Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Accounting for these features is often critical in quantitatively interpreting microscopy images, especially those gathering information at scales on par with or smaller than light's emission wavelength. Here the optics responsible for generating fluorescent images, fluorophore properties, and microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily probabilistic modeling tools imposed by the stochastic nature of light and measurement, are reviewed.

One of the fundamental limits of classical optical microscopy is the diffraction limit of optical resolution. It results from the finite bandwidth of the optical transfer function (or OTF) of an optical microscope, which restricts the maximum spatial frequencies that are transmitted by a microscope. However, given the frequency support of the OTF, which is fully determined by the used optical hardware, an open and unsolved question is what is the optimal amplitude and phase distribution of spatial frequencies across this support that delivers the "sharpest"possible image. In this paper, we will answer this question and present a general rule how to find the optimal OTF for any given imaging system. We discuss our result in the context of optical microscopy, by considering in particular the cases of wide-field microscopy, confocal image scanning microscopy (ISM), 4pi microscopy, and structured illumination microscopy (SIM). Our results are important for finding optimal deconvolution algorithms for microscopy images, and we demonstrate this experimentally on the example of ISM. They can also serve as a guideline for designing optical systems that deliver best possible images, and can be easily generalized to nonoptical imaging such as telescopic imaging, ultrasound imaging, or magnetic resonance imaging.

Single Molecule Localization Microscopy has become one of the most successful and widely applied methods of Super‐resolution Fluorescence Microscopy. Its achievable resolution strongly depends on the number of detectable photons from a single molecule until photobleaching. By cooling a sample from room temperature down to liquid nitrogen temperatures, the photostability of dyes can be enhanced by more than 100 fold, which results in an improvement in localization precision greater than 10 times. Here, we investigate a variety of fluorescent dyes in the red spectral region, and we find an average photon yield between 3.5 ⋅ 106 to 11 ⋅ 106 photons before bleaching at liquid nitrogen temperatures, corresponding to a theoretical localization precision around 0.1 nm.