<title>Physical wavelets: applications in optics</title>
Bibliographic record
Abstract
During the last decade, the optics community has shown interest in building bridges between mathematical wavelets and optical phenomena. In a first time, we review some of the previous works done on the subject. Namely, we discuss the optical implementation of the transform, as well as its utilization in relation with optical pattern matching. A short discussion on works, unfortunately falling short to explain scalar diffraction in terms of a wavelet transform, is presented. At this point, we introduce the physical wavelet (Psi) . After portraying the mathematical properties of (Psi) , we describe its contributions to the optical world. Actually, this wavelet being a solution of Maxwell's equations, we derive interesting optical properties from its mathematical behavior. For instance, looking more closely to the scalar projection of this wavelet, we demonstrate the equivalence between Huygens' diffraction principle and the wavelet transform using y as the transformation kernel. Another application involves a closely related form of this wavelet that can be used to generate limited diffraction beams.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.030 | 0.013 |
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".