Calibrating photomultiplier tubes beyond their performance envelope

Leading-edge research is done with blunt instruments when no instrument yet exists for an alluring investigation beyond the edge. Ambitious users then push the envelope of existing instruments to venture beyond the edge. Thus, here we calibrate photomultiplier tubes (PMTs) well beyond their performance envelope in order to achieve super-localization with an unmodified commercial two-photon fluorescence excitation microscope (2PM); deep in the scattering tissue of the mouse brain in vivo; and fast enough to enable nanoscale tracking of particles, capillary walls, and red blood cells [Kutuzov, Lauritzen, and Flyvbjerg (unpublished) (2025)]. This PMT-calibration comprises steps of generic interest: (i) characterizations of a time-dependent bias in the dark noise; (ii) elimination of this bias with a quick-and-noisy protocol; (iii) elimination of this bias with a noiseless protocol when the bias is periodic; (iv) characterization of residual dark output; (v) mathematical characterization of PMT-output for single-photoelectron input; and (vi) mathematical characterization of PMT-output for a given expected number of photoelectrons in input. The extreme attention to details in this calibration of the instrument and in our characterization of its output is necessary in order to squeeze optimal localization accuracy and precision out of quickly recorded-and hence faint-images that are contaminated with irrelevant details about the instrument's design because we use the instrument beyond its performance envelope.