Explanatory notes on spectrometer calibration

Calibration comprises measurement of calibration samples and determination of the functional relationship between the intensity I for the calibration function or calibration curve . It includes relationships between vaporization, excitation, radiation offtake, dispersion and the measured value. The steepness and curvature of calibration curves are largely determined by the radiation source; SR and LOD are additionally determined by the radiation source; SR and LOD are additionally determined by the radiation offtake and dispersion. Since spectrochemical analysis is a process of analysis by comparison, it is necessary to carry out calibration with samples of accurately known concentration, the calibration samples. The calibration function must not be confused with the function inverse to it-the read-out or evaluation function.

In practice, calibration function are often only stated in a form which is implicit in their inverse evaluation functions. To determine these functions, objective verifiable methods eg. regression methods, should be used ie. The popular bent ruler or curved ruler is out-dated.

In the case of the
calibration function I=f_{1}(c), the concentration of the calibration samples
are assumed to be free of error, and the errors are imputed entirely to the
spectrometer method, so that the preconditions for regression calculations are
created . Correlation calculation showing correlation coefficients as a quality
index are useless. With the evaluation function c=f_{2}(I) the
concentration c of an analyte in an analytical sample is determined, which is
accordingly subject to error.

For AES there is
no theory of calibration curves which can be used for practical purposes. These
are formulae for which it is assumed that it is possible to represent the
relationship between line intensity and concentration as a power function: I=I_{0}c^{k}.
It has been found, when testing calibration curves, that the deviations of the
true calibration from a calibration approximated by the exponential law are
often not acceptable.

The calibration function can be represented mathematically in various ways:

Linear calibration
function: I=f(c)=a_{0}+a_{1}c

None-linear
calibration function: I=f(c)= a_{0}+a_{1}c+a_{2}c^{2}+…a_{n}c^{n}.

The non-linear calibration function can be divided into sections in which linear or non-linear functions can again be formulated.

The extent to which the regression approaches the true course of the calibration curve can be discerned from the residual scatter, namely at the point when the addition of further terms to the approximation function does not produce any further improvement in the residual scatter.

As regressions
carry out calculations according to the equation Σ(ΔI)^{2}=min, because of the quadratic factor,
some measurement point remote from the main population will have a marked
effect on the course of the best fit curve and thus on quality, expressed in
the form of SR. Checks should therefore be carried out for these samples to
ascertain whether the measurement values are not subject to systematic errors
ple, wrong analysis, spectrum interference.

If the calibration curve is available in the form of a diagram, there are various possible approximation methods, the simplest being to store tables, but this method requires most storage space. A more practicable way is approximation by polygons and polynomials.

Some advice on drawing calibration curves:

Make sure that the co-ordinates are correctly assigned. The intensity should be plotted on the abscissa and the nominal value on the ordinate.

Co-ordinates should be clearly labelled and sensible sub-divisions should be used. The co-ordinate unit selected should be 1:1,1:2,1:5 or orders of magnitude of the variable, not 1:3or1:4. If the division value selected is wrong. It is easy to get lost. Calibration curves should carry a large quantity of data in order to simplify checks. Do not forget wavelengths, method conditions, characteristic calibration curve variables, types of sample and date. Measurement points for different sample qualities should be entered with different identification marks.

Be careful when drawing the best fit curve through the points. Be careful when extrapolating. The curve does not have to pass through the upper and lower measurement points at all costs. “Best fit” calculated curve for the measurement points and check whether the mathematical equation fits.

The co-ordinate system should be represented on graph paper with mm squares so that, after holes have been punched on the side provided for this purpose, the diagram can be read front or from the right.

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