Author's School

McKelvey School of Engineering

Document Type

Conference Proceeding

Publication Date



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.


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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: