Lens design distortion management using orthogonal polynomial functions
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Bibliographic record
Abstract
We propose the use of slope orthogonal polynomials as a tool to manage distortion. The object-to-image mapping of the whole optical system is reduced to a single refracting surface, which reproduces the same lens mapping function (LMF) as the original optical system. Using slope orthogonal polynomials to describe this LMF equivalent surface, the orthogonal properties of the polynomial can be leveraged for efficient use of ray tracing by relating coordinates mapping to a surface gradient. We demonstrate that this distortion measurement can be linked to a physical surface aspherical departure in the case of a double Gauss objective. This relationship can be established for any surfaces, after a calibration step. We also show that this same relationship can be used to obtain a target LMF by setting a precomputed aspherical surface departure on a given surface.
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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 it