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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.

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    $\begingroup$ 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. $\endgroup$ – Emilio Pisanty Aug 3 '17 at 9:23
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Temporal incoherence means the light is not monochomatic "enough".

Consider the double slit experiment. We lit the double slits with a single narrow slit --- why? Because this is where spatial coherence comes in. A wide slit can be thought of as two (or many) narrower slits combined. When given two different sodium lamps we usually do not expect their light to interfere and produce some visible patterns. If an ideal point-source emitted light and produced a wave front, we pick two parts of the wave at different locations, we know they come from the same source and are "related" to each other, i.e. coherent.

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.

This is also a reason why the two slits are very close to each other: if separated by a considerable distance, the region for which interferrence patterns can be observed becomes too narrow. Draw the sketch and you will see that by geometry.

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  • $\begingroup$ Thanks for your response. So is it fair to say that temporal coherence depends on the situation? Perfectly monochromatic light (if it existed) would be perfectly temporally coherent at all times. In reality, as long as the coherence length of the light is longer than you need for your experiment, then the light can be described as coherent? $\endgroup$ – James Aug 3 '17 at 12:56
  • $\begingroup$ @James Yes. Some lasers may have ceherence lengths of kilometers. $\endgroup$ – Carl Lei Aug 3 '17 at 13:34

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