## 6 Noise Sources and Identification Performance  
Each of the challenges described above impact the noise sources in the task to identify all radio-isotopes present in a sample. For example, to address issue (1), Figure 4 (top plot) is \(\sqrt{C}\) where \(C\) is the measured counts per second by a GR135 NaI detector for a \({}^{239}\)Pu spectra without shielding and when shielded by 0.5 inches of Pb or 4.0 inches of polyethylene. In the bottom plot, the measured ratio \(\left(\dfrac{C_{i}(j,z)}{C_{i}(j,\mathrm{ref})}\right)\) is plotted, which estimates the true count rate \(\left(\dfrac{\mu_{i}(j,z)}{\mu_{i}(j,\mathrm{ref})}\right)\) for each of the two shielded measurements of the \({}^{239}\)Pu spectra. Recall that the term \(C_{i}(j,\mathrm{z})\) refers to the measured count rate for isotope \(j\), shielded by absorber \(z\) in channel i. The term \(C_{i}(j,\mathrm{ref})\) refers to the reference, which is the no-absorber case. In Figure 4, the measurements were made by different models of the GR135 NaI detector [14]. Clearly the absorbers attenuate the peak counts, as described above by Beer's Law [15], which is an approximation. Beer's Law ignores the fact that when an incident \(\gamma\) undergoes an interaction, one result is a lower-energy \(\gamma\). In the case of the polyethylene shielding, notice the region where the ratio exceeds one. In effect, the shielding material acts as a source of lower energy \(\gamma\) s, thus modifying spectral shape. **Figure 4.** Example effects of Pb shielding on low-energy counts in \({}^{239}\)Pu spectra. Ratio 1 is \(\left(\dfrac{C_{i}(j,z)}{C_{i}(j,\mathrm{ref})}\right)\), for the 0.5 in. of Pb shielding, which estimates \(\left(\dfrac{\mu_{i}(j,z)}{\mu_{i}(j,\mathrm{ref})}\right)\) for isotope \(j\) (\({}^{239}\)Pu), channel \(i\), where \(\mu_{i}(j,\mathrm{ref})\) is the unshielded true count rate and \(\mu_{i}(j,z)\) is the shielded true count rate. The counts are noticeably smaller in Ratio 1, but the ratio is not constant, indicating a distortion of spectral shape. Ratio 2 is the same, but for the 4.0 in. of polyethylene shielding. There is a region of low energy counts that noticeably larger than one in Ratio 2. Regarding issue (2), nonlinear calibration requires multi-line sources and calibration drift is an important noise source. For example [3] and [16] showed that a typical peak centroid can shift by tens of keV in either direction. If in a given spectrum, all peak centroids shift in the same direction, then corrections such as those in [16] can be effective. Nevertheless, such adjustments cannot be expected to be perfect. Imperfections in estimated peak centroids will clearly impact any method that identifies peak locations. Figure 5 is an example using two different NaI models of the same detector (the GR135) of shifting peak centroids in which the peak centroid shifts are not all in the same direction. Isotope mixtures [issue (3)] can result in ambiguous spectra, so isotope identification performance will degrade. One reasonable strategy is to eliminate redundant spectra from the algorithm's library; however, a statistical assessment is required to identify \"redundant\" spectra as those having shapes that are \"too similar\" to distinguish. Issue (4) involving measurement protocols is an ongoing challenge. For example, temperature variation impacts the calibration of spectral channel to \(\gamma\) energy, and some protocols control the temperature to within a narrow range to minimize calibration shifts. The measurement standard [9] requires only that the instrument be operational at -20\({}^{\circ}\)C to 50\({}^{\circ}\)C, but calibration stabilization is not required. Even if calibration stabilization were required, such stabilization will never work perfectly, so that noise will be introduced by temperature variation. Each of several challenge problems [issue (5)], including the \"general problem\" described in the problem statement above has unique noise sources.