We designed three caps to analyze. The three caps feature various densities and extents.
We then simulated the system performance for each of these caps and collected resolution data. Intuitively, we would expect smaller caps with fewer sources or detectors to have poorer resolution than caps with more, and we expected caps that cover a small area to perform worse than caps that cover a more extensive region of the head surface.
The results of the simulation are summarized in the plots below.
The resolution trends across tissue depth describe the system performance of the three caps. The PSF full width at half maximum for each cap increases with increasing depth. This confirms our intuitions about the nature of the imaging system – we would expect that at greater depths, the imaging quality is poorer. A larger point-spread function is harder to distinguish from other PSFs, limiting the precision of the image reconstruction.
Note that the largest cap (the 48-by-48 full-head cap) performs the best, i.e. has the smallest PSFs for the majority of tissue depths. As expected, the full-head cap with fewer sources and detectors (the 16-by-16 full-head) performs next-best. The system with the largest PSFs for the majority of depths is the least extensive cap, the 16-by-16 small patch on top of the pigeon head.
The localization error trends also provides valuable data that aligns with out intuition. Localization error increases with higher tissue depth for all cap designs. The 48-by-48 full head performs the best, with the lowest overall localization errors, followed by the 16-by-16 full head, and the 16-by-16 patch cap produces the largest overall localization error.
The SNR results display a different trend. The highest SNR is found from the 16-by-16 full head cap. The 48-by-48 cap has lower SNR, with the 16-by-16 patch cap having the lowest SNR. Optimizing SNR for each cap depends on a process known as regularization, which is a parameter that determines how the system reconstructs the tissue image. Choosing the correct regularization is a careful balance between sensitivity to signal and amplification of noise and must be tuned for each cap. For the data displayed above, we used the same regularization for each cap for comparison purposes, explaining the apparent discrepancy.