[1] M2 can be measured by placing an array detector or scanning-slit profiler at multiple positions within the beam after focusing it with a lens of high optical quality and known focal length.
[1] Likewise, a beam intensity profile can appear very "un-Gaussian", yet have an M2 value close to unity.
In fiber-optic communications beams with an M2 close to 1 are required for coupling to single-mode optical fiber.
For a given laser cavity, the output beam diameter (collimated or focused) scales as M, and the irradiance as 1/M2.
It is difficult to obtain excellent beam quality and high average power at the same time due to thermal lensing in the laser gain medium.