Spatial Resolution of the Volume Emission Coefficient in Strongly Self-Absorbing Sources of Cylindrical Symmetry

Abstract

It is shown that the equations relating the radial profiles of the volume emission and absorption coefficients to the transmission and emitted intensity profiles in self-absorbing cylindrically symmetric sources, can be written in such a way that the problem of spatially resolving the volume emission coefficient gives rise to a Volterra integral equation of the second kind in a standard form. The theory of equations of this type is invoked to show the formal convergence of an iterative solution to the problem, subject only to a finite transmission and bounded slope to the absorption coefficient. A prescription for applying this iterative procedure is given that involves a series of numerical integrations and Abel inversions, and the convergence of some numerical solutions is demonstrated.

Generalized and attenuated radon transforms: restorative approach to the numerical inversion

“…where the dzk(x) are described by (7). Note that the Fourier transformation of dZk(r,O) is equal to:…”

Gas and liquid phases interaction at the FeO�Cr2O3 cathode of a direct-current arc discharge

“…Op z= L =0 (9) Also, one can write at any z value p=(n, + nj)kT (10) In Eqs. (6)- (10), and in the descriptive text, the indices i, j, and e designate the ionic, atomic, and electronic species, respectively, n is the species concentration, D is the diffusivity, ~ is the mobility, v,.…”

Cormack-type inversion of attenuated Radon transform

“…Historically, the circular harmonic decomposition (CHD) algorithm was first used by Cormack to study the problem of reconstruction from projections [9]. The Cormack method is widely used in technical experiments and has proved to be very suitable for reconstructing axially symmetric and nearly axially symmetrical objects [10,11]. Another application of CHD is connected to the solution of numerical inversion of the exterior Radon transform [12,13].…”