# Units conversion for spectrum representation

**Wavelength, Wavenumber, Frequency and Photon Energy Conversion **

The x-axis of a spectrum should be scaled in **frequencies** (in Hertz). The frequency representation is dedicated to applications such as measurements of atomic and molecular transitions, heterodyne spectroscopy or TeraHertz generation.

The optical frequencies are so large (from 400 to 750 TeraHertz in the visible range) that it is common to use **wavelengths** in micrometers (µm) or nanometers (nm). The wavelength λ is the distance between two consecutive maxima of the amplitude of an electromagnetic wave, which depends on the propagation medium index (in air : *n* = λ_{vacuum }/ λ_{air}). The use of this unit is highly generalized in all the disciplines of optical spectrometry (lasers characterization, absorbance, fiber Bragg sensors monitoring, etc.).

A magnitude proportional to the frequency is the **wavenumber** σ, the inverse of the wavelength. It is often used with specific unit, the centimeter^{-1} (cm^{-1}), in Fourier Transform InfraRed spectroscopy and in Raman spectroscopy for determining shifts in energy of the vibration modes of a matter excited by a laser source.

Some specific applications study the **energy** *E* of a photon, in electron-volt (eV), which is proportional to its frequency via the Planck’s constant *h*.

In vacuum: λ_{0} = *c */ ν with *c* ≈ 3.10^{8} m.s^{-1 }(speed of light)

σ = 1 / λ

*E = h.*ν with *h* ≈ 6,626 069 57×10^{-34} J.s (Planck’s constant)

*Schematic representation of the electromagnetic spectrum according to the frequency ν*

*and the wavelength λ*

*. The visible range (380 nm < λ*

*<780 nm) represents only a minor part of the overall domain, which extends from Gamma-rays of high energy and short wavelengths (λ*

*< 10 µm) to radiometric waves (λ*

*> 1 mm), passing by X-rays (10 pm < λ*

*< 10 nm), ultraviolet (10 nm < λ*

*< 380 nm), and the infrared (780 nm < λ*

*< 1 mm) ranges.*

*Credit: CSI/NASA.*

**Difference Conversion**

Non linear calculations are necessary in the case of converting **bandwidth, linewidth or spectral distance** measurements between wavelength, wavenumber and frequency domains.

Δσ = Δλ / λ² | Δν = c. Δλ / λ² |

Δλ = Δσ . λ² | ΔE = h.c. Δλ / λ² |

Please fill-in the following form to download the “**Units Conversion Form**” which lists the formulas between units and difference conversion, and provides a quick calculation form.