Realistic sub-Rayleigh imaging with phase-sensitive measurements
Bibliographic record
Abstract
Abstract As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh’s ‘curse’ can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call ‘adapted SPLICE’, requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".