Optical signal processing method and apparatus for analysing time-decay signals
Systems and methods for analysing a time-domain signal are described. The method comprising: in a mixer ( 150 ), mixing the time-decay signal ( 115 ) with a local oscillator signal ( 122 ) generated by a local oscillator ( 120 ), resulting in a mixed signal from which a Fourier transformed time-decay signal is generated comprising a fundamental transformed time decay signal at the fundamental frequency of the local oscillator signal ( 122 ) and a plurality of transformed time-decay signals at a plurality of frequencies; and determining the magnitude of each of the transformed time-decay signals at the fundamental frequency and at a frequency other than the fundamental frequency.
1. A method for determining a decay of an optical beam passing through a sample, said method comprising:
detecting, by an optical detector, the optical beam passing through the sample;
converting, by the optical detector, the detected optical beam into a time-domain signal;
mixing, in a mixer, the time-domain signal with a local oscillator signal generated by a local oscillator, the local oscillator signal comprising two or more sinusoidal waves, wherein the mixing generates a set of Fourier transformed time-domain signals corresponding to the two or more sinusoidal waves of the local oscillator signal;
determining the magnitude of each of the Fourier transformed time-domain signals;
determining a ratio of the magnitude of at least two Fourier transformed time-domain signals from the set of Fourier transformed time-domain signals, wherein the at least two Fourier transformed time-domain signals correspond to different frequencies;
determining a decay constant of the time-domain signal based on the determined ratio, wherein the decay constant is a rate of decay over time; and
determining the decay of the optical beam based on the determined decay constant.
2. The method as claimed in claim 1 , wherein the two or more sinusoidal waves comprises a first sinusoidal wave at a fundamental frequency and second sinusoidal waves at harmonic frequencies of the fundamental frequency.
3. The method as claimed in claim 1 , wherein the local oscillator signal is a square wave, the square wave comprising the two or more sinusoidal waves.
4. The method as claimed in claim 1 , wherein the local oscillator signal is a complex waveform comprising the two or more sinusoidal waves.
5. The method as claimed in claim 1 , wherein the optical beam is an absorbance signal.
6. The method as claimed in claim 1 , wherein the optical beam is a cavity-ring down signal.
7. The method of claim 6 , wherein the optical beam is generated by an excitation source selected from the group consisting of:
a continuous wave source,
a quasi-continuous wave source,
a pulsed source, and
a modulated source.
8. The method of claim 7 , wherein the excitation source is a laser source.
9. The method of claim 1 , wherein the optical beam is an interferogram signal.
10. The method of claim 1 , further comprising:
generating, by a modulator, a modulation signal and the local oscillator signal;
modulating an excitation source using the modulation signal;
resonating, in an optical cavity, modulated light from the excitation source; and
outputting, from the optical cavity, the optical beam,
wherein the decay of the optical beam corresponds to an absorbance of a sample.
11. The method of claim 10 , wherein the optical cavity is adapted to accept the sample so that, in use, the sample absorbs at least a portion of the resonating light.
12. The method of claim 1 , wherein the sample is disposed between reflectors, which form an optical cavity where the optical beam resonates in the optical cavity.
13. The method of claim 12 , wherein the reflectors each have a reflectivity at a wavelength of the optical beam.
14. A system for determining a decay of an optical beam passing through a sample, the system comprising:
a detector for detecting the optical beam passing through the sample, and converting the detected optical beam into a time-domain signal;
a mixer for mixing the time-domain signal with a local oscillator signal, the local oscillator signal comprising two or more sinusoidal waves, and generating a set of Fourier transformed time-domain signals corresponding to the two or more sinusoidal waves of the local oscillator signal; and
a determiner for determining the magnitude of each of the Fourier transformed time-domain signals, determining a ratio of the magnitude of at least two Fourier transformed time-domain signals from the set of Fourier transformed time-domain signals, wherein the at least two Fourier transformed time-domain signals correspond to different frequencies, determining a decay constant of the time-domain signal based on the determined ratio, wherein the decay constant is a rate of decay over time, and determining the decay of the optical beam based on the determined decay constant.
15. The system as claimed in claim 14 , wherein the optical beam is an interferogram signal.
16. The system as claimed in claim 14 , further comprising:
a modulator for generating a modulation signal and the local oscillator signal;
an excitation source adapted to be modulated using the modulation signal; and
an optical cavity adapted to resonate modulated light from the excitation source and to output the optical beam;
wherein the decay of the optical beam corresponds to an absorbance of a sample.
17. The system as claimed in claim 16 , wherein:
the optical cavity is adapted to accept the sample so that, in use, the sample absorbs at least a portion of the resonating light.
18. The system as claimed in claim 14 , wherein the optical beam is an absorbance signal.
19. The system as claimed in claim 14 , wherein the optical beam is a cavity-ring down signal.
20. The system as claimed in claim 19 , further comprising an excitation source selected from the group consisting of:
a continuous wave source,
a quasi-continuous wave source,
a pulsed source, and
a modulated source.
21. The system as claimed in claim 20 , wherein the excitation source is a laser source.
22. The system as claimed in claim 14 , wherein the system is adapted for analysing the time-domain signal in real time.
23. The system of claim 14 , where the two or more sinusoidal waves comprises a first sinusoidal wave at a fundamental frequency and second sinusoidal waves at harmonic frequencies of the fundamental frequency.
24. The system of claim 14 , wherein the local oscillator signal is a square wave, the square wave comprising the two or more sinusoidal waves.
25. The system of claim 14 , wherein the local oscillator signal is a complex waveform comprising the two or more sinusoidal waves.
26. The system of claim 14 , further comprising:
a pair of reflectors forming an optical cavity, each reflector have a reflectivity at a wavelength of the optical beam; and
the sample in the optical cavity.