How low can you go? A practical guide to the Limit of Detection

LOD from signal-to-noise ratio

Published 18th February 2017 by Andy Connelly. Updated 9th May 2017.

Introduction

Before you chose a piece of equipment or experimental method you need to ensure that it can detect the thing you want to measure (analyte) at the concentration present. For example, can your method detect 1ppb phosphate in sea water? If you can’t measure it then there is no point in making, or collecting, it!

  • Limit of Detection (LOD): Smallest concentration of analyte giving a significant response of the instrument that can be distinguished above the blank or background response.

An analogy for this would be, if you are trying to measure 5 μm then a 30cm ruler would not be suitable. 5 μm is effectively below the LOD of a 30cm ruler. An instrument with a suitable LOD might be a calibrated electron microscope as that would have the appropriate “Limit of Detection“ or LOD.

The LOD is only part of the story. Being able to detect something does not mean that you can quantify the results at these levels. You need to also work out the Limit of Quantification (LOQ):

  • LOQ: Smallest concentration of analyte that gives a significant response of the instrument and can be quantified to a reasonable level of accuracy and precision. It is also the the limit at which we can reasonably tell the difference between two different values of the amount of analyte.

While calculating the LOD it is vital to ensure you are measuring something that exists – not noise of the instrument. Demonstrating that your data are above the LOQ tells anyone looking at your data that trends in the data are real not just the result of noise.

DISCLAIMER: I am not an expert on statistics. The content of this blog is what I have discovered through my efforts to understand the subject. I have done my best to make the information here in as accurate as possible. If you spot any errors or admissions, or have any comments, please let me know

Sample LOD vs instrument LOD

Each analysis you run will have an associated LOD for the analyte in question. This LOD is dependent on many factors but I have collected them into two terms:

  • Sample LOD: this is caused by background contamination from reagents or the method you have used. Also, interferences from the nature of your sample. It can, to an extent, be controlled during the sample preparation process.
  • Instrument LOD: this is generally due to the technical limitations of that instrument and the method being used. This is down to your choice of instrument and method for your particular samples.

Presenting data

When presenting data, it is vital that you do not report data with values below the LOD. These values are just noise and have no physical meaning. It is also useful to let people know whether the values are below the LOQ as this tells them not to trust the accuracy of this value but also lets them know that the value is not below detectability (effectively zero). Table 1 shows an example of data presentation.

Data LOD/LOQ
Table 1: Example data for analysis of heavy metals. The Cd and As concentrations are below LOQ / LOD and so written as such. It is important to give the value of LOQ / LOD (LOQ=5ppm, LOD=3ppm).

Table 1 can be read as showing that in this sample there is no detectable amount of As. It may be 0ppm it may be 2ppm it is impossible to know but it is effectively zero for this analysis. The table also shows that while there is a detectable amount of Cd the exact amount cannot be quantified; there is definitely some present but the amount is below 5ppm.

How to measure and calculate LOD

There are three main methods for estimating the limit of detection. However, many others are available (see reference [1]). These will give a limit of detection in terms the instrument measures (e.g. peak height, counts, etc.). This would then need to be converted into a measurement (e.g. ppm, percentage, etc.)

  • Blanks
  • Signal-to-noise
  • Intercept

Blanks measurement with a value

A blank is normally a sample that has been through all of your experimental processes but has no sample present (experimental blank). It could also be a solution/material which is made up with the same composition as your matrix (matrix blank) e.g. 10% HCl.

When making up standards you should use the same matrix as the analyte of interest is sitting in (e.g. 10% acid). You should also include “matrix blanks” which have the same matrix as your samples but with none of the analyte. These, in most cases, should also be included in your calibration.

To calculate the LOD you will ideally need a matrix blank. You measure this blank six to ten times. This gives you enough data to calculate statistically robust values for the mean (and standard deviation). Equation 1 can then be used to calculate LOD.

eqn_lod_blank
Equation 1. where y-bar bl is the mean blank value and sbl is the standard deviation of the blank values.
Example of a LOD calculation
Figure 1: Example of a LOD calculation where results are measured in counts, LOD is calculated and then recalculated as a ppm.

Signal to noise ratio

If you get a signal from the blank then you can use the signal-to-noise ratio using Equation 2 (see Figure 2). This method is used in techniques where data exists as peaks on a continuous trace. A good example of this is ion chromatography where a peak exists against a background of noise. In such techniques, the LOD effectively tells you whether the peak you are seeing is real or just part of the back ground noise. Figure 2 shows three traces measured from three separate “blanks”.

A. The signal at the peak position is very low and so the LOD for this analyte is low. This suggests that if there is some contamination, or a false signal, it is within the noise.

B. Comparing this trace to spectra A there is a much greater signal at the peak position. The LOD for this system is larger and so we will not be able to detect the analyte to the same level.

C. As the signal gets larger compared to A and B this may indicate a contamination of the blanks. Certainly, the LOD will be much higher and so not as useful for measuring low concentrations.

D. This spectra highlights one of the issues with signal-to-noise ratio for calculating LOD. The signal is the same as in spectra B; however, the noise is much less suggesting an instrument that is better set up. The calculated LOD for this system will be much higher than in spectra B event though the instrument is better set up.

signal_and_noise
Figure 3: Spectra with various signal-to-noise ratios.
eqn_lod_sig_noise
Equation 2

Intercept

In techniques where we have a calibration curve we can use the intercept to calculate the LOD (see Equation 3&4). The calibration curve is an easy way to calculate the LOD of a technique. However, it relies on your calibration standards being matrix matched to your samples, otherwise you are only looking at the LOD of the instrument without taking into account any contamination or method interferences from your samples. You also need to ensure that your calibration curve is not fixed to go through the origin.

LOD intercept
Equation 3
eqn_sxy
Equation 4

Limit of quantification

The LOD is only part of the story. Being able to detect something does not mean that you can quantify the results at these levels. You need to also work out the Limit of Quantification (see Equation 4, 5, and 6). These calculations can only ever give an estimate of the LOQ. If the estimated LOQ is near the values you want to measure then further work would be required to get a more accurate idea of the LOQ

If LOD or LOQ are really important, for example if your data are very close to your calculated values, then it is good practice to analyse a test solution containing the estimated LOD or LOQ (or a range of test solutions around these values). This is the only way to be sure of these values and so sure you are measuring something that exists – not noise of the instrument.

eqn_loq_signoise
Equation 5
eqn_loq_blank
Equation 6
Intercept LOQ
Equation 7

Experimental limit of detection

Experimental science is never simple and LOD is no exception. The sample and instrument LOD is only the start. We also need to look at what happened to the sample beforehand. Figure 3 shows how, from an initial extraction, the concentration of the sample decreases significantly. This also means that the LOD changes dramatically.

You may have picked an instrument with a LOD of 0.5ppm for your rock sample. However, before giving the sample to the analyst you have dissolved it in acid and diluted the acid so it doesn’t damage the instrument. When analysing the blanks the analyst also finds some background contamination. All this together means that while the instrument has a LOD of 0.5ppm when this result is recalculated for your original sample the LOD might be as much as 1000ppm (0.1%).

So, when you are designing your experiment you need to think not only about what the machine is capable of but ALSO what you are going to do to your sample before it arrives at the machine.

Experimental LOD
Figure 3: Experimental LOD. This figure shows the effect of dilution and background contamination on LOD.

Summary

The LOD is a really important parameter in deciding what methods and equipment to use in experiments. Always check before you start that the instrument can “see” what you are looking for. If it is below the LOD then you may be wasting your time.

Glossary

lod_glossary

References

[1] Alankar Shrivastava, Vipin B Gupta,“Methods for the determination of limit of detection and limit of quantitation of the analytical methods”, Chronicles of Young Scientists, Vol. 2 | Issue 1 | Jan-Mar 2011.

Further reading

  1. Statistics and Chemometrics for Analytical Chemistry, Miller & Miller, 5th ed. Pearson (2005)
  2. Data analysis for chemstry: An introductory guide for students and laboratory scientists, Hibbert & Gooding, 2006
  3. Statistics: A guide to the use of statistical methods in the physical sciences. Roger Barlow, John Wiley & Sons, 1989.
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