FT-IR Data Processing

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Table of Contents

1. Organize and Import Your Data
2. Baseline Correct the Spectra
3. Normalize the Spectra
4. Calculate the Mean Spectrum
5. Calculate the HQI
6. Save & Turn In Your Work

Use the following link to download the notebook template for this lab:

https://raw.githubusercontent.com/chem370/chem370.github.io/master/docs/project/ft-ir/ftir-notebook-template.jl

The following video walks you through the data processing portion of this lab.

Having trouble viewing this video? Click here to view it on Panopto instead.

Organize and Import Your Data

1. Create a folder for this lab on your computer.
2. Copy your data files from NEON into your lab notebook folder for this lab.
3. Import the data using CSV.read() from CSV.jl.

Baseline Correct the Spectra

1. Baseline correct your spectra by subtracting the minimum value from each data point. After this step the minimum value in each spectrum should be 0.

\[y_{i,corrected} = y_{i} - y_{min}\]

Normalize the Spectra

1. Normalize your spectra by converting from absorbance units to relative absorbance. You do this by dividing the whole spectrum by the maximum absorbance value. After this step your data should range from 0 to 1.

\[y_{i,normalized} = y_{i,corrected} \div y_{max,corrected}\]

Calculate the Mean Spectrum

1. Calculate the mean of your 3 replicates using the normalized spectra.

\[\bar{y_i} = \sum_{i=1}^{i=n} \frac{ y_{1,i,normalized} + y_{2,i,normalized} + y_{3,i,normalized} + ... + y_{n,i,normalized}}{n}\]

Calculate the HQI

1. Calculate the Hit Quality Index according to Eq. 2 in Rodriguez et al (2011):

   \[\text{HQI} = \frac{(\text{Reference} \cdot \text{Sample})^2}{(\text{Sample} \cdot \text{Sample}) \times (\text{Reference} \cdot \text{Reference})}\]

   Be mindful of the difference between “x” (multiplication) and “·” (dot product).

   For any two vectors, $\mathbf{a} = [a_1, a_2, …, a_n]$ and $\mathbf{b} = [b_1, b_2, …, b_n]$, the dot product is:

   \[\mathbf{a} \cdot \mathbf{b} = \sum^{i=n}_{i=1} a_ib_i = a_1b_1 + a_2b_2 + ... + a_nb_n\]

   When $\mathbf{a}$ and $\mathbf{b}$ are row vectors the calculation is simply:

   \[\mathbf{a} \cdot \mathbf{b} = \mathbf{a} \times \mathbf{b}^\text{T}\]

   where $\mathbf{b}^\text{T}$ represents the transpose of $\mathbf{b}$, as in:

   \[\mathbf{a} \cdot \mathbf{b} = \mathbf{a} \times \mathbf{b}^\text{T} = [a_1, a_2, ..., a_n] \times \begin{bmatrix} b_{1} \\ b_{2} \\ \vdots \\ b_{m} \end{bmatrix}\]

   Julia does matrix multiplication by default, so this is easily calculated in Julia. Assuming a and b are row vectors, then $\mathbf{a} \cdot \mathbf{b}$ is simply a*b' in Julia (or, equivalently, a*transpose(b)) where the ' operator is identical to calling transpose(b).

   An alternative (more cumbersome!) approach is to use the dot() function from LinearAlgebra.jl, as in using LinearAlgebra; dot(a, b).

   The dot product of two vectors is a scalar (single value); it is sometimes called the scalar product for this reason.

Save & Turn In Your Work

1. Save your work as a .jl (Julia) file and .html (static HTML).
2. Attach your .jl, .html, and .csv files to the MS Teams assignment for this lab when turning it in.

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