instrument

spectrometer

A spectrometer is an instrument that measures properties of light or particles, such as temperature or spin, often miniaturized.
32 related articles · 2 formulas · 1 who worked here

Description

A spectrometer is an instrument for measuring the distribution of electromagnetic radiation by wavelength or frequency. Main components: an entrance slit, a dispersive element (prism or diffraction grating), focusing optics, and a detector (CCD array, photomultiplier). Spectrometers are distinguished by range: ultraviolet, visible, infrared, X-ray, etc. A spectrograph is an instrument that records the entire spectrum simultaneously. Key characteristics are spectral resolution and light throughput.

History

The history of the spectrometer began with the experiments of Isaac Newton in 1666, who decomposed sunlight with a prism. Newton introduced the term “spectrum,” calling the colored stripe a “ghost” (spectrum). In 1814, Joseph von Fraunhofer, replacing the prism with a diffraction grating of his own making, discovered dark lines in the solar spectrum (Fraunhofer lines) and measured their wavelengths. This laid the foundation for astrospectroscopy. In 1859, Gustav Kirchhoff and Robert Bunsen created the first spectroscope with a gas burner and prism, linking spectral lines to chemical elements. In the 20th century, the development of electronics led to photoelectric registration. Today, space observatories are equipped with spectrometers operating from X-ray to infrared ranges (for example, the STIS instrument on the Hubble telescope).

How it works

The principle of an optical spectrometer: the radiation under study passes through an entrance slit to a collimator, which forms a parallel beam. Then the beam hits a dispersing element—for example, a reflective diffraction grating with rules. According to the diffraction condition d(sin α ± sin β) = mλ, where d is the grating period, α and β are the angles of incidence and diffraction, m is the order, light of different wavelengths is deflected at different angles. Then a focusing mirror forms images of the slit in monochromatic light on the detector (CCD line or array). The signal intensity from each pixel is proportional to the photon flux of the corresponding wavelength. Calibration converts pixel number into wavelength. An alternative type is the Fourier spectrometer: it uses a Michelson interferometer, where the interferogram (intensity dependence on path difference) is measured, and the spectrum is recovered by Fourier transformation. The advantage is high resolution and light throughput.

In practice

In medicine, mass spectrometers detect traces of drugs in blood, while optical spectrometers test water quality by identifying contaminants.

Fun fact

Every chemical element leaves a unique “fingerprint” in the spectrum—a set of bright lines. This is how astronomers determined that the Sun and other stars are composed mainly of hydrogen and helium.

Concept graph →

Formulas

$$n_s - 1 = \frac{d\ln\mathcal{P}_\mathcal{R}}{d\ln k}$$
The scalar spectral index measures the deviation from scale invariance of primordial perturbations.
What is in the formula
n_svariablescalar spectral index — scalar spectral index
P_Rvariablepower spectrum of curvature perturbations — power spectrum
kvariablewavenumber — wavenumber reciprocal metre
d/d ln koperatorderivative with respect to natural logarithm of wavenumber — logarithmic derivative
n\equiv\frac{d\ln\mathcal{p}_\mathcal{r}}{d\lnk}=-5 · 2606.23307
n_s\approx1+\frac{5}{12}(4\frac{\dot{h}}{h^2}-\frac{\dot{\gamma}}{h\gamma})\bigg|_{t_*} · 2607.27193v1
$$A(\omega) = \sum_n |\langle n | \mathcal{O} | 0 \rangle|^2 \delta(\omega - (E_n - E_0))$$
Measures the probability of excitations at energy ω.
What is in the formula
A(ω)variablespectral function value at energy ω — spectral function
ωvariableenergy variable (frequency) — energy joule
nvariableindex labeling excited eigenstates
|n⟩variableexcited eigenstate of the system — quantum state
|0⟩variableground state of the system — quantum state
Ovariableoperator whose excitations are probed — operator
E_nvariableenergy of excited state n — energy joule
E_0variableenergy of ground state — energy joule
⟨n|O|0⟩operatorinner product of states with operator applied — matrix element
δ(...)operatorselects only contributions at exact energy difference — dirac delta
∑_noperatoradds contributions from all possible excitations — summation
a_n(ω)=\sum_{α=x,y,z}\langleω|s_n^αδ(ω-h+e_ω)s_n^α|ω\rangle · 2606.29281

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