## Limits of Detection:

Earlier, we mentioned that the uncertainty in the intercept of the regression line had implications for the lowest detectable signal and corresponding concentration. Remember that there is always some error (or uncertainty) associated with any measurement, even if that measurement is taken under conditions for which no analyte is present - the blank, background, or baseline measurement.

If we could continuously monitor the raw electrical signal (voltage or current) inside an instrument during a set of measurements, we might see something like the diagram shown below: here, the signal is subject to both short-term (high frequency) and long-term (low frequency) noise, as well as some long-term drift. The red line shows the drift in the background, or baseline, signal, while the green line shows that in the sample signal. The blue line represents the average difference between the sample and background, which is the value our instrument reports to the user. Continuous monitoring of the raw signal within an instrument

In terms of the instrument signal, therefore, we are interested in determining the smallest signal that is distinguishable from the background (baseline) noise. Various criteria have been applied in quantifying this limit, but the generally accepted rule is that the signal must be at least three times greater than the backgound noise.

When performing chemical measurements, however, we are more interested in the concentration of the species being measured within a particular sample that is necessary in order to generate the minimum detectable signal. We can therefore distinguish between the measurement limit of detection (yLOD) and the concentration limit of detection (CLOD).

### Obtaining the LOD from Multiple Readings:

One way to calculate the background noise is to calculate the mean and standard devation of multiple readings in the absence of any analyte. This is typically done using a calibration blank – a solution representing the background sample matrix (solvent and any chemical substances commonly found in the samples). Often, the instrument response is also initially set to zero using this blank.

By alternating at least 20 readings of the blank with that of a single, known concentration sample or standard, and correcting the readings for any drift, both the instrument and concentration limits of detection can be calculated, provided that the response function is linear.

First, the instrument LOD is calculated from the mean and standard deviation of the replicate blank readings, yblank ± sblank:

yLOD = yblank + 3sblank

We then convert this to the concentration limit of detection using the blank-corrected mean response (ys) for our known concentration sample or standard (Cs):

CLOD = Cs × yLOD ÷ ys

Practically speaking, this method is not used often in contemporary chemical analysis. This is because the repetitive measurements are time- and chemical-consuming. More signficantly, we can obtain the same information from linear regression analysis of the calibration data and, since we need to do this anyway to confirm linearity, the latter method is preferred.

### Obtaining the LOD from the Regression Line:

It is not always practical to perform multiple blank determinations. An alternative procedure is therefore to make use the of the calibration data and regression line directly. In this case, the lowest detectable signal is calculated from the intercept and standard error of the regression line as shown below: Graphical representation of calculating the limit of detection from the regression line.

Given the definition of the instrument LOD in terms of the standard error of the regression:

yLOD = 3sy/x + a

we can calculate the corresponding concentration LOD from the regression line:

CLOD = (yLODa) ÷ b

which can be combined into the single equation:

CLOD = 3sy/x ÷ b

### The Significance of the LOD:

The limit of detection expresses the lowest concentration of analyte that can be detected for a given type of sample, instrument, and method. If a sample is measured as having a concentration below this value (or gives a reading indistinguishable from the baseline), the best we can say confidently about the sample is that any analyte present is below the LOD; you can never claim that the sample does not contain the analyte in question, since there is always the possibility that it does, but not in detectable amounts.

Whenever you perform an instrument calibration, you should always calculate the corresponding limit of detection; any result below this value should be quoted as being “< LOD”, with the LOD being clearly stated.

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