A fast Abel inversion algorithm

The inversion formula of Abel’s integral equation has numerous applications in many scientific fields. In practice, its input is experimentally obtained data that contains inevitable measurement noise. Avoiding error amplification is, therefore, a main concern of every algorithm. We present a new fast Abel inversion algorithm that, in contrast to other methods, requires a negligible number of transcendental operations. Storage requirements are reduced as well. The advantage of the algorithm is especially noticeable when multiple data sets need to be inverted. As demonstrated in the paper, the new algorithm attenuates the input errors.