DOE OSTI · 1398889
Error Budgeting
Abstract
We calculate opacity from k (hn)=-ln[T(hv)]/pL, where T(hv) is the transmission for photon energy hv, p is sample density, and L is path length through the sample. The density and path length are measured together by Rutherford backscatter. Δk = $\partial k$\ $\partial T$ ΔT + $\partial k$\ $\partial (pL)$. We can re-write this in terms of fractional error as Δk/k = Δ1n(T)/T + Δ(pL)/(pL). Transmission itself is calculated from T=(U-E)/(V-E)=B/B0, where B is transmitted backlighter (BL) signal and B 0 is unattenuated backlighter signal. Then ΔT/T=Δln(T)=ΔB/B+ΔB 0 /B 0 , and consequently Δk/k = 1/T (ΔB/B + ΔB$_0$/B$_0$ + Δ(pL)/(pL). Transmission is measured in the range of 0.2<T<0.6 so that 1.5<1/T<5.
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Vinyard, Natalia Sergeevna, Perry, Theodore Sonne, Usov, Igor Olegovich. 2017-10-04. Error Budgeting. https://doi.org/10.2172/1398889
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