A useful relationship among the parameter called paraxial estimator [ Opt. Lett. 32, 927 (2007) ] and two parameters concerning the beam quality, the $M^2$ factor, and the beam spot size was derived. This relationship allows one to quantify the paraxiality for a monochromatic laser beam from standard measurements extending the applicability of such an estimator for real beams even if the beam profile shape does not have a closed-form representation. Hence, the paraxial estimator might be a suitable tool for deepening the analysis on the quality of a laser beam.

© 2009 Optical Society of America

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