The modulation transfer function (MTF) of an imaging system may be used as a figure of merit to assess its geometrical resolution. As such it is often derived from the point spread function (PSF) through a Fourier transformation, or through a FFT in case of digital images. Using the special features of the convolution-backprojection algorithm and making some simplifying assumptions about the number of rays, it is shown that the desired MTF is also obtainable without a Fourier transformation of the PSF, different shapes and sizes of the beam-profile are then analyzed, and finally it is shown that calculated and measured MTF functions are in good agreement. The effects of aliasing on the cutoff frequency are also discussed.