Figure 7. The FTIR spectral data for the nitrogen dioxide component in a multi-compo-nent mixture shown as an overlay; concentrations of the curves indicate a range from
0.35 to 3. 33 ppm in nitrogen.
17686
Actual
+
+
+
64
64
+
Uncorrected
Calibration
+ Validation
Correction
17686
Figure 10. This demonstrates an attempt to
fit a non-linear carbon monoxide calibration data set with a 1st order regression
analysis. Clearly not effective.
Scatter Plot With Fit
3. 5
3
2.5
Concentration
2
1.5
1
+
0.5
0
-0.5
-0.5 0 0.5 1 1.5 2 2.5
Area
+
Figure 8. Actual spectral data points overlaid with the 1st order regression function
along with the 95% confidence interval.
+
Uncorrected
Calibration
+ Validation
Correction
17686
Linear Versus Non-Linear
Calibration Behavior
All gases have non-linear absorbance
regions and may or may not have linear
regions. An additional complication to this
statement is that linearity is dependent upon
concentration and/or intensity of absorption. At this point it would be wise to remember that any calibration curve is not just a
function of the gas of interest but includes
the FTIR operational characteristics of the
specific instrument used. Therefore, after any
repairs or changes in the FTIR system, the
calibration curves must be, at a minimum,
validated and usually regenerated in their
entirety. In the case study we just reviewed,
the nitrogen dioxide data taken over that
specific absorbance region, in that specific
concentration range, and on that specific
instrument, exhibited linear behavior to a
high degree of accuracy. Not all gases are
this well behaved. Generally speaking, methods using large concentration ranges and
gases with sharp spectral features tend to
exhibit the worst non-linearity profile.
64 Actual 17686
One of the worst gases for non-linear
behavior is carbon monoxide. Figure 10
shows a calibration data curve for carbon
monoxide using a 1st order curve fit.
Clearly, this is not good technique. Figure
11 demonstrates that a 3rd order fitting
function yields a higher degree of accuracy.
Figure 12 plots the residual data verifying
the “goodness of fit.” Table 2 shows the
numerical values and the error associated
64
with each data point versus the fitting function. Figures 10, 11, and 12 and Table 2 were
generated using TQ Analyst – a total solutions calibration program available from
Thermo Fisher for the Nicolet product line
of FTIR instrumentation.
2.6
+
Figure 11. The same data as Figure 10
but now fit with an appropriate 3rd order
regression.
2
Standardized Residual
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-0.5
Residual Plot
Difference
+
+
0
0.5 1 1.5
Peak Area
2
2.5
-1.5
64
Actual
17686
Figure 9. The residual error plot showing
% error versus peak area data points for
the calibration data used to generate the
regression analysis; this is a graphic portrayal of the error data in Table 1.
Figure 12. The residual error plot for the
regression data set shown in Figure 11;
notice all data is within +/-3% of actual
value.
