Conditions for Correct Measurements of the Laser-Beam Characteristics Based on Determination of Initial Moments of the Spatial Intensity Distribution

In the work, we study the convergence conditions for initial moments of the spatial distribution of the laser-beam intensity. These moments serve as the basis for determining the beam characteristics (the width, the divergence angle, and the propagation ratio M²) when using modern standards such as the ISO 11146:2005 standard and the ISO 11146-2008 state standard of Russia. On the basis of the parabolic equation of quasioptics in the Fraunhofer approximation, it is shown that the existing method for measuring the above-mentioned parameters, which does not take into account the finite size of the radiation aperture, can lead to divergence of the measurement results. Special attention is paid to the fact that this can also take place for continuous intensity distributions and, therefore, the replacement of the finite aperture by the infinite one is inadmissible when determining the initial spatial moments in the general case. It is proved that to obtain correct results of the measurements of the second moments, the spatial distribution of the amplitude at the aperture edge should be equal to zero. An example confirming the presence of the problem and the basic conclusions of this work is considered.