Accurate estimation of the three-dimensional (3D) position of particles is critical in applications like biological imaging, atom/particle-trapping, and nanomanufacturing. While it is well-known that localization accuracy better than the Rayleigh resolution limit is possible, it was recently shown that, for photon-limited cases, 3D point spread functions (PSFs) can be shaped to increase accuracies over a 3D volume [Pavani and Piestun, Opt. Express16, 22048 (2008)]. Here, we show that in the detector-limited regime, the gain in accuracy occurs in all three dimensions throughout the axial range of interest. The PSF is shaped as a double helix, resulting in a system with fundamentally better 3D localization accuracies than standard PSF systems, capable of achieving single-image subnanometer accuracies.

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See EPAPS supplementary material at http://dx.doi.org/10.1063/1.3158923 for information on Poisson CRBs, effect of SNR, standard and DHPSF movie, Table I listing positions and standard deviations, PSF calculation, calibration, information-theoretical calculations, effect of a large particle, position estimation, and system component details.

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