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A red laser with a wavelength of 600nm would have a frequency of 5E14 Hz. If it had a frequency spread (noise or finite cavity Q) of 6 MHz, we'd say it has a coherence length of 50 meters. You could build a Michelson interferometer and when one arm was 30 meters longer than the other (60 meters total path difference) the fringe contrast would be greatly reduced.

Suppose the frequency stability of the laser were not so good; +/- 600 MHz, but with a maximum slew rate of 6 MHz per second (it's due to some thermal instability and has a time constant associated with thermal inertia).

What is the simplest way to explain that a laser can have a frequency stability of 600 MHz and yet at the same time have a coherence length associated with a spread of only 6 MHz?

This is a numerical example, I'm trying to find a better way to address this comment which is mixing stability and coherence.

hint: the interferometer uses photodiodes or CCDs which are read out much faster than once a second.

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The stability of the laser, which has to do with how the frequency drifts over time scales larger than the integration time of the detector, is something different from the bandwidth of the laser, which gives rise to the coherence length of the laser. The finite bandwidth means that there are multiple frequencies present at any time. These frequencies would move gradually out of phase when you compare different points along the beam. That gives rise to the incoherence along the beam for separation larger than the temporal coherence length.

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