Gilchrist and Reynolds
164
order then it is possible to also measure the light from 375 nm and 250 nm in their second
and third orders respectively. This is an important phenomenon that can be eliminated by
using either an additional dispersive element or a filter to separate or remove these orders
from the acquired signal. In addition, the diffraction order can be either positive or negative in direction (www.newport.com). In the case of a negative order the monochromator
can exhibit retro-diffraction effects that can also superimpose signals of the wrong spectral
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 several 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, f-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:
R
D
d
dx
L
L
=
=
1
λ
(5.7)
The limiting aperture in the actual instrument determines the
•
f-number and solid angle
(Arecchi et al., 2007). The 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 grating itself, as this is usually the most expensive element in the instrument. Lower f-numbers are usually associated with higher light gathering power or throughput because the
light collected (or flux) is inversely proportional to the square of the f-number. The light
collection efficiency is the solid angle that an optic makes with an object. The f-number
describes this angle: f-number: f /# = l /d, where l is distance and d is the diameter of
the lens.
With a limiting aperture diameter of
•
L, a projected area of A, and the focal length of the
collimating mirror of, the f-number (f /#) is approximately f /# = f /L, the solid angle (Ω)
is then:
Ω =
= ( )
A
f
f
2
2
4
π
/ #
(5.8)
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
164
order then it is possible to also measure the light from 375 nm and 250 nm in their second
and third orders respectively. This is an important phenomenon that can be eliminated by
using either an additional dispersive element or a filter to separate or remove these orders
from the acquired signal. In addition, the diffraction order can be either positive or negative in direction (www.newport.com). In the case of a negative order the monochromator
can exhibit retro-diffraction effects that can also superimpose signals of the wrong spectral
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 several 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, f-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:
R
D
d
dx
L
L
=
=
1
λ
(5.7)
The limiting aperture in the actual instrument determines the
•
f-number and solid angle
(Arecchi et al., 2007). The 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 grating itself, as this is usually the most expensive element in the instrument. Lower f-numbers are usually associated with higher light gathering power or throughput because the
light collected (or flux) is inversely proportional to the square of the f-number. The light
collection efficiency is the solid angle that an optic makes with an object. The f-number
describes this angle: f-number: f /# = l /d, where l is distance and d is the diameter of
the lens.
With a limiting aperture diameter of
•
L, a projected area of A, and the focal length of the
collimating mirror of, the f-number (f /#) is approximately f /# = f /L, the solid angle (Ω)
is then:
Ω =
= ( )
A
f
f
2
2
4
π
/ #
(5.8)
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