Techniques d'observation spectroscopique d'astéroïdes

CHAPTER 2. WHY SPECTROSCOPY? 45
0.4
500 nm
501.5 nm
503 nm
0.4
400 nm
700 nm
0.3
0.3
I/I 0
0.2
I/I 0
0.2
0.1
0.1
0
0
(a)
−0.1
2.85 2.86 2.87 2.88 2.89 2.9
teta[deg.]
(b)
−0.1
2 4 6 8 10 12 14
teta[deg.]
Figure 2.1: The diffraction pattern produced by a diffraction grating having b=d = 5µm and N=1000. Different
wavelengths are considered.
tel-00785991, version 1 - 7 Feb 2013
It can be computed by deriving Eq. 2.3.
d· sinθ
λ = (2.3)
m
In practice most gratings use mirrors in place of the slits. On a well-polished surface of a
metal, very thin, parallel grooves are drawn. The waves reflected from these grooves behave
exactly as the transmitted waves in the case of the transmission gratings. They can be designed
such that the main part of the incoming radiation is diffracted selectively on a given order.
Because a blaze of light is seen when the grating is viewed at the correct angle, this is called
blazed grating [Cristescu, 2004].
The prism acts as a disperser through the effect of differential refraction. This follows from
the fact that the refractive index of a material depends on the wavelength. This dependence can
be described by the empirical Hartmann formula - Eq. 2.4.
n λ ≈ A+ B
λ −C
where A, B, C are the Hartmann constants for a particular material [Kitchin, 1995].
(2.4)
The spectral resolution of a prism is given by:
√
ABL 1−0.25n 2 λ
R≈
(λ −C) 2 (2.5)
where L is the length of the face of the prism. For a typical prism used in astronomy made of
a dense flint and a side length of 10 cm, the spectral resolution could be up to 15,000 [Kitchin,
1995]. Compared to the diffraction gratings which can have higher spectral resolution, this is
one of the disadvantages of prisms.
In order to produce a reliable spectrum, the dispersive element should be combined with