Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale
Bibliographic record
Abstract
ABSTRACT Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Previously, it has been assumed that the Fresnel scale, RF, is the relevant physical scale that separates these two regimes. With the recent introduction of Picard–Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by $R_F/\sqrt{\kappa }$, where κ is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive interstellar scintillation.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".