# Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

## Abstract

This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performing a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1291184

- Report Number(s):
- LA-UR-16-25235

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Armstrong, Derek Elswick.
```*Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra*. United States: N. p., 2016.
Web. doi:10.2172/1291184.

```
Armstrong, Derek Elswick.
```*Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra*. United States. doi:10.2172/1291184.

```
Armstrong, Derek Elswick. Tue .
"Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra". United States.
doi:10.2172/1291184. https://www.osti.gov/servlets/purl/1291184.
```

```
@article{osti_1291184,
```

title = {Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra},

author = {Armstrong, Derek Elswick},

abstractNote = {This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performing a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.},

doi = {10.2172/1291184},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Jul 19 00:00:00 EDT 2016},

month = {Tue Jul 19 00:00:00 EDT 2016}

}