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Multiplying a finite interferogram by a smooth window reduces sharp-edge artifacts. In the recovered radiation spectrum this convolves the true spectral density with the window's Fourier transform. Smoother windows generally lower sidelobes while broadening the main lobe, so a resolution figure must specify the window and criterion. Apodization does not recover unmeasured long-delay information.^[ref]

A physicist who authored a National Bureau of Standards introduction to Fourier transform spectroscopy. It explains how scanning a Michelson interferometer produces an interferogram from which a Fourier transform recovers a spectrum. The reference connects optical path difference and sampling to practical spectral resolution, making the mathematical transform part of a reproducible measurement procedure.^[ref]

In Fourier transform spectroscopy, a scanning Michelson interferometer measures intensity against optical path difference $\ell$ rather than selecting one narrow wavelength at a time. After subtraction of the constant background, an ideal stationary source gives an interferogramA cosine Fourier transform recovers the spectral power density $S(\nu )$ after instrumental calibration. A mirror displacement $x$ changes the round-trip path by $2x$; the zero-path-difference burst aligns the scan, and a reference laser can calibrate the displacement.

Finite maximum path difference $L$ multiplies the interferogram by a window and convolves the recovered radiation spectrum with that window's Fourier transform. Thus $\delta \nu$ is of order $c/L$; precise factors depend on scan range and resolution convention. Uniform path samples of separation $\Delta \ell$ need ${\nu }_{\max }<c/(2\Delta \ell )$ to avoid aliasing without bandpass information. interferogram apodization reduces sidelobes at the price of broader lines. The broad accepted optical throughput can be advantageous; the multiplex signal-to-noise advantage depends on detector noise and is not universal in photon-noise-limited measurements. Source drift during a scan, finite beam divergence, imperfect sampling and wave phase errors require control. The finite-window reasoning is the delay-range resolution in Fourier transform spectroscopy.^[ref]