Detector Linearity

Detector linearity is the most important specification for a detector that is to be used for quantitative analysis. It is defined as the concentration range over which the detector response is linearly related to the concentration of solute passing through it. That is, over the linear dynamic range then,

(2)

where (V)	is the detector output,
(Cm)	is the concentration of solute sensed by the detector,
(A)	is a constant.

In practice, true linearity is not obtainable. Thus, it is important to have some measure of linearity that can be specified, so that comparisons can be made between detectors. Fowlis and Scott [13] proposed that for a closely linear detector, the response could be described by the following power function

(3)

where (r) is defined as the Response Index and the other symbols have the meanings previously ascribed to them.

Thus, for a truly linear detector, r = 1, and the proximity of (r) to unity will indicate the extent to which the response of the detector approaches true linearity. The response of some detectors that have different values for (r) are shown as curves relating the detector output (V) to solute concentration () in figure 12. It is seen that the individual curves appear as straight but significant errors can arise if linearity is assumed. Consider a binary mixture containing 10 %w/w of one component and 90 %w/w of the second component. By assuming all five detectors with responses indices defined in figure 1 are in fact linear, the errors involved can be calculated and the results are shown in table 2. Examination of table 2 shows that errors in the level of the smaller component can be as much as 12.5% (1.25% absolute) for, r = 0.94 and 9.5% (0.95% absolute) for r = 1.05.

Figure 12 Graph of Detector Output against Solute Concentration for Detectors with Different Response Indices