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@@ -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.