A general method for Doppler determination of cylindrically symmetric velocity distributions: An application of Fourier transform Doppler spectroscopy

A general method is developed for determination of cylindrically symmetric velocity distributions from Doppler profile measurements. This method applies Kinsey’s Fourier transform Doppler spectroscopy [J. L. Kinsey, J. Chem. Phys. 66, 2560 (1977)] to distributions arising from photodissociation and uses an orthogonal polynomial expansion to perform the integral transforms analytically. This method is shown to offer an improvement in stability over direct numerical solution of the integral equation and to have applicability to distributions which are not ‘‘separable,’’ that is, which cannot be separated into a product of speed- and angle-dependent factors. The method is applied to experimental measurements of the collisional relaxation of a fast anisotropic distribution of I[2P1/2] atoms in a thermal bath (preceding paper). It is shown that the nascent distribution is separable, but the distribution does not remain separable throughout the relaxation process.