# FTS: Fourier Transform Spectroscopy

The purpose of this experiment is to give students a physical feeling for Fourier transforms, which are used throughout science and engineering. In particular, Fourier Transform Spectroscopy (FTS) is a powerful method for measuring emission and absorption spectra, with wide application in areas as diverse as atmospheric remote sensing, NMR spectrometry, and forensic science.

The interference pattern from a Michelson interferometer is investigated as a function of mirror separation in the interferometer. The resulting interferogram is the Fourier transform of the power spectrum of the source. Computer analysis of experimental interferograms allows one to determine the transmission characteristics of several interference filters.

A brand new Michelson Interferometer has been set up in August 2014, and so the system is still under development.

**Preliminary cut-and-paste slapdash draft Write-Up in PDF Format or Microsoft Word Format.**

(The experiment is currently located in MP242; no current write-up.)

Additional Resources:

- A 'Brief' Introduction to the Fourier Transform by David Harrison.
- Previous Fourier Transform Spectrometer 2006 write-up.
- Appendices II and III in PDF Format or Microsoft Word Format.
- Skeleton code in Python for integrating HeNe laser fringes to calibrate the FTS mirror displacement. Includes functions that can determine the displacement of the mirror based on the HeNe intensity and interpolate the sampled data onto an evenly spaced grid. This is useful as a module, but students is still expected to write code for the FFT in the main program.
- 2013 ESC471F Capstone documents
- MATLAB analysis program and as yet untested Python version.

- A short video from Brigham Young University showing Fourier Transform Spectroscopy with a HeNe and a Femtosecond laser.

New Michelson Interferometer Fourier Transform Spectrometer, 28 August 2014.

White Light Interference Fringes observed September 2014.