Principle of Grating Spectrometer

1. Spectroscopic principle of plane diffraction grating
(I) Grating equation
A reflective plane diffraction grating is an element formed by engraving a series of grooves of equal width and equal spacing on a high-precision plane. A general grating has dozens to thousands of grooves within one millimeter, and the engraved area can reach 600mm×400mm.

As shown in Figure 12-7, when a beam of parallel composite light is incident on the grating, the grating can decompose it into a spectrum in space according to wavelength. This is the result of multi-slit diffraction and interference. The position of the spectrum produced by the grating is determined by the main maximum condition in the multi-slit diffraction pattern.
As shown in Figure 12-7, the optical path difference between the light and the light corresponding to two adjacent lines is:

See «Objective Light» P196 (5-71)
From wave optics, we know that the intensity distribution formula of multi-slit Fraunhofer diffraction is:

The conditions for the maximum interference of coherent beams are:

From equations (1) and (2), we can get the condition of the maximum interference between two adjacent light rays - the grating equation is:

Where i is the incident angle
θ, the diffraction angle
d is the spacing between notches, usually called the grating constant
m is the spectral order, m=

Formula (3) can be rewritten as:

2. Discussion

From formula (4), we can see that when the grating pitch d and the incident angle i are constant,

1.
Starting from the first order, the main wave of the same order with different wavelengths is the largest, and spreads out from short wave to long wave in order of wavelength (Figure 12-8).

2. When m=0, all wavelengths of zero-order light are mixed together without dispersion, which is called zero-order spectrum. Its position corresponds to the reflection direction, that is, on both sides of the zero-order light, m>0 is called positive spectrum; m<0 is called negative spectrum.

(III) Restrictions
The highest spectral level is subject to the conditions

It is inversely proportional to the grating constant d. Under the condition of complying with formula (5), a small d can obtain a large dispersion rate.

In practice, the inverse linear dispersion rate is often used to express it, and the unit is generally nm/mm.

3. Raster resolution

Formula (8) is the theoretical resolution formula of the grating. It can be seen that:

In Figure 12-11, the incident slit S1 and the exit slit S2 are both located on the same side of the dispersion system, both on the focal plane of M. The light beam emitted from the incident slit S1 is reflected by the concave reflector M and becomes a parallel light beam, which is projected onto the grating G. The light beam after light dispersion is re-projected onto M, and is focused by M and turned to the S2 slit by the plane mirror M1 and emitted.

4. Rotation mechanism of grating
When the incident angle i is fixed, the wavelength scanning relationship of the grating can be expressed as follows:

In the monochromator and spectrophotometer, the positions of the incident and exit slits are fixed, so once the grating is installed, the angle δ between the incident light and the exit light is fixed, as shown in Figure 12-13 (Figure