Dynamic parameter compensation algorithms for periodic nonlinearity errors in spatially separated heterodyne interferometers
Bibliographic record
Abstract
Planar grating interferometric displacement measurement technology, known for its superior resolution and robust environmental adaptability, is crucial in six-degree-of-freedom displacement measurements for ultra-precision motion stages. This study introduces a spatially separated heterodyne grating interferometer to explore the inadequacy of traditional ellipse fitting algorithms caused by non-coaxial transmission of measurement and reference beams. A dynamic parameter PNL error model that integrates random error influences was developed to overcome these limitations. A novel, simplified real-time compensation algorithm for constant parameter PNL is proposed to enhance hardware feasibility and computational efficiency. Furthermore, an advanced algorithm for dynamic parameter PNL was designed, achieving real-time calibration and significant reduction of dynamic parameter PNL error from 11 nm to 20 pm. This advancement crucially addresses the challenge of attaining high-speed, high-acceleration displacement measurements with sub-nanometer precision using laser interferometers.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".