Fourier transform spectroscopy

Fourier transform spectroscopy
Name	Fourier transform spectroscopy
Caption	Interferometer schematic with movable mirror
Type	Spectroscopic technique
Invented	19th century–20th century development
Inventor	Joseph Fourier, Albert A. Michelson, Harvey A. Schuster
Related	Infrared spectroscopy, Raman spectroscopy, Nuclear magnetic resonance, Optical coherence tomography

Fourier transform spectroscopy Fourier transform spectroscopy is a class of spectroscopic techniques that record an interferogram and obtain a spectrum by applying a mathematical Fourier transform. It unites experimental hardware such as interferometers with computational methods developed in Joseph Fourier's legacy and in contexts including Michelson interferometer research by Albert A. Michelson and developments in Nuclear magnetic resonance by practitioners connected to Erwin L. Hahn. The method underpins numerous instruments used in laboratories affiliated with institutions like National Institute of Standards and Technology, Massachusetts Institute of Technology, and industrial research at Bell Labs.

Overview

FTS measures spectral information by encoding frequency content into time- or space-domain interferograms collected by devices such as the Michelson interferometer, the Mach–Zehnder interferometer, and the Fizeau interferometer. Practitioners in facilities like Jet Propulsion Laboratory and European Space Agency mission teams employ FTS for remote sensing, while analytical chemistry groups at Harvard University and University of Cambridge use it for molecular identification. Comparable paradigms appear in Nuclear magnetic resonance and Fourier transform ion cyclotron resonance where time-domain signals are converted to frequency spectra via algorithmic processing. Funding and standards work occurs in agencies including National Aeronautics and Space Administration and European Space Agency.

Principles and Theory

The theoretical basis rests on Fourier analysis originally formalized by Joseph Fourier and expanded in mathematical treatments by scholars at institutions such as École Polytechnique and University of Göttingen. An interferometer produces an interferogram whose coordinate relates to optical path difference; the spectrum emerges after applying the Fourier transform operations studied in the context of Fast Fourier transform algorithm research by James Cooley and John Tukey. Quantum and semiclassical treatments link to spectroscopy work by Arnold Sommerfeld and experimentalists at Royal Society laboratories. Signal-to-noise considerations connect to statistical frameworks developed by researchers at Bell Labs and measurement standards from National Institute of Standards and Technology.

Instrumentation and Techniques

Key instruments include the Michelson interferometer used by Albert A. Michelson and variations implemented in spaceborne instruments on missions from European Space Agency and National Aeronautics and Space Administration. Detectors span cryogenic bolometers associated with teams at Jet Propulsion Laboratory, mercury-cadmium-telluride detectors used in industry labs like Bell Labs, and photon-counting modules developed in collaborations involving Rutherford Appleton Laboratory. Precision mirror translation systems trace lineage to precision engineering groups at Massachusetts Institute of Technology and Swiss Federal Institute of Technology in Zurich. Techniques such as step-scan and rapid-scan modes evolved in laboratories at University of Cambridge and University of Oxford to address time-resolved spectroscopy challenges encountered by research groups studying dynamics following protocols from Max Planck Society centers.

Data Processing and Fourier Transform Algorithms

Processing involves discrete Fourier transform methods, notably the Fast Fourier transform by James Cooley and John Tukey, as well as windowing and apodization functions analyzed in publications from Institute of Electrical and Electronics Engineers. Phase correction, zero-filling, and filtering protocols draw on numerical analysis advances from researchers at Stanford University and California Institute of Technology. Calibration uses standards maintained by National Institute of Standards and Technology and comparison with atomic reference data compiled by institutions such as Royal Society archives. Computational implementations leverage libraries originating in projects influenced by work at Bell Labs, Massachusetts Institute of Technology, and University of Cambridge.

Applications

FTS is applied across astronomy in observatories like European Southern Observatory and missions by European Space Agency and National Aeronautics and Space Administration, atmospheric sensing programs at National Oceanic and Atmospheric Administration, materials studies at Argonne National Laboratory, and biomedical imaging efforts at Johns Hopkins University. It underlies techniques in Infrared spectroscopy for chemical identification in industrial settings such as DuPont and pharmaceutical research at Pfizer and GlaxoSmithKline. Remote sensing deployments feature on satellites from European Space Agency and agencies like Japan Aerospace Exploration Agency, while trace gas monitoring is conducted by research groups at Scripps Institution of Oceanography and Woods Hole Oceanographic Institution.

Limitations and Sources of Error

Limitations include instrumental line shape distortions originating from mirror misalignment issues historically investigated by Albert A. Michelson and calibration uncertainties addressed by National Institute of Standards and Technology. Noise sources studied in laboratories at Bell Labs and Max Planck Society include detector noise, phase error, and sampling artefacts tied to mechanical translation stages developed with precision engineering teams at Massachusetts Institute of Technology and Swiss Federal Institute of Technology in Zurich. Atmospheric absorption complications encountered by teams at Royal Netherlands Meteorological Institute and National Oceanic and Atmospheric Administration affect ground-based measurements; spaceborne instruments mitigate some issues as done by European Space Agency and National Aeronautics and Space Administration missions. Algorithmic artifacts from inadequate apodization or windowing are topics in the literature from Institute of Electrical and Electronics Engineers.

History and Development

Roots trace to Joseph Fourier's 19th-century mathematical work and to interferometric experiments by Albert A. Michelson in the late 19th century. Twentieth-century maturation occurred through cross-disciplinary efforts at Bell Labs, Harvard University, and Massachusetts Institute of Technology, with computational advances by James Cooley and John Tukey enabling practical FFT processing. Institutional programs at National Institute of Standards and Technology and mission teams at European Space Agency and National Aeronautics and Space Administration drove spaceborne FTS development, while national laboratories such as Argonne National Laboratory and Rutherford Appleton Laboratory advanced instrumentation and applications.

Category:Spectroscopy