Biomedical Engineering Reference
In-Depth Information
Fig. 4.11 Blazed grating.
The angle of the blazes forms
high reflection at the
so-called Littrow condition.
The dashed lines are
perpendicular to the grating
surface and to the blaze
surface
where m is an integer describing the diffraction order, is the wavelength of light,
˛ and ˇ are the incident and the diffracted angles with respect to the normal to the
grating surface, and d is the grating groove spacing. In addition, the blazed grating
provides the highest efficiency when the so-called Littrow condition is satisfied:
B D 2d sin
(4.5)
where is the angle of the blaze.
Both grating and prism can be used for spectroscopy. In general, the prism has a
higher transmission that can reach 90 %, while the gratings usually have up to 65 %
transmission. On the other hand, the gratings can provide a better spectral resolution
when used in certain monochromatic configurations [ 30 ].
4.4.3.1
Spectral Imaging System Based on a Grating
Grating and prisms form the vast majority of single-point spectrometers. When used
for spectral imaging with an array detector such as CCD, the inherent property
of these dispersive elements, namely, the dispersion of the spectrum along one
axis, forces sampling of only one line of the image at a time thus a scan along
its perpendicular axis is required. In principle, a point detector such as PMT or a
line detector can also be used, but these would require even more scans in order
to construct a single spectral image. With an array detector, one axis is used for
measuring the spectrum so that the other axis is left for measuring one line from
the perpendicular axis of the image (Fig. 4.12 ). This requires one to scan the object
line by line to collect the entire spectral image. The data is therefore collected as
I.x; y i ;/ where y i represents a single point along the y axis from the x-y plane,
thus the scan along the vertical axis [ 31 ]. These methods have an advantage when the
measured object is moving linearly and can be applied, for example, for an airborne
system that can scan along its pathway or measuring substances that are moving
along a conveyer. For other applications such as microscopy, a single-axis scanning
mechanism must be added externally. Figure 4.12 describes only the concept of the
system while the actual one looks much different due to aberrations that must be
corrected, as explained below.
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