The Sharpness Tradeoff

Resolution and precision sound like the same thing. A sharper image should let you locate objects more accurately. In classical optics, they’re aligned: better resolution generally improves localization.

At the quantum limit of coherent microscopy, they’re antagonists (arXiv:2510.03034). Using the framework of quantum Fisher information, the analysis of three-dimensional localization in interferometric scattering microscopy (iSCAT) reveals that rotating coherent scattering microscopy (roCS) — which incoherently averages over oblique illumination angles — achieves higher spatial resolution but lower localization precision. Seeing more finely makes you worse at pinpointing where things are.

The mechanism is information loss through averaging. Each oblique illumination angle carries specific phase information about the scatterer’s three-dimensional position. This phase encodes the Fisher information needed for precise localization. When you average over many angles to achieve a sharper image, you destroy the angle-specific phase relationships that localization depends on. The image sharpens because averaging removes interference fringes; precision degrades because those fringes were the signal.

The paper shows that tilting the illumination — using a single oblique angle rather than averaging over many — enhances localization precision per detected photon while also increasing robustness to defocusing. The optimal strategy for precision is not to see as sharply as possible but to see with the right amount of structure in the illumination.

The structural insight: at quantum limits, resolution and precision measure different things about the light field. Resolution asks “how small a feature can you distinguish?” — a spatial frequency question. Precision asks “how accurately can you locate a known feature?” — a Fisher information question. They’re not the same measurement, and optimizing one actively degrades the other. The quantum limit makes explicit a tradeoff that classical optics hides.

“When Higher Resolution Reduces Precision: Quantum Limits of Off-Axis Interferometric Scattering Microscopy,” arXiv:2510.03034 (2025).