252
T. Okura
by the wavelength dispersion of the grating. Other factors such as the aberration of
the optics, optical surface accuracy, and insufficient adjustment of the focal point
increase the wavelength resolution of spectrometer. These factors will cause differences in the wavelength resolution even between the same spectrometer designs, and
the instrumental differences will be larger depending on the different wavelength
resolutions. The difference between the wavelength resolutions of the instruments
should be within 10% to avoid any instrumental differences.
The wavelength resolution resulting from the dispersion caused by the entrance
and exit slits can be described as follows [6, 13].
The dependence of the position deviation on the entrance slit and wavelength can
be calculated by differentiating Eq. 10.3. The relationship between the wavelength
and incident angle α or slit position can be expressed using Eq. 10.19. The slit
wavelength width corresponding to the mechanical slit width can be expressed using
Eq. 10.20.
dλ
dα
=
10
6
N
· cos α ·
dλ
dw in
=
10
6
N · f
· cos α
(10.19)
ω in =
10
6
N · f
· cos α · W in
(10.20)
ω in Entrance slit wavelength width
W in Mechanical entrance slit width
f
Focal length of the spectrometer.
At the exit slit, the relationship between the wavelength and diffracted angle or
slit position can be expressed in terms of Eq. 10.21, while the exit slit wavelength
width caused by the mechanical slit width can be expressed by Eq. 10.22.
dλ
dβ
=
10
6
N
· cos β ·
dλ
dw exit
=
10
6 d · cos α
N · f
(10.21)
ω exit =
10
6
· cosα
N · f
· W exit
(10.22)
ω exit Exit slit wavelength width
W exit Exit slit mechanical width.
The shape of the total slit function of the spectrometer will be trapezoidal, with the
top side and base line given by ω in − ω exit and ω in + ω exit , respectively (Fig. 10.23b).
When ω exit is small, the shape in Fig. 10.23a is obtained, while a triangle shape is
obtained when ω exit = ω in (Fig. 10.23c).
In a wavelength scanning grating spectrometer, the ω exit = ω in condition is
selected to achieve the highest intensity at the same wavelength resolution.
In a linear array grating spectrometer, the pixel width is assumed to be the exit
slit width and ω exit · ω in . The slit function is illustrated in Fig. 10.23b.
T. Okura
by the wavelength dispersion of the grating. Other factors such as the aberration of
the optics, optical surface accuracy, and insufficient adjustment of the focal point
increase the wavelength resolution of spectrometer. These factors will cause differences in the wavelength resolution even between the same spectrometer designs, and
the instrumental differences will be larger depending on the different wavelength
resolutions. The difference between the wavelength resolutions of the instruments
should be within 10% to avoid any instrumental differences.
The wavelength resolution resulting from the dispersion caused by the entrance
and exit slits can be described as follows [6, 13].
The dependence of the position deviation on the entrance slit and wavelength can
be calculated by differentiating Eq. 10.3. The relationship between the wavelength
and incident angle α or slit position can be expressed using Eq. 10.19. The slit
wavelength width corresponding to the mechanical slit width can be expressed using
Eq. 10.20.
dλ
dα
=
10
6
N
· cos α ·
dλ
dw in
=
10
6
N · f
· cos α
(10.19)
ω in =
10
6
N · f
· cos α · W in
(10.20)
ω in Entrance slit wavelength width
W in Mechanical entrance slit width
f
Focal length of the spectrometer.
At the exit slit, the relationship between the wavelength and diffracted angle or
slit position can be expressed in terms of Eq. 10.21, while the exit slit wavelength
width caused by the mechanical slit width can be expressed by Eq. 10.22.
dλ
dβ
=
10
6
N
· cos β ·
dλ
dw exit
=
10
6 d · cos α
N · f
(10.21)
ω exit =
10
6
· cosα
N · f
· W exit
(10.22)
ω exit Exit slit wavelength width
W exit Exit slit mechanical width.
The shape of the total slit function of the spectrometer will be trapezoidal, with the
top side and base line given by ω in − ω exit and ω in + ω exit , respectively (Fig. 10.23b).
When ω exit is small, the shape in Fig. 10.23a is obtained, while a triangle shape is
obtained when ω exit = ω in (Fig. 10.23c).
In a wavelength scanning grating spectrometer, the ω exit = ω in condition is
selected to achieve the highest intensity at the same wavelength resolution.
In a linear array grating spectrometer, the pixel width is assumed to be the exit
slit width and ω exit · ω in . The slit function is illustrated in Fig. 10.23b.