Improved Abel Inversion Algorithm for Schlieren Based on Gray-scale Compensation

Abstract The Abel inversion for schlieren is an important mathematical tool for inverting temperature fields of long sparks. In this paper, an improved algorithm based on grey-scale compensation (GSC) is proposed for the Abel inversion, which has a large error in inverting the temperature field of the discharge channel. The algorithm constructs the temperature value of the discharge channel and continuously adjusts the temperature value until the grey value change obtained by the Abel forward transform of the temperature value is basically the same as the measured grey value change. The corresponding temperature value is the result of the Abel inverse transform. The algorithm is simple and has the ability to reduce noise interference. Meanwhile, the feasibility of this algorithm provides a direction for further improving the accuracy of the algorithm.