Beamfit: Algorithmic Wavefront Reconstruction of Laser Beams Using Multiple Intensity Images and Laguerre- or Hermite-Gaussian Basis

Wavefront errors are a common artifact in laser light generation and imaging. They can be described as an aberration from the spherical wavefront of an ideal Gaussian beam by combinations of higher-order Hermite- or Laguerre-Gaussian terms. Here, we present an algorithm called Beamfit to estimate the mode composition from a series of CCD images taken over the Rayleigh range of a laser beam. The algorithm uses a user-defined set of Hermite- or Laguerre-Gaussian modes as the basis of its theoretical model. A novel method reduces the number of calculations needed to compute the model's intensity profiles. For a given model containing $N$ modes, the number of Hermite-Gaussian complex amplitudes needed to calculate are reduced from orders of $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ and replaced by simple multiplications. Additionally, non-beam parameters are pre-calculated to further reduce the search space dimension and its resulting calculation time. It is planned to release the Beamfit software to the public under an open-source license.