Determination of penumbral widths from ion chamber measurements

We have investigated methods of reconstructing beam profiles in the penumbral region using a set of axially symmetric chambers, differing only in the detector radius. In principal, the transfer functions, or kernels, of such chambers should be functions of radius only. Three chambers of radii 0.297, 0.556, and 0.714 cm have been used. The transfer functions of the chambers can be determined by deconvolving the profiles measured with each detector with the PPMC profile. The results indicate that the transfer functions can be parametrized accurately as a Gaussian cutoff at 1.75(r), with (r) the average radius of the chamber. Deconvolution of the measured profiles with the transfer functions yields a profile that agrees with the PPMC profile to +/- 0.5 mm over the 20-80% penumbra.