Spatial resolution refers to the minimum limit of the system's spatial representation of an object due to the measurement process. It is the limiting distance in distinguishing juxtaposed point sources. Spatial resolution is usually characterized by measuring the width of the profile obtained when an object much smaller than the anticipated resolution of the system (less than half) is imaged. This blurring is referred to as the spread function. Common methods to measure this in emission tomography are to image a point source (giving a point spread function (PSF)), or, more usually, a line source (line spread function (LSF)) of radioactivity. The resolution is usually expressed as the full width at half maximum (FWHM) of the profile. A Gaussian function is often used as an approximation to this profile. The standard deviation is related to the FWHM by the following relationship:
where a is the standard deviation of the fitted Gaussian function. There are many factors that influence the resolution in a PET reconstruction. These include:
(i) non-zero positron range after radionuclide decay,
(ii) non-collinearity of the annihilation photons due to residual momentum of the positron,
(iii) distance between the detectors,
(iv) width of the detectors,
(v) stopping power of the scintillation detector,
(vi) incident angle of the photon on the detector,
(vii) the depth of interaction of the photon in the detector,
(viii) number of angular samples, and
(ix) reconstruction parameters (matrix size, windowing of the reconstruction filter, etc.).
Resolution in PET is usually specified separately in transaxial and axial directions, as the sampling is not necessarily the same in some PET systems. In general, ring PET systems are highly oversampled transaxially, while the axial sampling is only sufficient to realize the intrinsic resolution of the detectors. The in-plane over-sampling is advantageous because it partially offsets the low photon flux from the center of the emitting object due to attenuation. Transaxial resolution is often subdivided into radial (FWHMr) and tangential (FWHMt) components for measurements offset from the central axis of the camera, as these vary in a ring tomograph due to differential detector penetration at different locations in the x-y plane (see Fig. 3.16). Due
Figure 3.16. Transaxial resolution is separated into tangential and radial components. As the source of radioactivity is moved off-axis there is a greater chance that the energy absorbed in the scintillator will be spread over a number of detector elements. This uncertainty in localizing the photon interaction to one discrete detector degrades the spatial resolution in this direction.
to the limited, discrete sampling in the axial direction with block detector tomographs (one sample per plane), it is inappropriate to measure axial resolution (FWHMz) on such systems from profiles of reconstructed data as there are insufficient sampling points with which it can be accurately estimated (only one point per plane). However, measurement of axial slice sensitivity of a point source as it passes in small steps through a single slice can be shown to be equivalent to 2D axial resolution, and thus can be utilized to overcome the limited axial sampling to measure the axial resolution.
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