Effect of optical aperture on the derivation of volume emission coefficient from side-on intensity measurements of cycling cylindrically symmetrical sources

Abstract

An integral equation, analogous to the Abel integral equation for the derivation of volume emission coefficient from side-on observations, is developed which takes account of finite optical aperture. This integral equation is partially inverted and the solution is used to examine the effect of finite optical aperture for two simple distributions of volume emission coefficient. It appears that the error arising from the effect of finite optical aperture is negligible in most practical cases. One important and interesting result that emerges from this treatment is that the volume emission coefficient derived on the axis ( r=0) is independent of optical aperture and is therefore correct whatever the aperture.