Fig. 1
Principle and localization precision of the parallax-DIC microscope. a Schematic illustration of a gold nanorod placed in the 3D coordinate system. The x- and y-axes are set according to the polarization directions of the illumination light. The dipole shown here corresponds to the long axis of the gold nanorod, whose centroid locates at (x, y, z). The azimuthal angle and the elevation angle of the longitudinal axis of the gold nanorod are presented as ϕ and ψ, respectively. b Bright (left), dark (middle), and half-bright/half-dark (right) images of a gold nanorod (40 × 80 nm) at different orientations and vertical positions. The half-plane images are aligned by the nanorod’s center of mass at the focal plane (z = 0 μm). The yellow dashed lines indicate the z-position of the center of the gold nanorod in focus. Scale bar is 1 μm. c Calibration of the 5D-SPT technique. The distance between the two half-plane images changes linearly with the z-position of the gold nanorod within ±0.5 μm of the focal plane. The distance for an in-focus gold nanorod is defined as d 0. The error bars reflect the standard deviations of the distances measured when the nanorod’s azimuthal angle ϕ changes in the range of 0–180° with 5° steps (error bar ± s.d., n = 36). The calibration curve returned a slope of +0.626 (d/Δz) and R 2 of 0.997. d Three-dimensional localization distribution of the gold nanorod with standard deviations of 11 nm in x, 14 nm in y, and 17 nm in z. e The in-focus half-plane image patterns of a gold nanorod at different azimuthal angles when the sample slide is rotated in 5° steps for 180°. The scale bar represents 1 μm. f The normalized bright part (blue) and dark part (brown) intensities of the half-plane images on the top in each pair in E
