Fig. 1: Comparison of different particle tracking methods and their accuracy.
a Conventional single particle tracking algorithms utilize a particle-sized filter to blur the particle image, followed by fitting the blurred image with a Gaussian to determine the center position 22,56. Image overlap introduces tracking errors when tracking multiple particles in close proximity leading to a systematic error in the determined position. The plot shows the tracking error as a function of the distance between a pair of particles, polystyrene beads of size (diameter) 2R = 500 nm. b A masking approach, considering only the parts of the image that are non-overlapping, can be employed to improve the tracking accuracy57,58,59. While the masking approach outperforms the conventional method, it becomes ineffective for small particles where the residual area reduces to zero. c An alternative, model-independent approach for tracking two or more particles involves generating a synthetic image of the particle assembly using the individual particles' known image or shape function. The shape function can be acquired by imaging the particles before bringing them close together. The difference between the measured image (upper panel) and the reconstructed image (lower panel) is minimized by varying the particle positions. The arrows on the images indicate the corresponding intensity gradient. The full reconstruction method shows minimal bias across the entire distance range. The positional accuracy is about ± 2 nm or < 10−2R close to contact, comparable to the statistical noise limiting the tracking precision (indicated by the shaded area). d The color-coded map displays pixel-by-pixel the residual (target error function, Eq. (3)), for the case with the best match. e The mean of the residuals as a function of the mismatch between a chosen and optimal position where the residuals become minimal. Scale bars are 1 μm.
