diff --git a/README.md b/README.md index 6dd0eba..9fa1687 100644 --- a/README.md +++ b/README.md @@ -4,7 +4,7 @@ Repository : [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.4655294.svg)](h Repository containing programs implementing the procedure for obtaining wavelength-dependent sensitivity for calibration of Raman spectrometers based on multi-channel detectors. The present scheme is a multi-step procedure based on following three steps: - C0 : Correction for non-linear sampling of photons in the wavenumber scale. -- C1 : Correction for channel-to-channel variation in the sensiticity of the spectrometer. +- C1 : Correction for channel-to-channel variation in the sensitivity of the spectrometer. - C2 : Final correction derived from Raman spectroscopic intensities. In order to determine the final correction (C2) the relative band intensities between all pairs of bands are analyzed simultaneously by a comparison with the analogous reference intensities. Least squares minimization is used to determine the coefficients of a polynomial used to model the wavelength-dependent sensitivity representing the C2 correction. @@ -19,11 +19,12 @@ The general scheme is given as follows. Explanation for the steps of the scheme are following : - - The experimental data available as 2D array is used to generate the $\mathbb{R}_{\text{obs}}$ matrix. Using the errors in band areas, the weights are generated. - - The reference data computed at the given temperature is used to generate the $\mathbb{R}_{\text{true}}$ matrix. + +- The experimental data available as 2D array is used to generate the **R**obs. matrix. Using the errors in band areas, the weights are generated. + - The reference data computed at the given temperature is used to generate the **R**true matrix. - Next, using the band positions and initial coefs of the polynomial, the $\mathbb{S}$ is generated. - The dimensions of the four matrices are checked before moving to the next step. - - Difference matrix, \\(\mathbb{D}\\), (for each species) is generated using the $\mathbb{R}_{\text{obs}}$, $\mathbb{R}_{\text{true}}$ and $\mathbb{S}$ matrix. + - Difference matrix, **D**, (for each species) is generated using the $\mathbb{R}_{\text{obs}}$, $\mathbb{R}_{\text{true}}$ and $\mathbb{S}$ matrix. - The elements of the difference matrix are weighted using the corresponding elements of the weight matrix. - The norm of the difference matrix is computed. The norm is minimized by varying the coefficients of the polynomial (recomputing the $\mathbb{S}$ matrix and the reference matrix, $\mathbb{R}_{\text{true}}$ using the temperature ). - Use the optimized coefficients of the polynomial to generate the \\(C_{2}\\) correction. Check temperature for physical correctness. @@ -31,6 +32,7 @@ Explanation for the steps of the scheme are following : + ## References In the following works, the ratio of intensities from common rotational states are compared to the corresponding theoretical ratio to obtain the wavelength dependent sensitivity curve.