Axial point source localization using variable displacement–change point detection

Abstract

A three-dimensional point-source localization technique is demonstrated using two-photon photoluminescence and four-wave mixing nonlinear optical signals from plasmonic gold nanorods (AuNRs), imaged at the single-particle level. Introduction of position-dependent latitudinal astigmatisms into the imaging system, in combination with a change point detection (CPD) algorithm, resulted in localization of single particles with high precision in three dimensions. Astigmatisms were generated using axial sample-position displacements spanning the range from ±10 to ±90 nm with a minimum step-size resolution of ±3 nm. Based on the current data, 20 nm point source localization was achieved in the axial dimension using a single imaging objective. This technique is named variable displacement–change point detection (VD-CPD). The influence of plasmon enhancement on achievable axial localization was also quantified. Two AuNR systems with different length-to-diameter aspect ratios (AR, where AR=1.86 and 3.90) were selected for this purpose; the AR=1.86 and AR=3.90 had nonresonant and resonant longitudinal surface plasmon resonances (LSPR) energies, respectively, with the laser fundamental. Matching the fundamental wave LSPR energies resulted in increased axial localizations. Power-dependent analysis of the LSPR-mediated nonlinear optical images revealed that resonantly excited AuNRs results in third-order signals. The axial localization provided by VD-CPD exceeds what could be obtained using astigmatic imaging alone by a factor of 2.5. This advance will facilitate the in-depth study of photonic materials and complex biological environments that can benefit from increased axial position determinations.