Optical remote sensing inside an inhomogeneous axisymmetric medium: the absorption field measurement
Bibliographic record
Abstract
It is shown that the absorption field inside an inhomogeneous, rotationally symmetric medium with a spatially variable refractive index can be reconstructed by means of a tomographic technique. The classic Abel transform is extended to non-Euclidean optical media. The optical behavior of such a medium is described and, provided that the product of the refractive index with the radial distance is a monotonic function, an exact inverse formula is found. Both a numerical and an analytical test on a phantom function is carried out to prove the exactness of this formula. In contrast, when the assumption of a monotonic function is not true, it is shown that the reconstruction problem becomes subdeterminate because of the presence of annular regions, known as blind areas, inside of which no curved path reaches an extremum. The spatial localization and the size of these regions are related to the extrema of the index of refraction times the radial distance.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".