Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 130

Fig. 4.10 a Prism dispersion depends on the wavelength of light, the prism head angle, and
the dependence of the index of refraction on the wavelength. b The dependence of the index
of refraction on wavelength (left y axis) and dispersion angle for a prism with a head angle of
˛ D 60 ı (right y axis)

Lastly, an advantage of the AOTF lies at the fact that the AOTF acts like a grating,
resulting in two diffracted beams of the orders +1 and -1 at similar angles around
the non-diffracted zero-order unfiltered spectrum transmitted. The two first-order
beams have orthogonal polarizations and, in principle, they can be used by either
directing each order to a different CCD or by combining the two separate images to
be imaged side by side on a single CCD. This will provide an advantage for different
polarization-dependent applications.

4.4.3 Spatial-Scan Methods

In this method, the dispersion of light is achieved by using either a grating or a
prism. The dispersion of a prism is given by

n p ./
n 0

sin..˛ C ı/=2/
sin.˛=2/

D (4.3)

where ˛ is the head-angle of the prism, n p ./ is the wavelength-dependent index
of refraction of the prism material, and ı is the diffraction angle (Fig. 4.10 ).
Figure 4.10 b shows the index of refraction of quartz crystal (left y axis) and the
resulting diffraction angle as a function of the wavelength for prism with a head
angle of 60 ı (right y axis). As one can see, the difference is significant and provides
the basis for spectroscopy.
A grating can also be used for dispersion (Fig. 4.11 ). The diffraction to a certain
angle is strong when the following equation is fulfilled [ 29 ]:

m
d

sin ˛ C sin ˇ D (4.4)