Optimization of beam shaping and error quantification of calibration approach using E-FISHG based electric field measurements

Electric-field measurement based on the electric-field-induced second-harmonic generation (E-FISHG) method is a promising tool for a noncontact field measurement in plasmas and gases. For the E-FISHG method, a probing laser beam is focused at the measurement target by a lens, and the signals integrated along the laser path are acquired. Although the signal is frequently calibrated under uniform electric fields, the yielded value is erroneous if one does not consider the difference in the electric-field-profiles between the calibration and measurement. In this paper, we review the calibration and measurement targets of relevant studies, assess the error in the conventional method for the streamer discharge measurement, and give guidelines on which calibration approach to use depending on the electric field profile to be measured. Our approach uses cylindrical-to-cylindrical electrodes and multipoint measurement corresponding to the target length along the optical path, gas, and pressure.