# Determining the Maximum Achievable Wavelength of a Monochromator or Spectrograph

Grating efficiency and its variation with wavelength and spectral order are important characteristics of a diffraction grating. For a reflection grating, efficiency is defined as the energy flow (power) of monochromatic light diffracted into the order being measured, relative either to the energy flow of the incident light (absolute efficiency) or to the energy flow of specular reflection from a polished mirror substrate coated with the same material (relative efficiency). A diffraction grating may be very efficient at a particular wavelength, but might not be usable at that wavelength due to mechanical limitations of the monochromator or spectrograph into which it is installed.

### Maximum Achievable Wavelength

A spectrograph mechanism can only rotate the grating through a limited range of angles. The angle and groove density determine the transmitted wavelength. All gratings can be rotated to 0 degrees, so the lowest possible wavelength for a UV grating is set by the transmittance of air at about 180 nm. To determine the theoretical upper wavelength limit of a grating, the following formula is utilized. This formula is often referred to as "the grating equation."

a (sin l + sin D) = mΛ

Where:

m = the order, which is always an integer value

a = the groove spacing or pitch, which is the inverse of the groove density

Λ = the wavelength to be produced by the spectrograph

l = angle of incidence

D = angle of diffraction

In this example, the first order shall be considered, so m = 1. For a 1200 l/mm grating, a = 833 nm. The maximum value of any sine value is 1, so the maximum value of sin l + sin D is 2. Therefore, the longest wavelength achievable in the first order with this grating is 1666 nm. With a 2400 l/mm grating, it the theoretical upper wavelength would be half that of a 1200 l/mm grating. Practical considerations restrict the angles D and L, so the longest usable wavelength is lower than this theoretically possible maximum. Therefore, the upper wavelength limit for this grating may be closer to 1620 nm. This can be considered a "mechanical limit", as it is not related to the efficiency of the grating at the highest achievable wavelength. Although the grating may still be very efficient at this limit, it is the mechanical considerations which prevent the grating from being used at higher wavelengths.

### Mechanical Limits of Oriel Monochromators and Spectrographs

 Grating Groove Density (lines/mm) Maximum achievable wavelength in nanometers* 77250 Monochromator MS125 Spectrograph MS257 Monochromator and Spectrograph CS130 Monochromators CS260 and MS260i Monochromators and Spectrographs 3600 330 - - 530 - 2400 500 500 700 800 700 1800 670 670 925 1070 925 1200 1000 1000 1400 1600 1400 600 2000 2000 2800 3200 2800 400 - 3000 4200 - 4200 300 4000 4000 5600 6400 5600 246.16 - 4800 - - 6800 200 6000 - 8400 9600 8400 150 8000 - 11200 12800 11200 121.6 - - 13800 - 13800 75 16000 - 23000 25600 22400 50 24000 - - 38400 -

* All mechanical upper limits are theoretical. When calibration is performed, a grating offset is introduced. This may slightly lower the actual upper limit of the grating. Note that the mechanical limit may go to a higher wavelength than the actual usable area of the grating itself.