Design strategy for a dual-wedge prism imaging spectrometer in spectroscopic nanoscopy.

Spectroscopic single-molecule localization microscopy (sSMLM, or spectroscopic nanoscopy) has been established as a key tool in functional super-resolution imaging by providing spatial and spectral information of single molecules at nanoscale resolution. A recently developed dual-wedge prism (DWP) imaging spectrometer, a monolithic optical component, has broadened the accessibility of sSMLM with an improved imaging resolution of more than 40%. It also improved the system reliability by reducing the number of discrete optical components. However, achieving its optimal performance requires the comprehensive understanding of the underlying constraints of the key system parameters, such as the refractive index of the DWP, spectral dispersion (SD), axial separation for three-dimensional (3D) biplane reconstruction, and the overall dimensional constraints. In this work, we present a generalized design principle for the DWP imaging spectrometer. Specifically, we develop the theoretical framework capturing the influence of the primary design parameters, including the achievable SD and localization performance, for different design cases. It further establishes the workflow to design and optimize the DWP imaging spectrometer for better multi-color functional imaging. This will give practical guidance for users to easily design the DWP imaging spectrometer, allowing for straightforward 3D sSMLM implementation.