On the Dynamic Response of the Ideal Paraboloidal Reflector
Bibliographic record
Abstract
The ideal paraboloidal reflector (IPR) is analyzed as a 4D spatio-temporal linear system having a dynamic focal plane response that is characterized by an idealized scalar Dirac plane-wave (PW) signal on the aperture. Using the same path-difference equations that are used for classical steady-state quasi-monochromatic (QMC) analysis, simple algebraic expressions are derived for the spatio-temporal focal plane response$h_{fp}\left ({\boldsymbol {x},ct }\right)$to the Dirac-PW. These expressions for$h_{fp}\left ({\boldsymbol {x},ct }\right)$are used to directly determine the focal plane response to far-field on-axis short-time transient signals, thereby avoiding the complexities of QMC-based methods for the analysis of such signals. The derived first-order approximation of$h_{fp}\left ({\boldsymbol {x},ct }\right)$describes its spatio-temporal region of support (ROS) and amplitude whereas the second-order approximation includes a further spatio-temporal distortion that is the dynamic equivalent of the Petzval aberration. Examples of the focal plane response to highly transient far-field pulses are described.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".