A 2-D electrostatic Lagrangian two-fluid code for the direct inversion of deflectometry data

Deflectometry is a diagnostic that relies on the measurement of intensity modulations caused by the deflection of probe rays in an object, in the absence of attenuation. The intensity modulations can be related to a line-integrated transverse force in the object, provided that the total deflection angle is small (<< 1 rad or 57.3 degs). Examples of deflectometry include proton radiography, where the force is the Lorentz force, and shadowgraphy, where the force is the refractive index gradient. Direct inversion provides a solution for the line-integrated transverse force given the measured intensity and the source intensity (the measured intensity in the absence of deflection). If ray trajectories do not cross then the solution is unique, otherwise there is no unique solution and direct inversion gives the minimum deflection solution. The provided 2-D electrostatic Lagrangian two-fluid code achieves direct inversion by treating the measured or source intensity as an initial electron distribution and the other as a fixed ion distribution. Electrostatic forces cause the electron distribution to evolve to the ion distribution. The displacement of the electrons from their initial to final positions determines the line-integrated transverse force. Oscillations are avoided by critically- or over-damping the electrons by applying a drag term with a collision frequency of twice the electron plasma frequency or greater. The total energy of the system, electrostatic plus kinetic, goes to zero in equilibrium since drag is removing energy from the system, providing a simple convergence criterion. The code is written as a Matlab function and Matlab is required to run it. The parallel processing toolbox would be useful. The code does not work for large intensity modulations and is far from being optimal.