System and method for finding the peak wavelength of the spectrum sensed by an LSPR spectrometer
A system and method for fording the peak wavelength of the spectrum sensed by an LSPR spectrometer is described herein. The method comprises reading an image representing the reflected/absorbed spectrum, using a mathematical model of the LSPR spectrometer system to estimate a parametric curve representing the absorbance/reflectance spectrum, and adjusting or optimizing the parameters of the parametric curve so as to increase the likelihood of the parametric curve representing the sensed spectrum. Also described herein is a novel method to achieve LSPR peak wavelength signal noise reduction using an adaptive regularization algorithm.
1. A method for finding a peak wavelength of a spectrum sensed by a spectrometer comprising:
providing a sample comprising an analyte;
analyzing the analyte using SPR analysis to produce a signal;
using an imaging device to measure and store data from the signal, thereby yielding stored image data; and
using a computer to:
estimate from the stored image data a model spectrum representing an absorbance or reflectance spectrum;
estimate from the model spectrum a mathematical modeling function comprising a parametric curve representing the absorbance/reflectance spectrum; and
adjust parameters of the parametric curve thereby increasing the likelihood of the model spectrum representing the spectrum sensed by the spectrometer.
2. The method of claim 1 , wherein the stored image data represents a reflected or absorbed spectrum of the signal.
3. The method of claim 2 , wherein the stored image data comprises a function of an angle of incident light.
4. The method of claim 1 , wherein increasing the likelihood of the model spectrum representing the spectrum sensed by the spectrometer comprises maximizing a probability function representing the spectrum sensed by the spectrometer.
5. The method of claim 1 , wherein increasing the likelihood of the model spectrum representing the spectrum sensed by the spectrometer comprises maximizing a weighted sum of the probability function representing the spectrum sensed by the spectrometer and a regularization term.
6. The method of claim 5 , wherein the regularization term uses an autoregressive filter formulation.
7. The method of claim 5 , wherein a weight of the weighted sum is not constant.
8. The method of claim 5 , comprising determining the weight of the weighted sum by using the computer to calculate an approximate peak wavelength signal for a lookahead number of spectral images.
9. The method of claim 5 , wherein the weight of the weighted sum is determined by using a computer to calculate a slope of the approximate peak wavelength signal for the lookahead number of spectral images.
10. The method of claim 5 , comprising determining the weight of the weighted sum by using the computer to calculate a binary modeling function of the slope of the approximate peak wavelength signal for the lookahead number of spectral images.
11. The method of claim 5 , comprising determining the weight of the weighted sum by using the computer to calculate a discrete modeling function of the slope of the approximate peak wavelength signal for the lookahead number of spectral images.
12. The method of claim 5 , comprising determining the weight of the weighted sum by using the computer to calculate a linear modeling function of the slope of the approximate peak wavelength signal for the lookahead number of spectral images.
13. The method of claim 5 , comprising determining the weight of the weighted sum by using the computer to calculate a bounded quadratic modeling function of the slope of the approximate peak wavelength signal for the lookahead number of spectral images.
14. The method of claim 5 , comprising maximizing the probability that the model spectrum represents the spectrum sensed by the spectrometer by using the computer to optimize parameters of the modeling function.
15. The method of claim 14 , wherein optimizing the parameters of the modeling function comprises using a Newton method to find a minimum of a sum of squared errors between the model spectrum and a spectral image.
16. The method of claim 15 , wherein the iterative Newton method comprises successive relaxation of each parameter in the mathematical modeling function.
17. The method of claim 15 , wherein the iterative Newton method comprises a stopping condition wherein the minimum of a sum of a squared error between the model spectrum and a spectral image is less than a constant.
18. The method of claim 15 , wherein the iterative Newton method comprises a stopping condition wherein the sum over all parameters of the ratio of the change in value to the previous value is less than a constant.
19. The method of claim 1 , comprising providing a computer output indicating the peak wavelength of the spectrum sensed by a spectrometer.