The Fraction Modern corrected for δC of a sample 10 separate times over the course of a run.
Using this measurement also corrects for any mass-dependent fractionation within the AMS system.
For small samples, blank contribution as a fraction of sample mass becomes a more important term, so a mass balance blank correction is applied.
This correction is performed as follows: $$Fm_ = Fm_ ( Fm_ - Fm_b)\frac$$ Where \(M\) is sample mass, and \(M_b\) and \(Fm_b\) are the mass and Fm of the blank.
Due to counting and measurement errors for the blanks and samples, statistical errors are higher for very old samples.
Thus, ages are limited by the age of the process blanks (more on that below) and by the statistical uncertainty of the C ratios of the blank, the sample and the modern reference, respectively.