Gaussian beam radius measurement with a knife-edge: a polynomial approximation to the inverse error function

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 us...

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Bibliographic Details
Published in:Applied optics (2004) 2013-06, Vol.52 (16), p.3849-3855
Main Authors: González-Cardel, Mario, Arguijo, Pedro, Díaz-Uribe, Rufino
Format: Article
Language:English
Subjects:
Approximation
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Summary: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 TEM(oo) 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.
ISSN:1559-128X
2155-3165
DOI:10.1364/AO.52.003849