you combine a bunch of out of phase, monochromatic waves, don't you just end up with one wave that's the average of each of them? Perhaps if the light is not spatially coherent, then the wave fronts could cross without superimposing? I can see how that would be temporally incoherent.

• Monochromatic light also needs to have been turned on, at a constant amplitude, for infinite time, and to continue thusly until eternity. In practice, having a 'monochromatic' light source means having a source that is monochromatic enough (for the purposes at hand) and that always involves some compromises. – Emilio Pisanty Aug 3 '17 at 9:23

After the spatial coherence problem is taken care of, we are usually able to observe the pattern, but only in a small region near the center. This is where temporal coherence comes into play: at points far away from the center, two paths are too different in their length, so that one path gives us the wavefront emitted at time $t_1$ and another path the one at $t_2$. The source may changed somehow between this time so that their frequency are subtly different; and when that "subtly" becomes "apparently" in the case too long a time has passed, they are no longer coherent.