Abstract
New graphical methods using the Delano y-ybar diagram are shown to yield simple alternative derivations of the M2 beam quality factor for Gaussian-like laser beams. Using M2 as a scaler for the Lagrange optical invariant, powerful methods of interpreting and calculating the beam factor become apparent. Elegant methods of determining M2 using strategic beam sample locations are also developed, taking advantage of the property that a freely propagating beam trace in the Gaussian beam y-ybar plane is a straight line. Application to non-Gaussian beams is explored.
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