  We provide optimized recursion relations for homodyne tomography. We improve
previous methods by mitigating the divergences intrinsic in the calculation of
the pattern functions used previously, and detail how to implement the data
analysis through Monte Carlo simulations. Our refinements are necessary for the
reconstruction of excited quantum states which populate a high-dimensional
subspace of the electromagnetic field Hilbert space. We also present a Julia
package for the analysis and the reconstruction method.
