SKEW RAY TRACING AND ERROR ANALYSIS OF OPTICAL LENS WITH CYLINDRICAL BOUNDARY SURFACE
Bibliographic record
Abstract
This study applies computational geometric algebra based on a 4 × 4 homogeneous transformation matrix and Snell’s law of geometrical optics to analyze skew rays and the errors of a light ray’s path as it passes through a cylindrical lens. The author addresses two important topics: (1) the determination of the direction of a reflected or refracted ray by Snell’s law and (2) the expression of the combination of two principal sources of light path error using error analysis. In topic (2), one of the sources is the translational errors Δd ix , Δd iy , and Δd iz and the rotational errors Δω ix , Δω iy , and Aω iz that determine the deviation of the light path at each boundary surface, while the other source is the differential changes induced in the incident point position and the unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The methodology presented in this study provides a comprehensive and robust approach for evaluating the error of a light ray path as it passes through a cylindrical lens.
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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 | 0.001 |
| 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".