Recovering plasma emissivity using optical fibers with large acceptance angle

Summary form only given. The problem of determining the plasma emissivity from optical emission spectroscopy is usually formulated in terms of Able´s equation, in which the measured plasma intensity I(y) along a horizontal line is related to the (cylindrically symmetric) emissivity by I=A/spl epsiv/ where A is the integral operator A/spl epsiv/=/spl int//sub /spl nu///sup R/ /spl epsiv/(r)r(r/sup 2/-y/sup 2/)/sup -1/2/ dr. The use of this model requires a rather careful experimental setup in which light emitted only along chords across the plasma is collected; the chords are parameterized by the perpendicular distance y from a fixed plasma diameter to construct I(y) and the known inverse operator A/sup -1/ used, in principle, to find /spl epsiv/=A/sup -1/ I. There are, however, two difficulties with this procedure: the operator A/sup -1/ is discontinuous (ill-posed) allowing the possibility that even small errors in I (experimental noise) can be magnified into large errors in /spl epsiv/; and the experiment requires a very precise and inherently low-light optical setup. The first problem is fundamental and requires careful construction of the inverse, but the second might be side stepped by basing the experiment on a different mathematical model.