## 2 Key Factors Contributing to Spatial Resolution in PET Imaging
### Design Strategies for Ultra-High Spatial Resolution PET Detectors  
Although it is challenging to mitigate the spatial resolution degradations caused by inherent factors such as the positron range and non-collinearity, other factors can be refined, and an optimized solution can be achieved through advanced detector design and readout strategies. A common approach to improve the spatial resolution is by reducing  
Figure 3: Illustration of the influence of detector element width on spatial resolution in a PET scanner. The theoretical resolution limit is \(\frac{d}{2}\) FWHM, defining the smallest separable distance between two point sources. Reducing detector width improves resolution but presents engineering challenges.  
Figure 2: The diagram illustrates the concept of positron range. A positron (\(e^{+}\)) is emitted from its originating radionuclide with a range of kinetic energies (e.g., for \({}^{18}\)F, from 0 to 635 keV), causing it to traverse a range of distances prior to annihilation with an electron (\(e^{-}\)). This annihilation produces two 511-keV photons emitted in opposite directions. Owing to the distance the positron covers, the annihilation event occurs away from the initial location of the positron emission. The resulting variations in annihilation event positioning over all positron decay events contribute to the spatial resolution in the final PET images.  
the size of the scintillation crystals [18; 29; 30]. Although employing narrower scintillation crystals improves spatial resolution, this approach introduces challenges such as more photodetector channels, complex readout configurations, and increased inter-crystal scatter. Optical and electronic multiplexing can simplify PET detector designs by reducing readout channels, lowering costs, and simplifying electronics. However, these methods complicate the data decoding process, potentially affecting the accuracy of energy, timing, and spatial information.  
Additionally, scatter within the crystal and photon penetration in the detectors further contribute to spatial resolution uncertainties [31]. The absence of depth-of-interaction (DOI) information for annihilation photons makes it difficult to precisely localize photon interactions within the crystals. This uncertainty can lead to image blurring, ultimately degrading the system's spatial resolution.  
Moreover, as the crystal element width decreases, the efficiency for collection of scintillating light photons reduces, and the variations in the light signals increase, further complicating the extraction of a sufficient number of photons for a high detection signal-to-noise ratio (SNR) [30].  
Thus, a fundamental design principle for high-resolution PET detectors is to employ a scintillation array with substantial light yield. Precise 3D localization of events within a scintillation crystal, especially for off-center interactions, can also augment spatial resolution. The one-to-one coupling approach, assigning a distinct photodetector to each crystal element in an array, can enhance the signal-to-noise ratio compared to multiplexing-based approaches, potentially boosting spatial resolution. However, this design necessitates an extensive array of photodetectors, significantly elevating costs and readout circuit complexity, introducing design challenges at the front-end and back-end readout electronics design. Therefore, a balanced degree of optical multiplexing in the scintillation arrays and electronic multiplexing in the readout circuit simplify high-resolution PET system design.