Fig. 8: Smart microscopy approaches to improve counting performance.

a The depth-dependent probability function D(z) of an imaging system is shown in blue. The cell’s cross-sectional density is given in red as a(z). The overlapping area between these two profiles (given by the cross-correlation a(z) ★ D(z)) gives an estimate of the fraction of the molecules which will be observed. To maximise the number of molecules detected, one can shift the objective by an optimal amount, given by δz_optimal, which is where the two functions have maximum overlap. b A schematic showing a cell in the optimal focal position relative to the detection probability function, thus detecting the maximum number of molecules possible. The true number of molecules can then be estimated by multiplying the observed count (green) by a correction factor (accounting for the lost molecules, shown in black), which intuitively is the reciprocal of the overlapping area (full derivation in Supplementary Information 21). Another approach to detecting more molecules is to modify a(z) by physically compressing the cell (using Microfluidics-Assisted Cell Screening (MACS)), bringing the entire cell’s volume within the maximum region of D(z). c Applying the correction factor or compressing the cell using MACS improves the counting performance compared to the naive estimate. Both of these approaches reduce the error from defocus, but undercounting errors at higher counts occur due to diffraction effects. d A schematic architecture of the Deep-STORM single molecule localisation network is shown, which was trained using synthetic single molecule images. e Applying Deep-STORM to molecule counting improves performance, but combining it with MACS leads to near-perfect detection and counting up to a higher density of molecules.