Accuracy of Superlocalization Imaging Using Gaussian and Dipole Emission Point-Spread Functions for Modeling Gold Nanorod Luminescence

Abstract

We present a study comparing the accuracy of superlocalization imaging of plasmon-mediated emission from gold nanorods (AuNRs) using both Gaussian and dipole emission point-spread function (PSF) models. By fitting the emission PSF of single AuNR luminescence, we have shown that a 3-axis dipole PSF gives improved localization accuracy over the Gaussian PSF, especially for nonplanar AuNRs, while also allowing the AuNR three-dimensional orientation and emission wavelength to be determined. On the other hand, when a single-axis dipole PSF model is applied to the AuNR emission, the fit estimates converge to values that are inconsistent with their experimentally measured values, affecting both the localization accuracy and precision of the fitted centroid position. These results indicate that when applying superlocalization techniques to plasmonic nanostructures, care must be taken to understand the nature of the emission before a correct dipole PSF can be applied.

Objective-Induced Point Spread Function Aberrations and Their Impact on Super-Resolution Microscopy

“…We have previously reported that we fit each AuNR twice using ϕ and ϕ ± 180°as the initial guesses and then choose the correct value of ϕ fit based on the value of the out-of-plane angle θ fit (see Supporting Information for full details). 20 Qualitatively, we observe the best agreement between ϕ fit and the orientation of the long axis of the AuNR for 100×-1, followed by 100×-2. The TIRF 60× calculates a ϕ fit value that is 180°away from the other three objectives.…”

“…In previous work from our group, we reported that λ fit is consistently red-shifted relative to the experimental value, most likely due to the fact that the image consists of multiple wavelengths, which is not accounted for in the threedipole fit. 20 Nonetheless, we find that the 100×-1 objective produces a λ fit value closest to the experimental value, as well as fits with the most random residuals and most consistent agreement with experimental values of ϕ; as a result, we will use this objective as a benchmark when determining the correct orientation of the measured value of ϕ (ϕ meas ) in subsequent studies.…”

“…The dark gray dotted line in Figure 4 represents the line of best fit from the previously reported results using the 100×-1 objective and is included for direct comparison. 20 The same AuNRs from Figure 3A were used in Figure 4. The Δ dipole-Gaussian values obtained from images taken with the 100×-1 and PSF-corrected 60× objectives follow the trend of increasing distances between the calculated centroid positions as θ fit increases, tracking well with the line of best fit.…”

Superlocalization Surface-Enhanced Raman Scattering Microscopy: Comparing Point Spread Function Models in the Ensemble and Single-Molecule Limits

“…30 Figure 2G,H show the results of the fit and associated residuals, and we find that this model exhibits smaller residuals than the one-dipole and Gaussian fits, indicating that including contributions from each dipole axis is important in modeling the correct PSF. This model also provides values for j and θ (Table 1), which are in reasonable agreement with the geometry of the dimer (Figures 2A and 3A).…”

“…33 As in previous studies, the selection between 1/3-dipole fits was accomplished via fixing the R and κ parameters in the fit. 30 The 3-λ dipole PSF fit was carried out by combining three one-dipole PSFs in a single fit simultaneously, where each component of the fit was restricted to have the same centroid and each dipole was fixed to be orthogonal to the other two. 30 Once the PSF models were constructed, fits were carried out using a bounded least-squares fitting algorithm in MATLAB.…”