KAHIBARO
17.6. Spatial Blurring
Table of Contents
Detector position resolution
In a real detector, the reconstructed interaction position is never perfectly known. Even if a gamma ray deposits all its energy in one crystal or pixel, light spread, sensor granularity, electronic noise, and reconstruction algorithms cause an uncertainty in position. This finite detector position resolution must be modeled in GATE if you want realistic images, realistic coincidence lines of response, or realistic spatial dose scoring linked to detectors.
Within the digitizer chain, spatial blurring acts on hits or singles that already contain an interaction position. The blurring modifies these positions according to a statistical model that represents the detector spatial resolution. You typically apply spatial blurring after energy summation and readout identification, and before applying energy and time thresholds or coincidence sorting. In PET and SPECT simulations, this step directly impacts the apparent sharpness of reconstructed images and the accuracy of measured spatial resolution.
Spatial blurring in GATE is usually modeled as a random shift of the true position, sampled from a chosen distribution such as a Gaussian. If the detector has different resolutions along different axes, you can configure separate standard deviations for each coordinate. The blurred position then replaces the ideal position, and all later analysis, for example energy spectra per detector pixel, detector occupancy maps, or coincidence lines of response, uses this blurred coordinate.
The key quantity that you must specify is the detector position resolution, often given as the full width at half maximum (FWHM) of the point spread function. For a Gaussian model, GATE internally converts this FWHM into the corresponding standard deviation $\sigma$.
For a Gaussian spatial response, the relationship between FWHM and standard deviation is
$$\text{FWHM} = 2 \sqrt{2 \ln 2} \, \sigma \approx 2.355 \, \sigma.$$
If you are given a FWHM in millimeters, always convert it to $\sigma$ correctly before entering it as a Gaussian width, or specify clearly that the parameter is a FWHM if the digitizer option expects it.
In practice, you choose the resolution parameters based on measurements or manufacturer specifications. For example, a PET detector might have a crystal-level intrinsic resolution of 2 mm FWHM transversely and 3 mm FWHM axially. You would therefore configure the spatial blurring digitizer with separate Gaussian widths in $x$, $y$, and $z$ that match these values. For pixelated detectors, you can use a blurring width that is comparable to or smaller than the pixel pitch if you want to mimic sub-pixel reconstruction, or simply reflect the intrinsic size of a pixel if the electronics report only a discrete pixel index.
Spatial blurring can be applied in the detector reference frame or in the global reference frame, depending on how the digitizer is configured. This choice matters especially for ring geometries or complicated detector assemblies where the local detector axes differ from the world axes. Applying blurring in the detector frame often provides a more natural representation of the intrinsic resolution along and across the detector surface.
When interpreting simulation results, always remember that spatial blurring is a statistical process. Two runs of the same simulation with different random seeds will produce slightly different blurred positions, even if the underlying hits are identical. This is expected and is part of the Monte Carlo model of detector response. If you need to reproduce exactly the same blurred distribution, keep the same random seed and the same digitizer configuration.
Finally, be careful not to double count resolution effects. If your geometry already has large pixels or crystals and your analysis later bins data on a coarse grid, an additional large spatial blurring might unrealistically degrade the performance of the detector. A good practice is to tune the blurring parameters such that the simulated point spread function in air or water matches measured spatial resolution data for the real detector.
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