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Statistically, LOD = 3 STD (Standard Deviation) or as it is called 3Sigma. You have to be careful about LOD detection calculations. It is the calculation of Sigma (STD) that is a bit tricky. The Sigma (STD.) is not a constant; it depends on time, %Pb, substrate, etc.
One can, as some XRF manufacturers do, base the calculation of the STD on counting statistics. Scientifically, the STD calculation for XRF application should not be based solely on statistical counting or precision calculations (Random error) due to the fact that one can achieve excellent precision by measuring for a long time. So, in this model, the square root of the longest measurement time count rate is used to represent the Sigma. Numbers as low as 0.05 mg/cm2 can be achieved by most XRF systems including the LPA-1 analyzer.
The true measurement of LOD should also include the Systematic errors into the calculation of STD. The most dominating factor into the Systematic error contributor is the NIST Standard.
No one can measure better than what the calibration standards represent. The uncertainty of the NIST 1.04 sample is 0.064 mg/cm2. This means the STD for this sample is 0.032. Therefore, the contribution from this samples error alone to LOD is 3 X (.032) = 0.096 or almost 0.1 mg/cm2.
We suggest that you also read the Methodology for XRF Performance Characteristic Sheet, EPA 747-R-95-008 that details how the HUD/EPA attempted these calculations. You can get a copy by calling 800-424-LEAD.
We hope this note is helpful to you.
Dynasil Products / RMD
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