On the methods for estimating beam parameters of super-imposed Hermite-Gaussian modes

In many applications, it is necessary to evaluate the beam parameters of the basis Hermite-Gaussian functions which are used to decompose a given laser beam. This paper compares two methods for estimating the beam parameters, both of which are based on intensity measurement. One is an exact optimization method, which can find the optimal beam parameters but has high computational demands. The other is a moment method which requires less computation but only yields approximations to the optimal beam parameters and whose application is limited to beams close to Gaussian or a mixture of incoherent Hermite-Gaussian modes. It is found that the moment method can provide sufficiently accurate results in certain circumstances.