--- title: "How total brightness reveals many infrared colors" description: "A moving mirror gives each wavelength its own brightness rhythm. Follow an interferogram from two colors to a recovered infrared absorption band." canonical_url: "https://sandboxphysics.com/stories/instruments/ftir-spectrometer/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/instruments/ftir-spectrometer/" last_modified: "2026-11-03" --- [How physics instruments measure](https://sandboxphysics.com/stories/instruments/) Inside the instrument # How total brightness reveals many infrared colors Total brightness can reveal separate wavelengths because a moving mirror gives each wavelength a different bright-dark rhythm. Recording brightness together with mirror position preserves these rhythms. A Fourier transform infrared spectrometer uses them to recover a spectrum with one detector. Sandbox Physics · 2026-11-03 ## Send each color down two paths Infrared light passing through a material becomes weaker at some wavelengths. These absorptions often relate to molecular vibrations and help characterize the material. Although infrared wavelengths are invisible, it is useful to think of them as different colors. One detector that adds all those colors together cannot identify the missing light from a single brightness reading. A Michelson interferometer gives each color a recognizable rhythm. A partially reflecting beam splitter divides the light between two mirrors. The returning beams meet at the splitter and share an output toward the detector. An extra half wavelength in one path makes the returning oscillations oppose each other. An extra full wavelength brings them back into step. Moving one mirror slowly therefore changes the measured brightness. Each color interferes with the other beam split from that same color; powers from different optical frequencies add. Sources: [1] ## Four micrometres of mirror travel gives an eight-micrometre round trip Light travels from the splitter to a mirror and back again. Move the mirror four micrometres farther away and the round-trip path grows by eight micrometres. This factor of two connects mirror displacement to optical path difference. For eight-micrometre light, each four micrometres of mirror travel carries brightness from one maximum to the next. That mirror step is four thousandths of a millimetre. A shorter wavelength completes more bright-dark cycles over the same travel. With two wavelengths, the detector records the sum of two rhythms. Nearby wavelengths produce fine oscillations inside a slowly changing envelope, much like the beats between neighboring musical tones. A sufficiently long record can distinguish their close rhythms. Sources: [1] ## A continuum builds a strong central burst A broadband source adds many wavelengths. At equal arm lengths, each wavelength reinforces its own returning partner. Their powers produce a prominent central burst. Farther from equal paths, their individual brightness variations fall out of step and partly cancel in the sum. Brightness recorded against optical path difference is called an interferogram. Sample numbers alone do not supply its distance scale. The instrument needs to know how far the mirror moved between readings. Spectra often use wavenumber, the number of wavelengths per unit length; eight-micrometre light has a wavenumber of 1250 per centimetre. The Fourier transform separates this curve into rhythms of different spatial frequencies. Faster variation corresponds to shorter wavelengths. Each rhythm contributes its spectral intensity. The detector follows brightness changes as the mirror moves, averaging over the much faster optical field oscillations. A real mirror has finite travel. Abruptly cutting off an interferogram creates ripples beside a reconstructed sharp line. Gradually weighting down the scan edges suppresses these sidelobes and broadens the reconstructed spectral main lobe. This weighting is apodization. Zero padding draws more intermediate spectral points; resolving closer lines still requires a longer useful path difference. Sources: [1] [2] ## Measure a reference and sample in the same output path An absorption measurement starts with a reference interferogram. The sample then enters the common output after the two arms have recombined. Its intensity transmittance reduces that whole output at each wavelength. Transform both records and divide the sample spectrum by the reference where the background contains enough light. Transmittance is the fraction of light left. Absorbance expresses attenuation on a logarithmic scale: one half transmitted gives about 0.301; one tenth gives one. Finite spectral resolution broadens a narrow absorption and can change its recovered depth. If $T$ is the recovered sample-to-reference intensity ratio and $A$ the absorbance, their relation is below. A denominator close to noise makes the ratio unstable. Unilluminated wavelengths carry no sample information. Calibration connects these scales to independent observations. Known lines test wavenumber; dark readings and known optical power test the detector. Reference and sample also need the same optical configuration and processing. The resulting absorption spectrum describes the sample over a specified illuminated band and finite resolution. $$ A=-\log_{10}T $$ Transmittance and absorbance are dimensionless. The ratio compares two spectra recovered from raw interferograms and retains their finite-window instrument response. Sources: [2] [3] [4] ## [Move the mirror and separate the rhythms](https://sandboxphysics.com/labs/ftir-spectrometer/) Compare two-line and broadband illumination, then insert a common-path sample and recover its absorption from saved interferograms. The ideal double-pass Michelson uses synthetic spectra and exposes finite-window, sampling, noise and independent calibration effects. It is not a measured molecular atlas. ## Sources and further reading 1. [Thermo Fisher Scientific — Advanced FTIR Spectroscopy, CT50845](https://assets.thermofisher.com/TFS-Assets/MSD/Scientific-Resources/CT50845-advanced-ftir-spectroscopy.pdf) Read printed p4 (PDF index3), §1.1 and §1.2: classical Michelson paths, monochromatic/continuum interferograms, displacement-tagged detection and optical path difference twice mirror travel. This model independently derives its single-port normalization and does not reproduce the laser-reference hardware described there. 2. [Shimadzu — Fourier Transform and Apodization](https://www.shimadzu.com.au/service-support/technical-support/analysis-basics/tips-ftir/apodization.html) Read Interferograms, Principle of Fourier Transform Spectrophotometry and Apodization. Finite box truncation rings; triangular weighting reduces sidelobes and widens the central response. HTML read28October2026; no stable revision shown. 3. [NIST — Wavenumber Calibration Tables, Description](https://physics.nist.gov/PhysRefData/wavenum/html/tables.html) Read Wavenumbers, Asterisks and Description of Spectra. Certified line position, blending, integrated intensity and calculated atlas spectra are distinct. The linked experiment uses explicitly chosen synthetic standards, not a certified NIST molecular line list. 4. [NIST — Fourier Transform Infrared Spectroscopy](https://www.nist.gov/laboratories/tools-instruments/fourier-transform-infrared-spectroscopy) Read the instrument description on molecular vibrations, transmission, reflectance and ATR. Page updated15November2019. This article discusses a transmission model only. 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