Optimal weighted averaging pre-processing schemes for laser absorption spectroscopy

A method of processing tunable diode laser absorption spectroscopy (TDLAS) signals to improve measurement precision, the method comprising:

• performing, using a TDLAS instrument, a series of laser scans through a sample gas and measuring a transmission amplitude for each laser scan output as a series of raw intensity measurement data points;
• modeling, by a digital signal processor, noise in the raw intensity measurement data points to select weighting coefficients for each laser scan, wherein the selected weighting coefficients are given as
• =
• C
• k
• Σ
• k
• ′
• =
• 1
• K
• ⁢
• C
• k
• ′
• 2
• in the case where the noise is dominated by electronic sources independent of measured volume, wherein the selected weighting coefficients are given as
• =
• 1
• KC
• K
• in the case where the noise is dominated by changes in measurement volume, and wherein the selected weighting coefficients are given as
• =
• C
• k
• (
• C
• k
• 2
• ⁢
• σ
• v
• 2
• +
• σ
• s
• 2
• )
• ⁢
• Σ
• k
• ′
• =
• 1
• K
• ⁢
• C
• k
• ′
• (
• C
• k
• ′
• 2
• ⁢
• σ
• v
• 2
• +
• σ
• s
• 2
• )
• in the general case where neither electronic noise nor measurement volume fluctuations dominate the noise, wherein, in each of the above equations, is the selected weighting coefficient, CK is the measured transmission amplitude of each laser scan k, σe2 is variance of electronic noise, and σv2 is variance of noise within the measurement volume;
• performing, by the digital signal processor, a weighted average calculation using the selected weighting coefficients upon the raw intensity measurement data points to output a resulting spectrum from the TDLAS instrument with a reduced noise contribution in the measurement data points;
• and
• analyzing the resulting spectrum output from the TDLAS instrument to produce a desired measured quantity for the sample gas.