Coherence - A Must for Interference?

[PFuser1232]

I can't get my head around the fact that for the interference of two waves to occur, the two sources producing the waves must be coherent (Well, that's what my A level Physics book says). Wouldn't it perhaps be more appropriate to say that coherence is only a necessary condition if an interference pattern is to be observed? (But not a necessary condition for intereference itself to take place.)

 

[Andy Resnick]

Minor comment- the sources must be mutually coherent. The degree of mutual coherence may vary between 1 (two perfectly coherent sources also coherent with each other) and 0 (perfectly incoherent sources), and the amount of interference (extend of the interference pattern in time and space) will vary depending on the degree of mutual coherence from everywhere, all the time (mutual coherence of 1) to the opposite.

 

[PFuser1232]

Minor comment- the sources must be mutually coherent. The degree of mutual coherence may vary between 1 (two perfectly coherent sources also coherent with each other) and 0 (perfectly incoherent sources), and the amount of interference (extend of the interference pattern in time and space) will vary depending on the degree of mutual coherence from everywhere, all the time (mutual coherence of 1) to the opposite.

So, the two waves may or may not be of the same frequency or wavelength?

 

[PFuser1232]

Besides, doesn't coherence refer to waves having a constant phase difference? Does that mean that two identical waves superposing to form a standing wave are not coherent waves? They sometimes add up, and sometimes cancel.

 

[Khashishi]

You are right; you don't need coherence for interference effects. It just makes it easier to see the effects. But, you don't necessarily need coherent light in a Mach–Zehnder interferometer, for example.

 

[sophiecentaur]

Superposition will cause a resultant field when any number of waves arrive at a point. The resultant will only be zero, for any length of time (an observable null / 'good' interference pattern) if the waves have a constant phase relationship. So the 'best' interference pattern will be seen when all the waves are coherent, everywhere. Using a point source and fairly monochromatic light will ensure that the coherence is good enough to get a two-slits pattern but not enough to produce a hologram because the coherence of the source is not good enough for interference to work over the range of distances and angles involved with making a hologram. That's why a laser is needed (there are several other details that need to be sorted out, too).
Excellent interference patterns are easily obtained, not at light wavelengths but with RF, where it is easy to produce well synchronised sources from a number of sources (antenna elements). Two RF oscillators can operate independently with minuscule mutual phase shifts. That's pretty difficult with different atoms, emitting light frequencies.

 

[PFuser1232]

Thanks Sophie and Khashishi! One more question about coherence; if two waves of the same wavelength and frequency travel in the opposite direction, is it correct to say that they are coherent? Despite the fact that their phase difference is constantly changing?

 

[sophiecentaur]

This is another 'classification' question and you shouldn't lose any sleep over it. If the two sources are synchronous then they are coherent. The resulting standing wave pattern is just a pattern. Imagine that a single source was forming an interference pattern (so the contributions to the pattern would be called coherent) and then you insert a mirror , which changes the direction of part of the wavefront (producing, effectively, two sources). You could still get an interference pattern / standing wave. Would you need to ask about "coherence" in that case?

 

[Andy Resnick]

So, the two waves may or may not be of the same frequency or wavelength?

If the sources are mutually coherent, then the two sources do not have to have the same frequency (see, for example, heterodyne detection).

 

[sophiecentaur]

If the sources are mutually coherent, then the two sources do not have to have the same frequency (see, for example, heterodyne detection).

Correct in principle but, using the common appreciation of an interference pattern (i.e. stationary and visible), it is stretching things a bit, I think. Won't the 'interference pattern' be constantly on the move? I think that's a bit outside the context of a question from and A level student.

Or do you mean that the sources have some common factors in their frequencies?