Spectroscopic single-molecule localization microscopy (sSMLM) is a novel super-resolution imaging technology, which simultaneously records the nanoscopic location and the corresponding full emission spectrum of every stochastic single-molecule emission event. This spectroscopic imaging capability of sSMLM necessitates the establishment of a theoretical foundation of the newly introduced spectral precision and to guide the system design and optimization. Based on numerical simulation and analytical solution, we introduced such a theoretical model to analyze spectral precision by considering the main system parameters, including signal and background shot noises, readout noise, and the spectral calibration procedure. Using this model, we demonstrated the delicate balance among these parameters in achieving the optimal spectral precision and discovered that the best spectral precision can only be achieved at a particular system spectral dispersion. For example, with a given signal of 3000 photons and a readout noise of 2 e-, a system spectral dispersion of 1.6 nm/pixel is required for sSMLM to achieve the highest spectral precision of 1.31 nm.
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