There are several ways to measure detection limits. A quick (rough) way is simply to divide the BEC (background equivalent
concentration, i.e. the concentration intercept on the calibration
curve) by a number, people usually use 50 or 30. The number depends on the typical noise level in the instrument. This is explained further below.
Another way is to determine the uncertainty on the BEC. A third
way is called the signal-to-noise ratio (SNR) method. A favoured
approach is the SBR-RSDB method.
The SNR method can be expressed as:
the sensitivity (the slope of the calibration curve of intensity versus composition), where xA is the net analyte signal (i.e. signal above background) and c0 the composition of the element in the sample.
Clearly with this method, the detection limit is largely determined
by the background signal: its size and its noise level, expressed
as RSDB. And the sensitivity of the technique, expressed
as the slope of the calibration curve.
The SBR-RSDB method can be expressed in two equivalent ways:
where > c is the mass % of the
element in the sample being measured, BEC is expressed as mass %,
and SBR is the signal-to-background ratio.
Again, the detection limit is largely
determined by the background signal: its size and its noise
level, expressed as RSDB. And the sensitivity of the technique,
expressed as SBR.
can see that if RSDB is 0.7%, then DL is approximately BEC/50 and the
limit of determination is 3xBEC/50. If RSDB is 1%, then DL is about 30,
and if RSDB is 2%, then DL is BEC/17.>[Note: if the RSDB is 1%,
which is often assumed, then BEC/50 corresponds to two times the noise
level on the background and so the limit of determination is taken to
be five times the DL, i.e. BEC/10, rather than three times in the more
Detection limits with more formulars
Since, in optical emission spectroscopy, we measure intensities to determine amounts, the
detection limit corresponds to the smallest intensity from the analyte that can
be measured and distinguished from the background. One method to determine the DL is to measure signals with
and without a tiny amount of the analyte. The signal without the analyte is
called a “blank”. An alternative to using a blank is to measure the signal
in the background at a n close to the emission line of interest. Thus
we have two means, one measured with the analyte
and one without it.
If the true means are m1 and m2,
then the difference between them is given by
where n1 and n2 are the
number of measurements for each and se is the combined
estimate of the standard deviation, given by
where s1 and s2 are the
standard deviations of the two sets of measurements.
To be sure of having a real signal from the analyte
The detection limit therefore corresponds to
If we make an equal number of
measurements with and without the analyte signal, then n = n1 = n2, where n is the number of measurements of the backgound or analyte; and if the
analyte signal at the detection limit is small compared with the background or
blank signal, then
where s is the standard
deviation of either the background or (background plus analyte) signal. Thus the
detection limit simplies to
If n is large (≥ 15), for a 95%
confidence, t = 2.0 and √2.t = 2.8, usually approximated
to 3. Hence
Immediately we notice that the detection limit depends on
the standard deviation of the background, i.e. on the noise in the background
signal, and not on the size of the background signal, though the higher the
background signal often the higher the noise. Also we notice that we can reduce
the detection limit by taking more measurements, though, as it depends on
√n, it is a matter of diminishing returns.
Further reading: P W J M Boumans,
in R Payling, D G Jones and A Bengtson (Eds), Glow
Discharge Optical Emission Spectrometry, John Wiley &
Sons, Chichester (1997), pp 440-451.
Th.Nelis and R. Payling, RSC Analytical Spectroscopy Monographs, Glow Discharge
Optical Emission Spectroscopy: A practical guide., RSC Cambrigde UK,
(2004) p 111.
First published on the web: 15 May 2000.
Author: Richard Payling