In early 1970, Larry Marshall [2] noted, 'Despite variations of intensity cross sections from gaussian shape, it is still convenient to define beam diameter as M times the 1/e^2 diameter of the equivalent gaussian mode'.
Anthony E. Siegman significantly advanced this formalism, providing a method that could be measured and used to compare different beams, independent of wavelength.
M2 can also give an indication of beam distortions due to, for example, power-induced thermal lensing in the laser gain medium, since it will increase.
It can be difficult to measure accurately, and factors such as background noise can create large errors in M2.
[6] Power-in-the-bucket and Strehl ratio are two other attempts to define beam quality.
Both these methods use a laser beam profiler to measure how much power is delivered to a given area.