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Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

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

Mario González-Cardel¹, Pedro Arguijo, Rufino Díaz-Uribe

¹Centro de Ciencias Aplicadas y el Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Mexico. mario.gonzalez@ccadet.unam.mx

|June 6, 2013

Summary

This study introduces a polynomial inversion method to approximate the inverse error function, crucial for calculating Gaussian beam radius. This technique offers a flexible approach for precise laser beam radius determination with defined error budgets.

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Area of Science:

Optics and Photonics
Laser Physics
Metrology

Background:

Accurate determination of Gaussian beam radius is essential in various optical applications.
The inverse error function is critical for these calculations but lacks simple analytical solutions.
Existing methods may have limitations in precision or applicability.

Purpose of the Study:

To develop a novel method for approximating the inverse error function.
To enable precise determination of Gaussian beam radius using polynomial inversion.
To analyze the error and validity of the proposed approximation method.

Main Methods:

A polynomial inversion technique was developed to approximate the inverse error function.
Analytic expressions were derived based on the polynomial approximation.
The method was applied to determine the radius of a TEM(oo) He-Ne laser beam using the knife-edge method.
Experimental intensity measurements were utilized.

Main Results:

The proposed method provides an approximation of the inverse error function with controllable accuracy.
Analytic expressions were successfully used to calculate the Gaussian beam radius.
The error and interval of validity were determined for different polynomial degrees.
Theoretical and experimental errors were analyzed, showing good agreement.

Conclusions:

The polynomial inversion method offers a viable and accurate approach for approximating the inverse error function.
This method facilitates precise determination of Gaussian beam radius, particularly for TEM(oo) laser beams.
The study provides a framework for error analysis and defines the validity range of the approximation.