Twin-Airy Point-Spread Function for Extended-Volume Particle Localization

The localization of point sources in optical microscopy enables nm-precision imaging of single-molecules and biological dynamics. We report a new method of localization microscopy using twin Airy beams that yields precise 3D localization with the key advantages of extended depth range, higher optical throughput, and potential for imaging higher emitter densities than are possible using other techniques. A precision of better than 30 nm was achieved over a depth range in excess of $7\mu \mathrm{m}$ using a $60\times$, 1.4 NA objective. An illustrative application to extended-depth-range blood-flow imaging in a live zebrafish is also demonstrated.

Figure 1

(a) Pupil function of the TA-PSF. (b) Simulated variation in TA-PSFs with defocus with an $\alpha =10$ phase mask on a $60\times$, 1.4 NA system. (c) Schematic of the experiment setup, based on a Nikon Eclipse Ti microscope. The TA refractive mask is located at the reimage the pupil plane of a $4f$ relay system with 100 mm focal lengths.

Figure 2

Cramer-Rao lower bounds for localization in $x$ (left), $y$ (middle), and $z$ (right) for the TA-PSF with various strengths ($\alpha =2$, 4, 6) and single Airy-beam PSF generated with a cubic phase mask ($\alpha =4$), assuming 3500 photons per localization and an average background of 50 photons per pixel (numbers chosen to compare with Ref. [4]). Simulations are based on the Poisson data model [21] and the high-NA PSF model proposed by Schnitzbauer et al. [22]. A $60\times$, 1.4 NA oil immersion system ($n=1.515$) and $13\mu \mathrm{m}\mathrm{pixel}$ size were assumed.

Figure 3

(a) Point-spread functions over a depth range of $10\mu \mathrm{m}$, acquired with $60\times$, 1.4 NA, averaged over 1000 frames. (b) Corresponding recovered PSFs, with recovery kernel being the in-focus PSF. (c) Calibration curves: Blue curve maps depth to disparity between the two recovered points and orange curve maps depth to lateral shift. (d) Superimposition of the recovered PSFs in (b). (e) Experimental measurements of statistical localization precision. The standard deviations ${\sigma }_x$, ${\sigma }_y$, and ${\sigma }_z$ for each $z$ position are calculated with 1000 images recorded in time sequence for the same quantum dot (see dataset in Ref. [28]).

Figure 4

3D blood-flow characterization in a live zebrafish (see dataset in Ref. [28]). (a) Fluorescent image of zebrafish blood vessels. The region of interest (ROI) is near the cloaca of the zebrafish as indicated with the red rectangle. (b) A raw image frame showing injected tracer beads in blood vessels. (c) Three-dimensional tracer trajectories. Each color corresponds to the trajectory of one tracer bead. (d) $xy$ view of the 3D tracer trajectories. (e) $yz$ view of the tracer trajectories (cross section perpendicular to the anteroposterior axis of the fish). A video showing the fluorescent beads flowing within the blood vessels can be found in the Supplemental Material [23].