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where a, b, and c are fitting parameters. Note that if the GRF was modelled by a Gaussian with a width linearly related to D, then fitting parameters a, b, and c can be interpreted as the resolution gradient, the FWHM of the GRF

at the face of the collimator, and the FWHM of the intrinsic resolution, respectively.

In understanding the properties of SPECT reconstructed images, it is often useful to know the behaviour of the GRF in the frequency domain. The geometric transfer function (GTF) is the Fourier Transform of the GRF divided by the geometric efficiency. For a round collimator hole, from Eq. 3 we find that the GTF is given by:

where J1 (x) is the Bessel function of order 0, n is spatial frequency and the other symbols are described above. Note that the GTF in Eq. 7 has the value 1 at n = 0. A sample profile of the GTF for round collimator holes for a LEHR and LEGP collimator at a distance of 10 cm is shown in Figure 4. From this, we find the frequency at which the GTF has its first zero, n0, which is given by:

0 0

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