The first rule of laser beam quality metrics states that any time you try to reduce the performance of a complex electric field with seven dimensions (three of amplitude, three of phase, and one of time) to a single number, there is inevitable loss of information:
E [x, y, z, t] = E [x, y, z] e jφ[x,y,z]e−jwt . (1.1)
Determining beam quality might seem simple-buy a commercial laser beam analyzer, plug it in, align it, and it will tell you how good your beam is. This seems fine, until you: attempt to use these numbers in calculations, question the assumptions behind commercial products, need to write contractual specifications, or attempt to meet contractual specifications.
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