Decomposition of experimentally measured transverse intensity profiles into set of high-order gaussians

[rob-shalloo]

One nice way to incorporate experimentally measured transverse intensity profiles (such as focal spot images, near field profiles or anything in between) would be to decompose it into a set of Hermite-Gaussian modes. These higher-order gaussian modes are a natural choice for data taken with a camera.

The process envisaged to get the data in would be:

• take an experimental image provided by the user
• Perform some background subtraction (or leave that up to the user)
• Perform a hermite gauss decomposition to get a set of mode coefficients
• Save either an xyz grid of data or perhaps just keep the coefficients? Alternatively, the Hermite Gauss coefficients could be converted to Laguerre-Gauss coefficients for implementing in and R,theta,Z grid.

If the data is stored as a series of coefficients, then you have effectively an analytic representation of the experimental pulse. This could be useful for speeding up propagation.

This style of method has already been implemented by LPGP, CNRS to get real pulses into FBPIC (https://journals.aps.org/prab/pdf/10.1103/PhysRevAccelBeams.25.101301) and worked quite well.

Something along these lines would be a powerful addition to LASY.

[MaxThevenet]

Great! Sounds good to me. And yes, we could probably have the option to just store the coefficient for a fast propagator. If the user needs to specify spatio-temporal couplings before propagating, I am not sure the profiles would still be fully analytic so we might need the general propagator, but that is no problem, it will be around anyway.

[MaxThevenet]

Probably after (or coordinated with) #58.