Axial point source localization using variable displacement-change point detection

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. Powerdependent 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.