How is it possible to achieve waves which are spatially, but not temporally, coherent? Can this be done with a bandpass filter?

Conversely, how is it possible to achieve waves which are temporally, but not spatially, coherent? Can this always be achieved with a pinhole?


Yes! Even at home you can see this.

First, a star is spatially coherent and not temporally coherent (not the sun, but any other star). It creates a near plane wave when illuminating Hubble or even many terrestrial telescopes. http://skullsinthestars.com/2008/09/03/optics-basics-coherence/

Second, a distant low-pressure sodium light is temporally incoherent and spatially coherent. Try this at home. At night, stand about 2 - 5 ft from a screen door or window screen. Look at a distance street lamp. You'll see a distinct sinc(x) pattern (repeating dots in the vertical and horizontal direction aligned with the lines on the screen). This can't happen with an extended source. See: http://en.wikipedia.org/wiki/Diffraction and http://en.wikipedia.org/wiki/Fraunhofer_diffraction_%28mathematics%29 for sinc(x) patterns.


You can create waves that are spatially but not temporally coherent using two pinholes (not one): place one pinhole in the other's far field. That way you get waves originating from the same point and whose wave vectors point in the same direction, but that are not necessarily all in phase.

(I suppose technically one pinhole gives you spatially coherent light with a very short coherence length.)

Temporal but not spatial coherence I'm not sure about. I think random lasers might give you this.


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