Method of calibrating a wavelength-modulation spectroscopy apparatus
Several methods of calibrating a wavelength-modulation spectroscopy apparatus configured to measure a concentration of an analyte in a sample gas are disclosed. Each of the methods allows for calibration and recalibration using a relatively safe gas regardless of whether the sample gas for which the concentration of the analyte can be determined is a hazardous gas. In one embodiment of the invention, calibration that is sample-gas specific is accomplished by determining a first slope coefficient and calibration function for the sample gas, after which a scaling factor can be determined based on the first slope coefficient and a second slope coefficient for the same or a different sample gas and used in a subsequent calibration (or recalibration) to scale the calibration function. In other embodiments of the invention, calibration that is not sample-gas specific is accomplished to allow for the determination of the analyte concentration in variable gas compositions and constant gas compositions.
1. A method of calibrating a wavelength-modulation spectroscopy apparatus configured to measure a concentration of an analyte in a sample gas, said method comprising the steps of:
determining a first slope coefficient corresponding to a reference pressure of a first sample gas and a reference temperature of said first sample gas, and determining an intercept coefficient reflecting contribution from the noise floor, said determinations based on a first plurality of harmonic spectra of known concentrations of said analyte at said reference pressure and said reference temperature of said first sample gas;
determining a plurality of values of a temperature-dependent constant reflecting spectral line intensity and determining a plurality of values of an effective pressure-broadening coefficient at a plurality of values of temperature of said first sample gas, said determinations based on said intercept coefficient and a second plurality of harmonic spectra of one or more known concentrations of said analyte at said plurality of values of temperature of said first sample gas;
determining a temperature-dependence exponent of said effective pressure-broadening coefficient for said first sample gas; and
determining a plurality of values of a calibration function for said first sample gas, said determination based on said plurality of values of said temperature-dependent constant and a plurality of effective pressure-broadening coefficient values computed based on said temperature-dependence exponent.
2. The method of claim 1 , further comprising the steps of:
determining a second slope coefficient corresponding to said reference pressure and said reference temperature of said first sample gas, and determining a second intercept coefficient reflecting contribution from the noise floor, said determinations based on a third plurality of harmonic spectra of known concentrations of said analyte at said reference pressure and said reference temperature of said first sample gas;
determining a scaling factor, said determination based on the ratio of said second slope coefficient and said first slope coefficient; and
scaling said plurality of values of said calibration function for said first sample gas by said scaling factor.
3. The method of claim 1 , wherein said method is performed for a second sample gas, wherein a plurality of values of a calibration function for said second sample gas are determined.
4. The method of claim 3 , further comprising the steps of:
determining a second slope coefficient corresponding to said reference pressure and said reference temperature of said first sample gas, and determining a second intercept coefficient reflecting contribution from the noise floor, said determinations based on a third plurality of harmonic spectra of known concentrations of said analyte at said reference pressure and said reference temperature of said first sample gas;
determining a scaling factor, said determination based on the ratio of said second slope coefficient and said first slope coefficient; and
scaling said plurality of values of said calibration function for said second sample gas by said scaling factor.
5. The method of claim 4 , wherein said second sample gas is hazardous and said first sample gas is relatively safe.
6. The method of claim 1 , wherein said method is performed during or before a manufacturing stage of said apparatus.
7. The method of claim 3 , wherein said method is performed during or before a manufacturing stage of said apparatus.
8. The method of claim 2 , wherein said method is performed during or after a manufacturing stage of said apparatus.
9. The method of claim 4 , wherein said method is performed during or after a manufacturing stage of said apparatus.