Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements
Bibliographic record
Abstract
The wavefront error (WE) of a surface with an optical coating (“filter”) is ideally measured at the in-band wavelength of the filter. However, quite often this is not possible, requiring that the filter be measured at an out-of-band wavelength (typically 633 nm), assuming that the filter transmits (for transmitted WE, or TWE) or reflects (for reflected WE, or RWE) at this wavelength. This out-of-band TWE/RWE is generally assumed to provide a good estimation of the desired in-band TWE/RWE. It will be shown in this paper that this is not the case for a large class of filters (i.e., bandpass) where the group delay is significantly different at the in-band and out-of-band wavelengths and where the optical filter exhibits a thickness non-uniformity across the surface. A theoretical explanation will be given along with an approach to predict the in-band TWE/RWE based on the coating non-uniformity, the measured out-of-band TWE/RWE, and the theoretical properties of the optical filter at the in-band and out-of-band wavelengths. A reasonable agreement between theory and measurement was demonstrated by measuring the TWE of an 11 nm wide bandpass filter (centered at 1048 nm) at both in-band ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1048</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> ) and out-of-band ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>625</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> ) wavelengths. A similar treatment is provided for RWE.
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 | 0.000 | 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 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".