# Coherent sources for interference

Regular interference pattern can be observed if the two wave sources are coherent.

Two sources are coherent if they have the same frequency and constant phase difference.

Could someone please explain to me what constant phase difference implies?

I agree with @Floris that the statement doesn't make sense at face value, but since I know what he is trying to say, I might be able to translate.

No signal has a single frequency. There is always a very small spread in a signal's frequency content. (Pure single frequency implies a signal that started in the infinite past and will continue into the infinite future.) But a nearly-single-frequency wave will be indistiguishable from a true-single-frequency wave if you look at it for a finite time interval.

So take two waves, and look at them during the same time interval. They both will look like waves with some frequency $f$, with some phase shift $\phi$ between them.

Now wait a while and look at the same two waves again. Again, they both will look like waves of frequency $f$. And they will have a phase shift between them, call it $\phi_\mathrm{new}$.

If you wait a short enough time between measurements, the two phase values will be the same. If you wait long enough, they will have been seen to have drifted apart.

Over time, $\phi_\mathrm{new}$ drifts away from $\phi$ because of those tiny fluctuations in the frequency. If $\phi_\mathrm{new} = \phi$ we could say that there is a constant phase shift; if not, then we can say that the phase shift is not constant.

Optical detectors average intensity over a long time, often on the order of seconds. If the phase shift is not constant during that interval (an incandescent source for example), interference patters will be washed out, and not visible. The light is incoherent over that interval. If the phase shift is constant over the (e.g. a laser), interference patterns are visible. The light is said to be coherent over the interval.

Really - if two signals truly have the same frequency, this ought to imply constant phase difference, because a changing phase really is the same thing as a slightly different frequency.

But here is one way to look at it. Imagine a Young's slits experiment. You get a certain fringe pattern. Now put a piece of glass in front of one slit that is just thick enough to change the phase by 180 degrees for one slit only. Now the fringe pattern will shift - where there used to be minima you will have maxima, and vice versa.

If you alternately have the piece of glass there, and to there, the interference pattern will keep shifting back and forth - and you end up with no pattern at all. This is why a constant phase difference is important.

Make sense?