System and method of data reduction for improved exponential decay measurements

• US 6,915,240 B2
• Filed: 11/29/2001
• Issued: 07/05/2005
• Est. Priority Date: 11/29/2001
• Status: Expired due to Fees

• Current Assignee: Princeton University
• Original Assignee: Princeton University
• Inventors: Lehmann, Kevin, Rabinowitz, Paul
• Primary Examiner(s): Hoff, Marc S.
• Assistant Examiner(s): O MALLEY, MARY CATHERINE
• Application Number:
  US09/998,518
• Publication Number:
  US 20030101026A1
• Time in Patent Office: 1,314 Days
• Field of Search: 702/66, 702/70, 702 74- 76, 702/111, 702189-191, 702193-195, 702/197, 356437-440, 356/432, 250/343
• US Class Current: 702/189
• CPC Class Codes: G01J 3/28 Investigating the spectrum using colour filters G01J3/51
• CPC Class Codes: G01J 3/42 Absorption spectrometry; Double beam spectrometry; Flicker spectrometry; Reflection spectrometry beam switching arrangements G01J3/08
• CPC Class Codes: G01N 21/39 using tunable lasers

Abstract

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.

Claims

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.