The Spectroscopy Net
Gateway to Spectroscopy > Data Acquisition > Calibration

Calibration

The quality of an analysis depends on the quality of the calibration. The quality of a calibration depends on attention to detail.

The quality of an analysis depends on the quality of the calibration. The quality of a calibration depends on attention to detail.

  1. Selection of calibration samples:
    - number
    - concentration ranges
    - families
  2. Preparation of calibration samples
  3. Choice of calibration function
  4. Precision during calibration
  5. Optimisation of calibration curve

In optical emission spectrometry a typical calibration function has the form:

[Calibration function]

where Ci is the content (or concentration) of element i; ai to ci and dj are fitting parameters; Ii is the signal from element i; and Ij is the signal from an interfering element j, where there may be up to N interfering elements. -ai is called the BEC (background equivalent concentration).

The calibration function given here is linear (in its dependence on the fitting parameters) and second order (the highest power of Ii). Sometimes higher order functions or non-linear functions are used. Several simplifications are also possible. If ci = 0 then the calibration function is first order. If all dj = 0 then there are no interference corrections.

To determine the best values for the fitting parameters it is usual to find the minimum of a least-squares function:

[Chi-squared]

where wi are the weights given to each calibration point i, Ci is the known content and and  C^i is the content estimated using the calibration function. By minimising the least-squares function we are endeavouring to make the estimated contents as close as possible to the known contents. A higher weight means that a point has a bigger effect. Generally, it is necessary, in optical emission spectrometry, to give different weights to different points, because the precision of measurement may vary from point to point or the accuracy of the known concentration may vary from sample to sample. The software will normally set appropriate weights automatically, but occasionally it is necessary to intervene manually.

Several parameters are available to determine the goodness of fit. Unweighted equations are shown here for simplicity though, of course, weighted functions should be used.

 

Submenu