A deep learning approach for electric field profile reconstruction based on the E-FISH method

Abstract Electric field induced second harmonic generation (E-FISH) is a laser-based method that has become increasingly popular for measuring electric fields in non-equilibrium plasmas. A key limitation of this diagnostic is that the signal magnitude tends to be influenced by regions beyond the focal volume, and more generally by the entire electric field profile along the probe beam path. One approach to resolving this issue, is to make multiple measurements of the E-FISH signal by translating the laser beam focus with respect to the electric field distribution. The objective is to use this resulting signal profile to reconstruct the unknown electric field profile. Termed here as the inverse ‘E-FISH problem’, this work describes a machine learning (ML) approach to perform the reconstruction in a systematic and efficient manner. Two commonly used deep learning (DL) algorithms—artificial neural networks and convolutional neural networks are applied to this inverse problem, with both producing promising results. These DL networks accept an E-FISH signal profile described by a stipulated number of data points (sampled along the beam path), and provides the unknown electric field profile along the direction of the laser beam as an output. Excellent predictive accuracy and good overall generalizability is obtained on test data, extending to cases where the input profile is formed by a smaller sub-sample of data points or when noise is artificially introduced. More importantly, good performance is maintained when the model is applied to experimental data. In its present form however, the model is applicable only to a large subset of symmetric profiles typical of canonical electrode geometries, and does not generalize to asymmetric (as well as antisymmetric) distributions, or those of an entirely random nature. However, with the appropriate training, we expect that these issues can be overcome, thereby extending the model’s applicability. This supports the continued use of ML methods for solving inverse problems of this nature, and to the field of non-equilibrium and low temperature plasmas in general.