Inversion of velocity map ion images using iterative regularization and cross validation

Abstract

Two methods for improved inversion of velocity map images are presented. Both schemes use two-dimensional basis functions to perform the iteratively regularized inversion of the imaging equation in matrix form. The quality of the reconstructions is improved by taking into account the constraints that are derived from prior knowledge about the experimental data, such as non-negativity and noise statistics, using (i) the projected Landweber [Am. J. Math. 73, 615 (1951)] and (ii) the Richardson-Lucy [J. Opt. Soc. Am. 62, 55 (1972); Astron. J. 79, 745 (1974)] algorithms. It is shown that the optimum iteration count, which plays the role of a regularization parameter, can be determined by partitioning the image into quarters or halves and a subsequent cross validation of the inversion results. The methods are tested with various synthetic velocity map images and with velocity map images of the H-atom fragments produced in the photodissociation of HBr at λ=243.1nm using a (2+1) resonantly enhanced multiphoton ionization (REMPI) detection scheme. The versatility of the method, which is only determined by the choice of basis functions, is exploited to take into account the photoelectron recoil that leads to a splitting and broadening of the velocity distribution in the two product channels, and to successfully reconstruct the deconvolved velocity distribution. The methods can also be applied to the cases where higher order terms in the Legendre expansion of the angular distribution are present.