We describe the use of direct multiple least-squares fitting of (unfiltered
) biological X-ray spectra. Test of this method on computer-generated spect
ra and experimental specimens shows that, for the average biological specim
en, direct fitting improves the precision of Ca measurements by an approxim
ate factor of 1.6 for a given electron dose. The influence of non-statistic
al, instrumental sources of measurement errors is considered, and we show a
simple method for reducing the effect of these sources of error in the dir
ectly fitted spectra.