Mathematical estimation of half‐value layer thicknesses
Bibliographic record
Abstract
OBJECTIVE: The objective of this article is to introduce a simplified and swift method to satisfactorily estimate the half-value layers (HVL), quarter-value layer (QVL), and tenth-value layer (TVL) from the x-ray spectra emitted by any diagnostic radiology or kV radiotherapy x-ray tubes. METHODS: A CdTe x-ray and Gamma detector (X-123 CdTe, AmpTek Inc.) is used to measure the x-ray spectra at four different x-ray energies (low, mid, high energy x-rays) with different external filtering. The software "SpekCalc GUI" (Developed in McGill University, Montreal, Canada) is also used to obtain the simulated x-ray spectra. Both measured and simulated spectra are used to compute the HVL thicknesses of Aluminum by a mathematical method presented in this article. Next, the HVL thicknesses for corresponding tube potentials are also measured by calibrated ionization chamber and varying thicknesses of aluminum plates. Finally, the computed and measured HVL, QVL, and TVL thicknesses are compared to evaluate the efficacy of the presented method. RESULTS: The results show acceptable concordance between computed and measured quantities. The disagreement rates between measured HVL and the values derived mathematically from the x-ray spectra are 10 to 90 micrometers of Aluminum at tube potentials of 31 kV to 120 kV. As it is shown, a negligible discrepancy is observed between the analytical estimation and the experimental assessments. CONCLUSION: The HVL is an essential component in the evaluation of the quality of an x-ray beam. However, its measurement could occasionally be challenging, time-consuming, or uncertain due to some technical difficulties. Although the scope of this study is not to undermine the value of conventional and widely accepted practice to determine the HVL thickness, the introduced method provides the fast, more convenient, and comparably reliable technique to estimate the HVL, QVL, and TVL by employing the given x-ray spectrum.
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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 | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".