Experimental determination of the convolution kernel for the study of the spatial response of a detector

One of the most important parameters in the characterization of a detector is its spatial convolution kernel. This kernel contains all of the information about the influence that the detector size has on the measured beam profile. In this paper we present an experimental method for the determination of the spatial convolution kernel for commonly used detectors that are employed in the x-ray profile measurement: film + densitometer, diode, and ionization minichamber. Our work is based on first assuming a step function pattern on a photographic film is known and is a perfect step function. The kernel of the densitometer system was then derived from the deconvolution of the scanned profile to the step function. Next a film was exposed to a penumbra area of an x-ray beam from a linac. The film was scanned using the same densitometer. The "real profile" that emerges from a linear accelerator was derived by the deconvolution of the scanned profile using the now known kernel of the film densitometer. Under the same irradiation condition the x-ray profile was measured with other detectors and with this information we obtained the convolution kernels for these detectors by solving numerically their basic convolution integrals. The results show that the Gaussian convolution kernel is the most consistent with the measurements. The best numerical values for the FWHM of the kernels are 1.1 mm, 2.2 mm, and 5.4 mm for densitometer, diode, and minichamber, respectively.