A computationally-efficient bound for the variance of measuring the orientation of single molecules
Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the CRB matrix from above; VUB overestimates the mean CRB by ~34%. However, compared to directly calculating the mean CRB over orientation space, we are able to calculate VUB ~1000 times faster.
Wu, Tingting; Ding, Tianben; Mazidi, Hesam; Zhang, Oumeng; and Lew, Matthew D., "A computationally-efficient bound for the variance of measuring the orientation of single molecules" (2020). Electrical & Systems Engineering Publications and Presentations. 9.
Atomic, Molecular and Optical Physics Commons, Electrical and Computer Engineering Commons, Numerical Analysis and Computation Commons, Optics Commons
Copyright 2020 Society of Photo-Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, and Matthew D. Lew, "A computationally-efficient bound for the variance of measuring the orientation of single molecules", Proc. SPIE 11246, Single Molecule Spectroscopy and Superresolution Imaging XIII, 1124616 (13 February 2020) DOI: https://doi.org/10.1117/12.2543813