Characterizing flat-top laser beams using standard beam parameters
Bibliographic record
Abstract
We examine the correspondence between various models describing flat-top laser beam profiles using two standard parameters; namely, the M2 factor and the kurtosis parameter. Numerical expressions for M2, based on the second moment of the beam irradiance distribution in the near and far fields and for the kurtosis parameter, k, based on the fourth moment at the near field, are obtained. Plots of k in the near field versus M2 demonstrate the similarities between the different analytical models used to describe flat-top profiles. Using the Padé approximation, a relationship between k and M2, a new reference formula, is derived that predicts the values of M2 to within less than a percent for these flattened beams. This method is then extended to define numerical expressions relating the beam parameters (i.e., M2 and k) and the parameters describing the beam characteristic in each analytical model (model parameters). The results obtained using the Padé method are used to describe the output beam profiles for a high power copper vapour laser fitted with an unstable resonator.PACS Nos.: 42.55.–f, 42.55.Lt, 42.60.–v
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".