A method for approximating the inverse error function involved in the determination of the radius of a Gaussian beam is proposed. It is based on a polynomial inversion that can be developed to any desired degree, according to an a priori defined error budget. Analytic expressions are obtained and used to determine the radius of a He–Ne laser beam from intensity measurements experimentally obtained by using the knife edge method. The error and the interval of validity of the approximation are determined for polynomials of different degrees. The analysis of the theoretical and experimental errors is also presented.
© 2013 Optical Society of America
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