by Dinesh » Sun Aug 17, 2014 1:50 pm
walschuler wrote:I would add that you can see that if you move a laser beam across a surface the speckle pattern moves, and if the beam is stable and you move your head your eyes sweep the pattern
It'll be a slightly different pattern, since the phase of the beam is different in each case.
jsfisher wrote:Seems like the brownian motion would destroy coherence.
I don't think it'd "destroy coherence", since the coherence of the beam is determined by the beam source. This is actually an interesting question that I have been mulling over every now and again. I think it will cause a phase shift due to Doppler effects. The Doppler shift causes, in turn, a frequency shift, which in turn affects the phase. In terms of the frequency, the wave vector is 2*pi*f*n/c. But, due to Doppler, the new wave vector is (2*pi*f*n)/(v*c), where v is the velocity of the Brownian particles. The size of the particles that cause Brownian motion is of the order of a few microns, let's say 10*lambda. It is possible using the Einstein/Smoluchowski equations, to determine the velocity of the Brownian motion. So, you now have the momentum of the Brownian particles. I'm assuming that the medium in which the Doppler particles are embedded does not change its index due to Brownian motion. Thus, it is possible to determine whether the phase shift is sufficient to deviate the fringe structure by lambda/4. If so, then, since Brownian motion is random, then the fringe structure will be altering too fast to take a recording. It's not coherence that's lost, it's the phase relationship between the two beams. Included in this, although slightly different, is of course, the effect on phase of a turbulent medium. In the case of a turbulent medium, the "Brownian particles" are a fluid and so vary continuously.
[quote="walschuler"]I would add that you can see that if you move a laser beam across a surface the speckle pattern moves, and if the beam is stable and you move your head your eyes sweep the pattern[/quote]
It'll be a slightly different pattern, since the phase of the beam is different in each case.
[quote="jsfisher"]Seems like the brownian motion would destroy coherence.[/quote]
I don't think it'd "destroy coherence", since the coherence of the beam is determined by the beam source. This is actually an interesting question that I have been mulling over every now and again. I think it will cause a phase shift due to Doppler effects. The Doppler shift causes, in turn, a frequency shift, which in turn affects the phase. In terms of the frequency, the wave vector is 2*pi*f*n/c. But, due to Doppler, the new wave vector is (2*pi*f*n)/(v*c), where v is the velocity of the Brownian particles. The size of the particles that cause Brownian motion is of the order of a few microns, let's say 10*lambda. It is possible using the Einstein/Smoluchowski equations, to determine the velocity of the Brownian motion. So, you now have the momentum of the Brownian particles. I'm assuming that the medium in which the Doppler particles are embedded does not change its index due to Brownian motion. Thus, it is possible to determine whether the phase shift is sufficient to deviate the fringe structure by lambda/4. If so, then, since Brownian motion is random, then the fringe structure will be altering too fast to take a recording. It's not coherence that's lost, it's the phase relationship between the two beams. Included in this, although slightly different, is of course, the effect on phase of a turbulent medium. In the case of a turbulent medium, the "Brownian particles" are a fluid and so vary continuously.