Tornado Wave-Encoded Point Spread Functions for Multi-Period Three-Dimensional Localization Imaging
Abstract
Three-dimensional (3D) localization microscopy using rotational point spread functions (PSFs) is fundamentally challenged by limited axial range, poor PSF compactness, and depth-decoding ambiguity -- particularly in dense specimens with heavy PSF overlap. To address these limitations, we introduce a 3D localization approach based on tornado wave (ToW)-PSFs, combined with a convolutional neural network (CNN) designed to decode continuous rotational patterns and resolve multi-period axial ambiguity. Our engineered PSF encodes the 3D position of each nanoparticle into a compact double-lobe pattern whose orientation rotates with axial position. This design yields a clean, well-defined structural evolution across an unprecedented 15 um axial range, with an average rotation rate of 21.8 degrees/um, ensuring robust long-range depth encoding. To recover coordinates from overlapping emitters, we systematically benchmark a conventional matching-pursuit (MP) algorithm against our CNN. While MP performs adequately in sparse scenes, the CNN demonstrates exceptional robustness in dense fields, achieving a 70.24% localization accuracy at 20 particles per image-substantially outperforming MP's 22.52% -- while also significantly suppressing axial period-jump errors. Experimental validation on nanoparticles confirms reliable single- and multi-particle localization throughout the entire working range. Our results establish ToW-PSFs as a powerful and practical optical encoding strategy for high-density, extended-range 3D localization imaging.
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BibTeX
@misc{chen2026tornado,
title = {{Tornado Wave-Encoded Point Spread Functions for Multi-Period Three-Dimensional Localization Imaging}},
author = {Lai Chen and Rui Wang and Li-Gang Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15606},
eprint = {2610.15606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15606},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tornado Wave-Encoded Point Spread Functions for Multi-Period Three-Dimensional Localization Imaging
AU - Lai Chen
AU - Rui Wang
AU - Li-Gang Wang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15606
UR - https://arxiv.org/abs/2610.15606
AB - Three-dimensional (3D) localization microscopy using rotational point spread functions (PSFs) is fundamentally challenged by limited axial range, poor PSF compactness, and depth-decoding ambiguity -- particularly in dense specimens with heavy PSF overlap. To address these limitations, we introduce a 3D localization approach based on tornado wave (ToW)-PSFs, combined with a convolutional neural network (CNN) designed to decode continuous rotational patterns and resolve multi-period axial ambiguity. Our engineered PSF encodes the 3D position of each nanoparticle into a compact double-lobe pattern whose orientation rotates with axial position. This design yields a clean, well-defined structural evolution across an unprecedented 15 um axial range, with an average rotation rate of 21.8 degrees/um, ensuring robust long-range depth encoding. To recover coordinates from overlapping emitters, we systematically benchmark a conventional matching-pursuit (MP) algorithm against our CNN. While MP performs adequately in sparse scenes, the CNN demonstrates exceptional robustness in dense fields, achieving a 70.24% localization accuracy at 20 particles per image-substantially outperforming MP's 22.52% -- while also significantly suppressing axial period-jump errors. Experimental validation on nanoparticles confirms reliable single- and multi-particle localization throughout the entire working range. Our results establish ToW-PSFs as a powerful and practical optical encoding strategy for high-density, extended-range 3D localization imaging.
ER -