Geoscience Reference
In-Depth Information
output at the exit slit (
www.horiba.com
). For illustration purposes the grating equation can
be illustrated graphically (Fortin,
2008
) as shown in
Figure 5.12
.
The slits themselves play an important role in determining the spectral resolution and
throughput of the monochromator. In most cases, the positions of the entrance and exit slits
are fixed but the width is adjustable. Typical slit widths can vary from a few microns to sev-
eral millimeters but it is usual for the exit and entrance slits to be the same width. Several
characteristics are important in a monochromator, such as the linear dispersion,
if
-number
of solid angle, resolution, stray light rejection, and throughput factors. These factors are
described in more detail below.
•
The linear dispersion (
D
L
) is how far apart spatially two wavelengths are in the focal
plane,
D
L
=
dx
/
dλ
, that is, at the exit slit in
Figure 5.11
. The more commonly quoted
figure is the reciprocal linear dispersion (
R
L
), as this represents the wavelength range
within a unit distance in the focal plane:
=
1
λ
d
dx
R
(5.6)
L
D
L
•
if
f-number and solid angle
(Arecchi et al.,
2007
). The
if
f-number of an optical system can be simply defined as the
focal length divided by the effective aperture diameter. Often this is the diffraction grat-
ing itself, as this is usually the most expensive element in the instrument. Lower
if
-num-
bers are usually associated with higher light gathering power or throughput because the
light collected (or flux) is inversely proportional to the square of the
if
f-number. The light
collection efficiency is the solid angle that an optic makes with an object. The
if
-number
describes this angle:
if
-number:
if
/# =
if
/
d
, where
if
is distance and
d
is the diameter of
the lens.
With a limiting aperture diameter of
The limiting aperture in the actual instrument determines the
•
L
, a projected area of
A
, and the focal length of the
collimating mirror of, the
if
-number (
if
/#) is approximately
if
/# =
if
/
L
, the solid angle (Ω)
is then:
A
if
π
/#
Ω= =
(5.7)
( )
2
2
4
if
•
The spectral bandpass (S
λ
) is the full-width half-maximum of the wavelengths passed
across the exit slit. The bandpass is controlled by the dispersion of the monochromator
(
R
D
) except at very small slit widths, where both diffraction effects and aberrations need
to be considered. The spectral bandpass ultimately defines the resolution of the instru-
ment and for a given slit width,
W
, this is given by: (5.8)
RRW
λ
=
D
(5.8)
•
The resolution of the monochromator is closely related to the spectral dispersion. The
dispersion governs how far apart two wavelengths are, while the resolution specifies
whether the separation can be distinguished. The Rayleigh criterion states that two
wavelengths,
λ
1 and
λ
2, are resolved if the central maximum of one line falls on a
