Detectors response nonlinearity

Further, peak overlap results in nonlinear detector response vs concentration. Therefore, some other detection method must be used in conjunction with either of these types of detection. Nevertheless, as can be seen from Figure Ilf, chiroptical detection can be advantageous if there is considerable overlap of the two peaks. In this case, chiroptical detection may reveal that the lea ding and tailing edges of the peak are enantiomerically enriched which may not be apparent from the chromatogram obtained with nonchiroptical detection (Fig. He). 

The peak symmetry, resolution, and detector response are directly dependent on the concentration of the sample. As the concentration of a sample increases, the retention time, separation, and peak symmetry generally decrease. These phenomena are due to isotherm nonlinearity. The detector response may also be nonlinear above or below certain concentrations. In some cases, small amounts of a dilute component are irreversibly adsorbed to the column, leading to reduced recovery. Above some concentration, the response of any detector will cease to be linear. The UV-VIS is one of the most linear detectors, generally exhibiting at least three decades of linearity, while RI, electrochemical, and fluorimetric detectors have a markedly narrower range of linearity. 

Accuracy is a measure of the closeness of a measurement to the true value. Precision is a measure of how reproducible the measurements are. For many detectors, the accuracy of a measurement is maintained by user calibration. For some detectors, however, such as photodiode array detectors, accuracy relies on internal calibration. The linear dynamic range of the detector is the maximum linear response, divided by the detector noise. The detector response is said to be linear if the difference in response for two concentrations of a given compound is proportional to the difference in concentration between the two samples. Most detectors become nonlinear as the sample concentration increases. 

Figure 18 Calibration curves using an internal standard (IS). Analytes are quantified against an IS that has been added as early as possible in the analytical procedure. The ratios of detector responses for the analyte (fiA) and IS (R S) are plotted against the ratio of known amounts of analyte (A) and IS. When a sample is analyzed, the ratio Ra/Ris is measured. Then knowing the amount of IS added into the sample, the amount of analyte present in the sample can be estimated. Curves that do not pass through the origin of the graph or which are nonlinear are diagnostic of (a) chemical interference or sample carryover, (b) sample loss during the assay due to adsorption, and (c) saturation or cross-contribution between the IS and the analyte.

Practical understanding and appreciation of detector saturation limits are critical when using any of the aforementioned detectors. The saturation limit can be defined as the point at which a nonlinear detector response is observed with an increase in ion concentration. The saturation characteristics of a detector can be proportional to concentration up to a critical point, at which no additional signal can be obtained, or can be nonlinear, where detector response changes with concentration but in a nonlinear way. 

With pulsed or transient illumination, lag also results in a nonlinear detector response to incident light intensity. The effects of lag on the linearity of detector response can be reduced by using multiple readout scans, long dwell times, both resulting in longer readout times, or other schemes (13,14, ID ... 

A linear dependence between detector response and the amount of sample entering the detector is expected for phosphorus. The response for sulfur is inherently nonlinear and is described by 1(82) = A [S]", where 1(82 ) is the detector response, A an experimental constant, [8] the mass flow rate of sulfur atoms, and n an exponential factor. The theoretical value for n is 2, but in practice, values between 1.6 and 2.2 are frequently observed for the single flame FPD. Non-optimized flame conditions, compound-dependent decomposition, hydrocarbon quenching, and competing flame reactions that lead to de-excitation all contribute to this deviation. Decoupling the... 

For nonlinear detector responses calibration curves may be also determined by curve fitting. For such more complex calibration functions with more than one unknown parameter, additional information (e.g., about the physical foundations of the measuring method) or pulse experiments with different concentrations are necessary. In any case, it is advised to check the validity of the calibration curves in the low and high concentration ranges by separate experiments with different feed concentrations. 

The advent of perturbation theory for altered systems (see Section V,F) opens a new field for the application of perturbation theory—the field of perturbation sensitivity studies. This is the study of changes in effects of perturbations, or system alterations, caused by uncertainties or variations in input parameters. Examples are (1) the uncertainty of the change in an integral parameter (such as the breeding ratio) resulting from design variations due to uncertainties in cross sections, (2) nonlinear effects of cross-section uncertainties, and (3) the effects of data uncertainties, approximations in computational models, or design variations on the detector response in a deep-penetration problem that is solved with a flux-difference or an adjoint-difference method (see Section V,E). 

The limit of linearity is the concentration at which the behavior of the detector becomes nonlinear—successive increases in concentration result in a lower than proportional increase in the signal. If the concentrations of the samples or standards are too high, then they must be diluted by a factor of between 10 and 1000 or more to achieve a linear detector response. It is important to calculate the error on each point and the overall error of the curve. 

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