Techniques d'observation spectroscopique d'astéroïdes

44 CHAPTER 2. WHY SPECTROSCOPY?
position of the object being observed, its temperature and its internal pressure or density, its
motion relative to the Earth, and the presence of a magnetic field.
2.1 Diffraction gratings and prisms
There are several methods that can be used to separate the light into its component wavelengths.
The simplest way is to use broad band filters before the detector in order to isolate different
spectral regions. This method is called photometry and is considered as a separate subject from
the spectroscopy.
Spectral resolution (or resolving power) is defined as the fraction of the wavelength - ∆λ,
that can be resolved relative to that of the operating wavelength - λ (Eq. 2.1). in general, the
spectroscopy is considered to involve spectral resolutions higher than 50.
tel-00785991, version 1 - 7 Feb 2013
R= λ
(2.1)
∆λ
The astronomical spectrometers are devices that measure the amount of radiation coming
from the celestial bodies at different wavelengths. To split the light into its component wavelength,
astronomers can use diffraction gratings, prisms, Fabry-Pérot etalons and Fourier transform
spectroscopes. Bellow are summarized the main characteristics of diffraction gratings and
prisms which were used during different observations that I performed.
The diffraction grating generally consists of a large number N, of parallel slits separated by
opaque spaces of comparable dimensions. Producing the spectra with the diffraction gratings
involves the interference of N waves and the diffraction on slit phenomena [Cristescu, 2004].
The distribution of intensity of the radiation in the diffraction pattern is described by the formula
Eq. 2.2.
[ ] [ ]
sin
πbsinθ
λ sin
Nπ(b+d)sinθ 2
I = I 0·
πbsinθ
2·
λ
λ sin π(b+d)sinθ
(2.2)
λ
where d is the size of opaque spaces, b is the size of the slit, θ is the angle between a certain
direction and the normal to the grating and I 0 is the total intensity passing through a slit
[Cristescu, 2004]. The minima and the maxima position depend on the wavelength and on the
diffraction grating parameters (b and d).
By increasing the number N of slits, the interference fringes become sharpest. Two wavelengths
( λ and λ + ∆λ) could be barely separated, if the minimum of the diffraction pattern
corresponding to λ is in the same position as the bright fringe corresponding to λ + ∆λ for
the same diffraction order m. From this condition it can be computed the spectral resolution
R=N· m. Thus the chromatic resolving power is proportional to the total number of slits and
it is higher in the higher orders. In Fig. 2.1 are shown the diffraction patterns obtained using a
diffraction grating having b=d = 5µm and N = 1000.
The dispersion of a spectrum is the rate of change of wavelength with the angular position.