BOREAL LASER GasFinderMC-2, Operation Manual

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9.5
Boreal Laser Inc. GasFinderMC Installation Manual — Appendices July 17th 2017
Appendix D — Explanation of R 2
When the GasFinderMC receives the returning laser signal after it has passed through the
sample gas, the electronics convert it to the shape of a specifi c waveform or curve. This
is the sample waveform. The
GasFinderMC also has a similar signal from the calibration
waveform. These curves are then digitised and compared as two numeric arrays.
An accepted mathematical procedure to compare curves or numeric arrays is the Linear
Least Squares Regression analysis. This analysis results in a measure of the similarity
( R 2 ), between the waveform of the sample gas and that of the reference cell gas. A perfect
similarity would give a value for R
2
of 1.0, and a total mismatch would be 0.0.
The blue line represents the Linear Least Squares fi t of the data and is the best fi t of a
straight line between the reference (X) and sample (Y) data points. The slope is a component
in the ratio-metric calculation of gas concentration.
Regression Analysis for
Waveform B
R2 = 0.04
Sample Waveform B
R2 = 0.04
Sample Waveform A
R2 = 0.98
Regression Analysis for
Waveform A
R2 = 0.98