System and method of data reduction for improved exponential decay measurements
A novel system and method for data reduction for improved exponential decay rate measurement in the present of excess low frequency noise. The system and method fit the tail of a record to a straight line wherein the straight line is extrapolated to the entire record and then subtracted from the initial data points before a logarithmic transformation is taken.
1. A method for determining an exponential decay rate of a signal in the presence of noise, said method comprising:
receiving an exponentially decaying signal from a detector;
digitizing said signal to form a first array of data points;
estimating a baseline value of said signal by averaging a final fraction of said data points;
subtracting said baseline value from said first array to generate a second array;
identifying a last data point on said second array occurring before a negative or nil valued data point on said second array;
scaling an ordinate value of said last data point by a factor greater than unity to determine a new first data point for a baseline fit on said first array;
fitting remaining data on said first array to a straight line to determine an estimate for a sloping baseline and said noise;
subtracting said straight line from said data points to establish a resulting array;
identifying a last data point on said resulting array occurring before a negative or nil valued data point on said resulting array;
performing a logarithmic transformation of said resulting array up to said last data point on said resulting array; and
determining said decay rate of said signal;
wherein said noise includes broadband noise and excess low frequency noise and wherein said low frequency noise has spectral components having a period greater than four times a record length.
2. The method of claim 1 wherein said determining step includes determining said decay rate of said signal by a weighted least squares fit to said transformed data.
3. The method of claim 2 wherein said weighted least squares fit includes weighting each transformed data point inversely proportional to a square of said value of said digitized signal minus said estimated baseline value.
4. The method of claim 1 wherein said signal is generated in a ring-down cell.
5. The method of claim 4 wherein said ring-down cell includes two or more mirrors in any geometry that produces a stable optical cavity.
6. The method of claim 4 further comprising energizing said ring-down cell.
7. The method of claim 6 wherein said energizing step includes utilizing a laser.
8. The method of claim 6 wherein said laser is a continuous wave laser.
9. The method of claim 6 wherein said laser is a pulsed laser.
10. The method of claim 1 wherein said detector includes a photodector.
11. The method of claim 1 further comprising removing transient points from said first array.
12. The method of claim 11 wherein said subtracting a baseline value includes subtracting a DC level.
13. The method of claim 1 wherein said subtracting a baseline value includes subtracting a DC level.