The use of deconvolution and total least squares in recovering a radiation detector line spread function

We present a method for obtaining the line spread function (LSF) of any radiation detector from measured data. The problem of finding a LSF is essentially a discrete deconvolution from known values of the input (Monte Carlo generated data) and the output (measured data) which can be put into matrix form. We applied the total least squares (TLS) method which is particularly useful when there are errors in both the input and output data. Results from computer simulation as well as from actual data are shown. In a practical application, however, our technique is currently limited by the ability of the Monte Carlo data to simulate correctly the inherent data from the head of the linear accelerator (linac). To overcome this difficulty we have solved by deconvolution and TLS for a more realistic inherent beam profile of our linac using the information from both profile data as measured with film and the film densitometer response function. The LSF of the densitometer was estimated with a simple method of direct measurement of a slit image and a full width at half maximum (FWHM) of 0.997 mm was recorded. Additionally, using the knowledge of this realistic inherent profile of the linac, a blurring function representing the finite source size effect missing in our current Monte Carlo profile simulation was determined. Finally, with the realistic inherent beam profile we have applied the deconvolution and TLS method to find a LSF for the Markus chamber and found a resulting FWHM of 5.39 mm. The TLS approach for deconvolving can find a useful application for both finding the LSF and correcting for the detector size effect once its LSF is known. This type of correction is required when a high spatial resolution is needed (e.g., in small field off-axis measurements). Convolved and measured profiles are also presented to illustrate the effect of the blurring due to different LSFs.