Autocollimators: plane angle measurand ambiguities and the impact of surface form
Bibliographic record
Abstract
A phase shifting interferometer and a deformable mirror were used to study the impact of surface form on autocollimators, which detect the orientation of a plane reflecting surface. As real surfaces are not strictly planar, autocollimators must reduce a distribution of local surface orientations to a single reported angle, implicitly defining a measurand. Plausible choices of the summary statistic used to collapse an angle distribution to a single number can disagree by \SI{4}{\arcsecond} for a surface with a \SI{35}{mm} diameter and \SI{130}{nm} standard deviation from the best-fit plane. Combining a general framework for specifying autocollimator measurand definitions with Monte-Carlo simulation of random test surfaces yields estimates of the plausible differences between autocollimator measurands as a function of surface deformation amplitude, and shows the existence of three separate classes of measurands according to their sensitivity to subsets of the Zernike polynomials. Uncertainties due to surface form and measurand ambiguity can be eliminated by explicitly specifying a plane angle measurand for imperfect surfaces, such as a least-squares plane fit realized using an interferometer.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 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".