Fig. 2: Comparative analysis of resolving power across four imaging modalities (wide-field, confocal, two-beam SIM, and ISM) based on information density I_d.

a Resolving power, indicated by \({I}_{d}\) from four imaging modalities for the case of planar specimens (no background). The resolvability threshold (\({I}_{d}=10{ra}{d}^{-2}\cdot {\mu m}^{-2}\)) marks the applied resolving criterion. Colored dashed lines correspond to the reciprocal of the information-based resolution (IbR) for each modality. b Resolving power in terms of information density \({I}_{d}\) in the case of volumetric specimens (30 μm thickness). c Visualize noisy images of an object at frequency \(\frac{1.85{NA}}{\lambda }\), slightly lower than the diffraction limit. The raw images in the SIM are the images of shifted frequency of the original sinusoidal grating object, as the structured illumination frequency is at optical transfer function (OTF) boundary, which would not appear in the image. d Influence of volume thickness on \({I}_{d}\) for each modality at frequency \(\frac{1.85{NA}}{\lambda }\). e Relationship between \({I}_{d}\) and photon count for an object at frequency \(\frac{1.85{NA}}{\lambda }\) on a logarithmic scale in planar specimen. f Emitted photons per area required for different sinusoidal grating structures to meet the resolving criterion (\({I}_{d}=10\,{ra}{d}^{-2}\cdot {\mu m}^{-2}\)) in planar specimen, ranging from zero to one hundred million photons per μm². Photon collection efficiencies were considered based on 4Pi solid angle emission, objective NA and the pinhole rejection, if present. The above simulation had photon collecting efficiency 32.05% for wide-field and SIM microscopy, 10.77% for confocal microscopy with a 0.5 AU pinhole, and 24.68% for ISM with a 1.3 AU FOV.