# Spatial Resolution

### General

The spatial resolution of a system is that distance, which is between two points that are just separable after the image reconstruction. There is another definition of spatial resolution. It can be expressed by the FWHM (full width at half-maximum) and FWTM (full width at tenth-maximum) of the PSF (point spread functions). Point sources are used in this measure base of the second definition. The point sources are suspended in air, so there is no scatter. No filter or smoothing is used during the measure.

### Purpose

The purpose of the measure is to determine the width of PSF of a compact radioactive source in reconstructed image. The width of the PSF is measured by its FWHM and FWTM.

### Method

The spatial resolution of every system is measured in the transverse slice. The transverse FOV (field of view) and the size of the image matrix characterize the pixel size. It’s necessary to have a source that is at least 3 pixels big so the width of the PSF can be measured.

The radionuclide for this measurement shall be 18F. The activity must be less than that at which either the percent dead time losses exceed 5%. or the random coincidence rate exceeds 5% of the total event rate. These conditions determine the activity of the point source around 1 MBq. (IAEA).

2. Source distribution
The point source is a small quantity of fluid with concentrated activity inside a glass capillary. The inside diameter of the capillary should be 1 mm or less, the outside diameter should be less than 2 mm. The axial extent should be less than 1 mm. The sources shall be placed in three-three positions parallel to the long axis of the tomograph as follows:

• x=0 cm; y=1 cm
• x=0 cm; y=10 cm
• x=10 cm; y=0cm

The 3 point sources shall be placed at the center of the axial FOV, than one-fourth of the axial FOV from the center of the FOV. Figure 1.: Position of source for spatial resolution measurement

3. Data collection
Measurements shall be collected at all six point mentioned before. Minimum one hundred thousand counts shall be acquired in each acquisition.

4. Data Processing
Filtered backprojection shall be used for the reconstruction. No smoothing or apodization shall be applied.

### Analysis

The FWHM and FWTM values of all six measured points shall be calculated. The slice with the highest maximum value shall be chosen from the slices that show the point sources. The calculation based on linear interpolation. The peak value of the PSF shall be calculated from the peak pixel value and the two neighbors by fitting a parabola. The maximum value of the parabola is the peak value of the PSF. The pixel-coordinates of the half-value and the tenth-value shall be calculated by linear interpolation. The value can be determined from the peak value of PSF. The half (tenth)-value coordinate must be calculated by linear interpolation from the two neighboring pixel value, and from their coordinates. From the half (tenth)-value coordinates the FWHM and FWTM of the PSF can be derived.

### Report

The FWHM and FWTM values shall be calculated for all the six points for each three dimension. The reported value shall be averaged over both axial positions. The formulas for the calculations are in the figure 2-3. RES means resolution; this can be the FWHM or the FWTM of the PSF either.