Linearity and Detection Limits
ICP Operations Guide: Part 7 By Paul Gaines, Ph.D.
Overview
An ICP can be wheeled into a laboratory and start collecting data the same day. But before it can be trusted, the operator needs to establish three performance characteristics: linearity, detectability, and spectral integrity. This section covers how to determine detection limits (LOD, LOQ, IDL) and the linear working range on your instrument, and how to use that data to decide whether a method is feasible before you commit to it.
The next few parts of this guide provide practical information for the operator in the realization and demonstration of the key performance characteristics designed into their ICP by the manufacturer.
Defining and being able to realize your instrument's performance characteristic is an investment that will save time over the years to come and allow you to make the right choices.
What Is the Limit of Detection (LOD)?
The limit of detection is the lowest concentration of an analyte that can be reliably distinguished from a blank. It is defined as three times the standard deviation of the measurement as the analyte concentration approaches zero:
LOD = 3 × SD0
where SD0 is the standard deviation at zero concentration. SD0 is obtained by extrapolation: plot standard deviation (y axis) against concentration (x axis), using three concentrations spanning the low, mid and high regions of interest, each analysed roughly 11 times, and extrapolate back to zero. The determination should be made in a matrix that matches the sample.
A result at the LOD tells you the analyte is present. It does not tell you how much is there — for that you need the limit of quantitation.
See also the IUPAC definition of limit of detection.
What Is the Limit of Quantitation (LOQ)?
The limit of quantitation is the lowest concentration that can be measured with acceptable precision. It is defined as ten times the standard deviation at zero concentration:
LOQ = 10 × SD0
A result reported at the LOQ carries an uncertainty of roughly 30% at the 95% confidence level. Below the LOQ but above the LOD, you can state that the analyte is present but you cannot put a defensible number on it.
LOD vs LOQ: What Is the Difference?
| |
Limit of Detection (LOD) |
Limit of Quantitation (LOQ) |
| Formula |
3 × SD0 |
10 × SD0 |
| Answers |
Is the analyte present? |
How much analyte is present? |
| Typical uncertainty |
Qualitative — presence only |
~30% at 95% confidence |
| Report as |
"Detected, < LOQ" |
A concentration with an uncertainty |
| Use |
Screening, presence/absence |
Quantitative results, regulatory reporting |
IDL, MDL and LOD: Which Detection Limit Do You Need?
| Term |
What it measures |
Where it comes from |
| IDL — Instrument Detection Limit |
What the instrument can detect in a clean acid blank, with no sample preparation |
Calculated by the instrument software from a blank and standards series |
| MDL — Method Detection Limit |
What the whole method can detect, including digestion, dilution and matrix |
Determined in the sample matrix, following the full procedure end to end |
| LOD — Limit of Detection |
The general term. In practice, usually means the method detection limit |
3 × SD0 in a matrix-matched blank |
The distinction matters commercially, and the page's own worked example shows why. An IDL of 0.0008 µg/mL Cr on the instrument becomes a detection limit of 4 ppm on the original sample once the 0.2 g into 1000 mL dilution is accounted for — and a realistic working figure of roughly 16 ppm, four times the IDL. Quoting an instrument detection limit as though it were a method detection limit overstates what the method can do by three orders of magnitude.
The formal MDL procedure is defined in EPA 40 CFR Part 136, Appendix B.
What Is Linearity and Linear Dynamic Range?
Linearity is the range over which instrument response is directly proportional to analyte concentration. The linear dynamic range runs from the limit of quantitation at the bottom to the concentration at which the plot of concentration against response departs from a straight line at the top.
Below the LOQ, the response is real but too imprecise to quantify. Above the upper limit, the detector begins to saturate and the calibration curve rolls over — results in this region read low, and will do so silently unless the range has been established in advance.
Modern ICP-OES instruments typically deliver five to six orders of linear dynamic range, and ICP-MS eight or more. The practical range for a given line is narrower than the instrument's headline figure, because it is bounded by the detection limit for that line at the bottom and by the onset of self-absorption or detector saturation at the top. This is why the linear range is established per line, not per instrument.
Defining ICP Performance Characteristics
The following steps are intended as a practical guide for the determination of an ICP's performance characteristics:
- Read the operating manual and familiarize yourself with the software, key instrumental parameters and preferred settings before the instrument is installed.
Most instruments are supplied with optimization and wavelength or mass calibration standards that will be used during set-up by the service technician and are intended for use on a regular basis by the operator. Discuss the optimization process with the manufacturer as well as the preferred settings for the key instrumental parameters.
The remaining steps assume that the operator fully understands and is able to perform the optimization process that has been defined by the manufacturer as well as the spectral limitations of the instrument.
- Select the lines to be studied for each element ('lines' is used in this document to mean either wavelength or mass).
Line selection is based upon spectral interference issues, detection limit requirements and working range requirements. Select as many lines as possible within practicality for each element. The greater the number of lines, the greater the flexibility.
- Prepare single element standards over the anticipated working range for each element. The range of standards depends upon the analytical requirements. The following ranges are suggestions only:
- Radial view ICP-OES: 0.0, 1, 10, 100, and 1000 µg/mL
- Axial view ICP-OES: 0.0, 0.1, 1, 10, and 100 µg/mL
- Quadrupole (R~ 300) mass filtered ICP-MS: 0, 1, 10, 100, and 1000 ng/mL
This step is important because these data can be used to determine instrument detection limits (IDL), linear working ranges, and spectral characteristics such as background equivalent concentrations (BEC) and spectral interferences. With most modern (if not all) instruments, the spectra obtained for each element at each concentration can be saved for review later. In addition, the software will calculate the IDL and BEC plus the linear regression of each line will establish the linear working range. All of this is typically done for the operator by the software that comes with the instrument. If at all possible, attempt to:
- Use single element standards that have the trace metals impurities reported on the certificate of analysis. Most chemical standards manufacturers provide this information with their single element standards. These data are important in identifying direct spectral overlap interferences and in not identifying an impurity as an interference of this type.
- Store all spectra on computer and collect the spectra for all lines of interest on each and every solution. This means that if you are interested in possibly using up to 6 lines for roughly 72 elements, then each solution spectrum totaling 72 x 6 = ~ 432 lines per solution and ~ 432 x 5 = 2160 spectra for each element need to be stored for future reference. Most ICP-MS applications would require far fewer data to be collected due to the reduced number of lines available and/or feasible.
- Wash blank acid solution through the instrument for several minutes 'between elements' and always analyze a blank at the beginning of each element concentration series. Look for the presence of the prior element analyzed to confirm that it has been completely washed out of the introduction system.
- Having the data available on a desktop computer is convenient and allows the analyst to construct potential spectra by calling up the element and the anticipated concentration for each element in the analytical sample. Having several lines available makes the job of line selection easy as well as the estimation of the line's sensitivity and linearity. Constructing these composite spectra from pure single element solutions eliminates confusion as to the identity of the line. The following example is intended to illustrate the process:
Examples of Spectra
FYI: All spectra were obtained using a concentric glass nebulizer with no problems around salting out or plugging.
The following example is for an application where a submitter has been obtaining minor levels (0.1 to 1.0 %) of Cr in an alloy containing roughly equal amounts of Fe and Ni. The laboratory where this alloy is analyzed uses a procedure where 0.2 grams of the sample is dissolved in 5 mL of a 1:1 HNO3 / HCl mixture and diluted to 1000 mL with DI water. The analyst is informed that a limit of detection (LOD = 3SD0) of 1 ppm Cr based upon the original sample and the ability to quantify the Cr to within ±10 % relative at the 10 ppm level is an absolute minimum requirement.
The submitter then asks the analyst the usual question, "I need the results tomorrow - can you do it?" The analyst does a quick calculation and determines that using the most sensitive Cr line and the current procedure, the lowest possible detection limit is 4 ppm and a more realistic estimation would be ~ 4 times the IDL or ~ 16 ppm. The analyst then pulls up the following spectra, instrument detection limits, and linear regression data which were obtained on their radial view instrument about four years ago when installed using pure single element solutions as described above.
The 205.552 nm Cr line was found to be the most sensitive of the 16 Cr lines originally characterized with an IDL of 4.0 ppm = [ (0.0008 µg/mL Cr IDL) x 1000 ] / 0.2 based upon original sample size and dilution as described above. However, the spectrum of a 0.1 ppm Cr standard shows significant interference from both Ni and Fe at a concentration of 100 ppm making the line useless at low ppm Cr levels (see Figures 7.1 and 7.2).
Figure 7.1:Spectra of pure 100 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 205.552 nm Cr wavelength
Click to enlargeFigure 7.2:IDL, BEC and regression data for the 205.552 nm Cr line
Click to enlarge
The analyst then begins the relatively simple process of identifying a Cr line with the most sensitivity that is spectrally clean. Figures 7.3 and 7.4 show the line identified using the same scan data shown for the 205 Cr line. The 267.716 nm Cr line looks clean at the current dilution factors and has an IDL of 0.0016 µg/mL Cr which increases the detection limit to somewhere between 8 to 32 ppm.
Figure 7.3:Spectra of pure 100 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 267.716 nm Cr wavelength
Click to enlargeFigure 7.4:IDL, BEC and regression data for the 267.716 nm Cr line
Click to enlarge
The good news is that the 267.716 line looks spectrally clean and the possibility of increasing the sample size while lowering the final volume by a factor of 100 is possible (i.e., 2 grams sample up to 100 mL using 20 mL of 1:1 HCl/ HNO3). The concentrations of the Fe and Ni in the final solution would be ~ 10,000 µg/mL each. This capability was confirmed when 40,000 µg/mL solutions of both Fe and Ni were scanned as shown in Figure 7.5. These spectral data indicate a realistic detection of << 1 ppm Cr.
Figure 7.5:Spectra of pure 40,000 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 267.716 nm Cr wavelength
Click to enlargeFigure 7.6:Simulated spectrum of a solution produced from 2 grams → 100 mL solution of a 50/50 wt. % Ni/Fe alloy containing 1.25 ppm Cr at the 267.716 nm Cr wavelength
Click to enlarge
The spectra in Figure 7.5 were used to artificially produce Figure 7.6 which approximates signals that would be measured for a Fe/Ni alloy where 2 grams to 100 mL dilution were made on a sample containing 1.25 ppm Cr. The entire investigation was performed using spectra that had been stored on computer (i.e., the analyst can literally provide an answer as to project feasibility while speaking on the phone with the client).
The above process is not intended to take the place of method validation, but rather to arm the analyst with sufficient data to make intelligent choices during the initial stages of method development.
How Detection Limits Fit into Method Validation
Establishing LOD, LOQ and linear range is one part of demonstrating that a method is fit for purpose. The full validation process also covers specificity, accuracy and bias, repeatability, and robustness. These are addressed in detail in Part 17: Method Validation of our Trace Analysis Guide.
Frequently Asked Questions
What is the limit of detection?
The lowest concentration of an analyte that can be reliably distinguished from a blank, defined as three times the standard deviation of the measurement as concentration approaches zero (LOD = 3 × SD0). It confirms the analyte is present but does not quantify it.
What is the difference between LOD and LOQ?
LOD (3 × SD0) is the lowest concentration that can be detected. LOQ (10 × SD0) is the lowest that can be measured with acceptable precision — roughly 30% uncertainty at 95% confidence. Between the two, you can say the analyte is there but not how much.
How do you calculate the detection limit?
Determine SD0, the standard deviation as concentration approaches zero, by analysing three concentrations spanning your range roughly 11 times each, plotting standard deviation against concentration, and extrapolating to zero. Multiply by three for the LOD and by ten for the LOQ. Do it in a matrix that matches your samples.
What is the difference between an instrument detection limit and a method detection limit?
The IDL is what the instrument achieves on a clean acid blank with no sample preparation. The MDL accounts for the entire method — digestion, dilution and matrix — and is always higher, often by orders of magnitude. An IDL of 0.0008 µg/mL becomes a 4 ppm detection limit on the original sample once a 0.2 g to 1000 mL dilution is applied.
What is the linear dynamic range of an ICP?
The concentration range over which response is proportional to concentration, running from the LOQ at the bottom to the onset of non-linearity at the top. It is established per emission line, not per instrument, because it is bounded by that line's detection limit and its saturation behaviour.
Why does a detection limit depend on the wavelength you choose?
Because sensitivity and spectral interference vary by line. The most sensitive line is not always usable: in the worked example above, the 205.552 nm Cr line has the better IDL but is unusable in an Fe/Ni matrix, while the less sensitive 267.716 nm line is spectrally clean and gives the better real-world detection limit.
