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I am currently studying the textbook Laser Systems Engineering by Keith Kasunic. Chapter 1.2.2 Spatial coherence says the following:

The concepts of spatial coherence and beam quality arise because there may be phase variations $\ge \lambda/4$ across the diameter of each mirror in any laser cavity.

The value of $\lambda/4$ seems quite specific, but, at the same time, the author seems to introduce it out of nowhere. Where does this value of $\ge \lambda/4$ come from? Is it derived from some physical property related to laser cavities?

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In high quality optical systems, $\lambda/4$ is often considered the maximum allowed peak to peak variation of the optical path difference allowed in the beam that forms an image. Many also use a maxiumum allowed rms (root mean square) variation of 0.07 waves.

Since ideally a laser cavity would be diffraction limited, so that it produces a diffraction limited beam, then it seems reasonable to put a $\lambda/4$ limit on allowed phase variations (or optical path difference) on optics inside the cavity. In practice, laser manufacturers would typically specify much tighter specifications on mirrors: $\lambda/20$ would be common. They are trying to get as high a beam quality and power as possible out of their laser. Since I'm not a laser expert, I can't comment on how much phase variations affect the extraction of power from within the laser cavity.

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