Normalization by Area

Table of contents

  1. Introduction
  2. How to use
  3. Behavior
  4. Method
  5. References

Introduction

Normalization by Area rescales each spectrum by its integrated area so spectra with different total signal levels can be compared.

How to use

To normalize your data by area:

  1. Upload data and select the spectra to be processed.
  2. Navigate to the sidebar and turn on the “Normalization” toggle.
  3. Select “Normalize by area” from the drop-down menu.
  4. Leave “Scale factor” at 1 for no additional scaling, or choose an integer from 1 to 100000 to multiply the normalized intensities by that constant.
  5. Click “Process” to update the display.

Behavior

Normalizing by area is good for standardizing data with different measurement conditions. With the default scale factor of 1, the magnitude of the integrated area is 1; for a positive-area spectrum, the area itself is 1. The area is calculated using a trapezoidal sum. A scale factor $c$ multiplies every normalized intensity by the same constant, so the magnitude of the resulting area is $c$. Mathematically, the normalized intensity $S(x)$ at Raman shift $x$ is determined by:

\[S(x)=c\frac{I(x)}{\left|\sum_{i=1}^n \frac{1}{2}\left(I(x_i)+I(x_{i-1})\right)\left(x_i-x_{i-1}\right)\right|}\]

where $I(x)$ is the intensity observed at Raman shift $x$, $n$ is the number of Raman shift intervals, and $c$ is the scale factor (default 1).

Method

The implementation divides each selected spectrum by the absolute value of its trapezoidal area over Raman shift, then multiplies by the scale factor:

\[I_{\text{norm}}(x)=c\frac{I(x)}{\left|\int I(x)\,dx\right|}\]
Parameter Tunable or fixed Implementation
Method choice Tunable Selected as Normalize by area
Scale factor Tunable Default 1 (no additional scaling); integer from 1 to 100000 multiplying normalized intensities
Integration Fixed Trapezoidal area using the Raman shift column

References

  1. SpectraGuru implementation, self-implemented area normalization.

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