A simplified approach for modulation transfer function determinations in computed tomography

In order to determine the modulation transfer functions (MTF's) for x-ray computed tomography (CT) scanners, a measurement must be performed to obtain either the point spread function (PSF) or the line spread function (LSF). Thereafter, the usual procedure is to interpolate between the measured points and to determine the Fourier transforms numerically in order to obtain the MTF. Since this must usually be done many times to evaluate various reconstruction kernels and scan modalities, the process is tedious. Fortunately, it can be greatly simplified by utilizing a mathematical function to describe the PSF or LSF. Measured data for five CT scanners indicates that the PSF can usually be described by a Gaussian function. Hence, the MTF can be written in a generalized form eliminating the necessity of performing Fourier transformations each time. The MTF is determined directly from a single performance characteristic related to the full width at half maximum. The accuracy of the approach is compared with detailed MTF calculations for five CT scanners and it is shown to agree favorably with this data.