The main purpose of a diffraction grating is to scatter light spatially by wavelength. The white beam incident on the grating is separated from its component wavelengths when diffracted from the grating, with each wavelength diffracted in a different direction. Dispersion is the measurement of the separation (angular or spatial) between diffracted light of different wavelengths. Role scatter represents the spectral range per unit angle, and linear resolution indicates the spectral range per unit length.
Characters are scattered
The angular spread of the m-order spectrum between wavelength and +δ can be obtained from δ differential grating equation, assuming that the angle of incidence is constant. Therefore, the change in diffraction angle per unit wavelength d is:
d = dβ/dλ = m / dcosβ = (m/d)secβ = gm secβ (2-13)
where is the diffraction angle, and the quantity d is called the role scatter. As the groove frequency g=1 d increases, the role scatter increases (meaning that the angular separation between wavelengths increases with order m).
In equations (2-13), it is important to realize that the measure m d is not a ratio that can be independent of other parametersSubstituting the grating equation into equation (2-13) yields the general equation for the following character scatter:
d = dβ/dλ = (sinα +sinβ) / λcosβ (2-14)
For a given wavelength, this suggests that the character scatter can be thought of as a mere function of the angle of incidence and diffraction. This becomes clearer when we consider the littrow configuration (=), in which case equation (2-14) is reduced to:
d = dβ/dλ = (2/λ) tanβ, in littrow. (2-15)
In littrow use, when |β|When increasing from 10° to 63°, it can be seen from equations (2-15) that the character scatter increases 10-fold, regardless of the spectral order or wavelength considered. Once the diffraction angle has been determined, it is important to choose whether to use a fine-pitch grating with a low diffraction order (small d) or a coarse-pitch grating with a high diffraction order (large d), such as a stepped grating. [However, fine-pitch gratings will provide a greater free spectral range;]]
Line dispersion
For a given m-order diffraction wavelength (corresponding to the diffraction angle), the linear dispersion of the grating system is the role dispersion d and the effective focal length r of the system'The product of ( ) :
r'd = r'(dβ/dλ) = mr'/dcosβ = (mr'/d)secβ = gmr'secβ (2-16)
Quantity r'δ = δl is the change in position along the spectrum (actual distance, not wavelength). Define the focal length r'( ) to make it clear that it may depend on the diffraction angle (which in turn depends on ).
The reciprocal dispersion p, which is more often considered;It's just the reciprocal of r'd :
p = dcosβ / mr' (2-17)
It is usually measured in nm mm (where d is in nm and r' is in mm). The quantity p is a measure of the change in wavelength (in nm) that corresponds to the change in position along the spectrum. [It should be noted that some authors use p to denote the amount of 1 sin, where is the angle of the spectrum to the line perpendicular to the diffracted ray (see Figure 2-6);]To avoid confusion, we refer to the amount of 1 sin as the tilt factor. When the image plane of a particular wavelength is not perpendicular to the diffraction ray (i.e., when ≠ 90°), p must be multiplied by the tilt factor to obtain the correct reciprocal linear dispersion in the image plane.
Figure 2-6 The recorded spectral image does not need to be in a plane perpendicular to the diffraction ray (i.e., ≠90°).