Quantifying Classical and Quantum Bounds Enables Super-Resolution Imaging of Closely Spaced Dipole Sources
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The challenge of distinguishing closely spaced light sources remains a fundamental problem in optical microscopy, yet recent advances suggest the possibility of overcoming traditional resolution limits. Armine Dingilian, Aarnah Kurella, and Cheyenne Mitchell, alongside colleagues at the University of Illinois Urbana-Champaign, investigate the theoretical limits of resolving two neighbouring, non-interacting light emitters. Their work demonstrates that precise separation measurements are possible even when the emitters are very close together, provided the analysis accounts for the full vectorial nature of light emission. By applying parameter estimation theory and considering both fixed and freely oriented emitters, the team quantifies the precision limits imposed by classical and quantum mechanics, ultimately revealing a pathway to achieve super-resolution imaging through careful filtering of collected light. Super-Resolution Microscopy and Single-Molecule Localization Advanced optical microscopy continually pushes the boundaries of resolution, allowing scientists to visualize structures far smaller than previously possible. This work focuses on super-resolution techniques, specifically single-molecule localization microscopy (SMLM), which relies on precisely determining the positions of individual molecules to create high-resolution images. Researchers continually refine these methods to improve localization accuracy and resolve finer details. A key aspect of this field is understanding the fundamental limits of resolution and how to overcome them. Polarization microscopy plays a crucial role, as the polarization of light emitted from single molecules provides valuable information about their orientation and position. By carefully controlling and analysing the polarization of light, scientists can significantly enhance the precision of localization, guided by the mathematical framework of Fisher information theory which quantifies the information contained in collected light.
Polarization Filtering Improves Nanoscale Separation Precision This work presents a comprehensive analysis of precision limits in super-resolution microscopy, focusing on image inversion interferometry (III). Researchers investigated how accurately the separation between two closely spaced, light-emitting molecules can be determined, a critical factor in resolving nanoscale structures. The study rigorously examines scenarios with both fixed and randomly oriented emitters, quantifying precision limits using Fisher information and the Cramér-Rao bound, a key concept defining the minimum achievable error in parameter estimation. Analyses reveal that filtering collected light using a specific azimuthal-radial polarization basis effectively salvages a previously proposed scheme to maximize information gain via image inversion interferometry. This filtering technique proves critical for achieving optimal resolution. Investigations explored different microscope modalities, including unpolarized and specially polarized III setups. In the polarized configuration, light is split into radially and azimuthally polarized components, processed separately, and then recombined, demonstrating that selectively retaining or discarding either component impacts the total information recovered, offering control over resolution. For randomly oriented emitters, representing molecules tumbling or an ensemble of randomly oriented dipoles, the team developed a model incorporating contributions from dipoles oriented along all three axes. This model allows for accurate calculation of the quantum and classical bounds on precision. Numerical calculations were performed to determine these bounds, providing a quantitative assessment of achievable resolution limits in various imaging scenarios, and providing a foundational understanding of information limits to guide the development of advanced super-resolution microscopy techniques.
Dipole Resolution Limits and Image Inversion This research establishes classical and quantum limits to resolving closely spaced pairs of light-emitting sources, relevant to high-numerical-aperture microscopy.
The team demonstrates that the full vectorial nature of light emission must be considered when analysing resolution limits, particularly at very small separations, unlike previous assumptions. Through rigorous application of parameter estimation theory, they quantify how accurately the distance between two dipole emitters can be determined, considering both fixed and randomly oriented emitters. The findings reveal that super-resolution imaging, exceeding the diffraction limit, is possible through image inversion interferometry, but requires careful filtering of the collected light. Specifically, analysing the azimuthally polarized component of emitted light provides sufficient information for enhanced resolution, even when discarding the radially polarized component, except when emitters are nearly aligned. Importantly, the calculated quantum Cramér-Rao bound, representing the ultimate limit to precision, is significantly lower than the resolution achievable with conventional imaging methods, indicating the potential for substantial improvement. The authors acknowledge that their analysis relies on a simplified model, assuming known emitter brightness and position, and that incorporating uncertainties in these parameters will complicate the resolution problem. Future work will focus on addressing these complexities and integrating additional factors into the analysis, while the study considers specific limiting cases of fixed or random emitter orientations, providing useful constraints for understanding the more general scenario. 👉 More information 🗞 Quantifying classical and quantum bounds for resolving closely spaced, non-interacting, simultaneously emitting dipole sources in optical microscopy 🧠 ArXiv: https://arxiv.org/abs/2512.10889 Tags: