Abstract
Single-photon avalanche diode (SPAD) arrays can be used for single-molecule localization microscopy (SMLM) because of their high frame rate and lack of readout noise. SPAD arrays have a binary frame output, which means photon arrivals should be described as a binomial process rather than a Poissonian process. Consequentially, the theoretical minimum uncertainty of the localizations is not accurately predicted by the Poissonian Cramér-Rao lower bound (CRLB). Here, we derive a binomial CRLB and benchmark it using simulated and experimental data. We show that if the expected photon count is larger than one for all pixels within one standard deviation of a Gaussian point spread function, the binomial CRLB gives a 46% higher theoretical uncertainty than the Poissonian CRLB. For typical SMLM photon fluxes, where no saturation occurs, the binomial CRLB predicts the same uncertainty as the Poissonian CRLB. Therefore, the binomial CRLB can be used to predict and benchmark localization uncertainty for SMLM with SPAD arrays for all practical emitter intensities.
Highlights
Ever since microscopes were invented in the 17th century, scientists have been developing increasingly advanced methods to improve their capabilities [1]
We show that if the expected photon count is larger than one for all pixels within one standard deviation of a Gaussian point spread function, the binomial Cramér-Rao lower bound (CRLB) gives a 46% higher theoretical uncertainty than the Poissonian CRLB
single-photon avalanche diode (SPAD) arrays are used for single-molecule localization microscopy (SMLM) [2,3,4], single-molecule tracking [5], and fluorescence lifetime imaging microscopy (FLIM) [6, 7]
Summary
Ever since microscopes were invented in the 17th century, scientists have been developing increasingly advanced methods to improve their capabilities [1]. Innovation in the image sensors used in microscopy such as the single-photon avalanche diode (SPAD) are important for this thesis. Where SMLM uses uniform excitation, modulation-enhanced single molecule localization microscopy (meSMLM) introduces patterned excitation to increase the information content in the emitted signal. The information of the SMLM processing and the illumination pattern is combined to get an improved location estimate This gives a higher resolution than SMLM because instead of fitting the photon distribution in a frame with a regular Gaussian distribution, a weighted Gaussian distribution is used. We focus on SPADs that measure one photon maximum per detection cycle, giving a binary output. [10]
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