Calibrating an optical FMCW backscattering measurement system
The object of the invention is to provide a method of calibrating an optical FMCW backscattering measurement system that improves the precision of the measurement. The problem is solved by a method comprising the steps of A. Converting said received sensor signal to a complex received electrical signal as a function of said modulation frequency fm, said complex received electrical signal being represented by a magnitude part and a phase angle part as a function of said modulation frequency fm; B. Performing a transformation of said received electrical signal to provide a backscattering signal as a function of location between said first and second ends of said sensor and beyond said second end; C. From said backscattering signal as a function of location determining characteristics of a curve representative of said backscattering signal beyond said second end; D. Correcting said magnitude part of said received electrical signal and said phase angle part of said received electrical signal in a predetermined dependence of said curve; and E. Repeating step B) on the basis of the corrected received electrical signal.
1. A method of calibrating an optical FMCW backscattering measurement system, the system comprising an excitation and evaluation part and a longitudinally extending sensor, the sensor having a first and a second end, the excitation and evaluation part being adapted for exciting a frequency modulated light signal with modulation frequency fm and for evaluating a sensor signal received from the first end of the sensor, the sensor being adapted for capturing a data signal based on the frequency modulated light signal from which physical parameters of spatially distributed measurement points of the sensor along its length between the first and second ends may be extracted, the method comprising the steps of
A. converting said received sensor signal to a complex received electrical signal as a function of said modulation frequency fin, said complex received electrical signal being represented by a magnitude part and a phase angle part as a function of said modulation frequency f m ;
B. performing a transformation of said received electrical signal to provide a backscattering signal as a function of location between said first and second ends of said sensor and beyond said second end;
C. indicating said backscattering signal as a function of location determining characteristics of a curve representative of said backscattering signal beyond said second end;
D. correcting said magnitude part of said received electrical signal and said phase angle part of said received electrical signal in a predetermined dependence of said curve;
E. repeating step B on the basis of the corrected received electrical signal.
2. The method according to claim 1 further comprising a step F of optionally repeating C, D, and E until a predetermined criterion is fulfilled.
3. The method according to claim 2 wherein said predetermined criterion is that said curve representing said backscattering signal beyond said second end of said sensor can be approximated by a straight line with a slope of approximately 0.
4. The method according to claim 3 wherein said slope is less than 0.5 samples.
5. The method according to claim 2 wherein said predetermined criterion comprise the criterion that the mean value of the samples for a part of or all of said backscattering signal beyond said second end is less than 0.5 samples.
6. The method according to claim 1 wherein said correction of said magnitude part of said received electrical signal comprises correcting the magnitude data by an initial correction amount ΔH 0 (0) at the modulation frequency f m equal to 0.
7. The method according to claim 6 wherein said initial correction amount AH 0 (0) is set to a predetermined value.
8. The method according to claim 6 wherein said initial correction amount AH 0 (0) is determined by the amount of deviation of the mean value of noise in the backscattering curve from 0.
9. The method according to claim 6 , wherein said correction of said phase angle part of said received electrical signal comprises determining an initial off-set value Δφ o (0) of the phase angle of the received electrical signal as a function of said modulation frequency f m around f m =0; and by subsequently correcting data representing said phase angle of the received electrical signal as a function of modulation frequency f m with said off-set value.
10. The method according to claim 9 wherein said initial off-set value Δφ o (0) is set to a predetermined value.
11. The method according to claim 9 , wherein said initial offset value Δφ o (0) is determined by linear extrapolation of the phase angle data for f m →0 Hz.
12. The method according to claim 1 wherein A, B, C, D, and E of said calibration procedure are performed in each measurement cycle.
13. The method according to claim 9 wherein D further comprises determining a residual correction factor ΔH res (0) and determining a residual off-set value Δφ res (0), both being based on backscattering data calculated from data representing said magnitude part and said phase angle part, respectively, as a function of said modulation frequency f m after correction by said initial correction amount AH 0 (0) and said initial off-set value Δφ o (0) respectively, wherein the value of said residual correction factor ΔH res (0) is based on the mean value of the average level of said backscattering signal beyond said second end of said sensor, and the value of said residual off-set value Δφ res (0), is based on the value of the slope of said backscattering signal beyond said second end of said sensor.
14. The method according to claim 13 wherein said determinations of correction factor ΔH res (0) and off set value Δφ res (0), are based on averaged backscattering curves.
15. The method according to claim 1 wherein said calibration is performed using a standardized optical sensor with well-known characteristics.
16. The method according to claim 13 wherein said calibration is performed if characteristics of the sensor changes or if other characteristics of the system have or are suspected to have changed.
17. The method according to claim 1 wherein said measurement system is a Raman backscattering system adapted for measuring a spatially distributed temperature profile.
18. The method according to claim 1 wherein said calibration method is performed for signals representative of Anti-Stokes as well as for Stokes signals.
19. The method according to claim 1 additionally comprising a cross talk correction procedure comprising:
G1) determining and storing cross talk between measurement channels of the measurement system with a specific measurement procedure during system manufacture, and
G2) within each measurement cycle of normal operation subtract the memorized crosstalk data from the measured complex frequency data.
20. The method according to claim 19 wherein said cross talk correction procedure is carried out prior to other corrective calibration steps.
21. The method according to claim 1 wherein the sensor comprises a reference part serially connectable to a measurement part.
22. The method according claim 1 additionally comprising taking into account the theoretical convolution between the frequency and spatial domain, wherein in
H1, the expected complex frequency curve is determined from a mathematical model, and a complex frequency error function constituted by the complex ratio of the measured data of the FMCW backscattering system S RM to the calculated complex frequency function S R is determined, and stored in a memory, and
H2 at the start of a following measurement cycle, the measured frequency data S RM is corrected with the complex frequency error function.
23. The method according to claim 22 additionally comprising a cross talk correction procedure carried out after other corrective calibrations, said cross talk correction procedure comprising
G1) determining and storing cross talk between measurement channels of the measurement system with a specific measurement procedure during system manufacture, and
G2) within each measurement cycle of normal operation subtract the memorized crosstalk data from the measured complex frequency data.
24. An optical FMCW backscattering measurement system comprising a computer readable medium having stored thereon a computer readable program code for executing a calibration method according to claim 1 .
25. A computer readable medium having stored thereon a computer readable program which when run on a computer can execute a calibration method according to claim 1 .
26. The method according to claim 2 wherein said predetermined criterion comprise the criterion that the mean value of the samples for a part of or all of said backscattering signal beyond said second end is less than 0.05 samples.
27. The method according to claim 7 , wherein the predetermined value is an estimated value.
28. The method according to claim 13 , wherein said determinations of correction factor ΔH res (0) and off set value Δφ res (0) are based on averaged backscattering curves of more than 5 measurements.
29. The method according to claim 13 , wherein said determinations of correction factor ΔH res (0) and off set value Δφ res (0) are based on averaged backscattering curves of more than 10 measurements.
30. The method according to claim 28 , wherein said determinations of correction factor ΔH res (0) and off set value Δφ res (0) are based on averaged backscattering curves of more than 20 measurements.
31. The method according to claim 13 , wherein said calibration is performed if optical characteristics of the sensor changes.
32. The method according to claim 1 , wherein said correction of said phase angle part of said received electrical signal comprises determining an initial off-set value Δφ o (0) of the phase angle of the received electrical signal as a function of said modulation frequency f m around f m =0; and by subsequently correcting data representing said phase angle of the received electrical signal as a function of modulation frequency f m with said off-set value.
33. The method according to claim 3 wherein said slope is less than 0.05 samples.
34. The method according to claim 3 wherein said slope is less than 0.005 samples.