Signal processing using non-linear regression with a sinusoidal model
A method for processing signals, such as a tomography signal, in the time domain provides both high spatial resolution and high frequency resolution but at low cost. The method uses non-linear regression with a sinusoidal model to fit a sine wave to a portion of the signal that is less than a full cycle of a wave of the signal.
1. An optical coherence tomography method using an optical coherence tomography system having a light source, a detector, an analog to digital converter and a processor comprising:
generating an optical coherence tomography signal using the light source and the detector;
digitizing the optical coherence tomography signal to provide digital data points; and
processing the digital data points representing a portion of the signal in the time domain using non-linear regression with a sinusoidal model to fit the sinusoidal model to the digital data points.
2. A method as recited in claim 1 wherein the sinusoidal model is:
I ( t )= A sin(2πf 0 t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal and φ 0 is the phase lag.
3. A method as recited in claim 1 wherein the sinusoidal model is:
I ( t )=( A+αt )sin(2π( f 0 +σt ) t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal, φ 0 is the phase lag, α models changes in amplitude and σ models a rate of change of frequency.
4. A method as recited in claim 1 wherein the non-linear regression is optimized for a known frequency range.
5. A method as recited in claim 1 wherein the processing determines the coefficients of the sinusoidal model including amplitude and frequency.
6. A method as recited in claim 5 wherein the processing eliminates components that fail to converge correctly.
7. A method as recited in claim 1 wherein the digital data points represent a portion of the signal that is less than a full cycle of a wave of the signal.
8. An optical coherence tomography method using an optical coherence tomography system having a light source, a detector, an analog to digital converter and a processor comprising:
generating, using the light source and the detector, an image signal representing an image of materials that are changing or moving during imaging;
receiving digital data points representing a portion of the image signal;
processing the digital data points in the time domain by non-linear fitting of a sinusoidal model to the digital data to determine a frequency of the signal,
wherein the digital data points represent a portion of the signal that is less than a full cycle of a wave of the signal.
9. A method as recited in claim 8 wherein the frequency of the signal is within a known frequency range.
10. A method as recited in claim 9 wherein the processing is optimized for the known frequency range.
11. A method as recited in claim 8 wherein the sinusoidal model is
I ( t )= A sin(2π f 0 t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal and φ 0 is the phase lag.
12. A method as recited in claim 8 wherein the sinusoidal model is:
I ( t )=( A+αt )sin(2π(f 0 +σt ) t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal, φ 0 is the phase lag, α models changes in amplitude and σ models a rate of change of frequency.
13. A method as recited in claim 8 wherein the processing eliminates components that fail to converge correctly.
14. A method of processing an optical coherence tomography signal in the time domain to determine a frequency of the signal where the frequency is within a known range using a system having an analog to digital converter and a processor comprising:
digitizing the signal to provide digital data points; and
processing the digital data points representing a portion of the signal in the time domain using non-linear regression with a sinusoidal model optimized for the known frequency range to determine parameters of the sinusoid fitting the digital data, the parameters including frequency,
wherein the digital data points represent a portion of the signal that is less than a full cycle of a wave of the signal.
15. A method as recited in claim 14 wherein the processing eliminates components that fail to converge correctly.
16. A method as recited in claim 14 wherein the sinusoidal model is
I ( t )= A sin(2 πf 0 t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal and φ 0 is the phase lag.
17. A method as recited in claim 14 wherein the sinusoidal model is:
I ( t )=( A+αt )sin(2π(f 0 +σt ) t+φ 0 )
where I is the intensity of the optical coherence tomography signal, A is the amplitude, f 0 is the frequency of the signal, φ 0 is the phase lag, α models changes in amplitude and σ models a rate of change of frequency.
18. A method as recited in claim 14 wherein the
parameters include amplitude and a rate of change of frequency.