What is a spectrometer 1

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6.7 Spectrometer

There are different types of spectrometers

  1. Dispersive optical elements such as prisms or gratings are used to separate the different wavelengths.
  2. Resonators (Fabry-Perot resonator, Michelson interferometer, Lummer-Gehrcke plate) suppress parts of the light spectrum
  3. Other e ff ects such as acoustic waves can be used for high-resolution spectroscopy.

The structure of a spectrometer with dispersive optical components is explained below.

The common characteristic of all dispersive components is that a plane wave is deflected by a wavelength-dependent angle α (λ). So every spectrometer has to

  1. Prepare the light to be examined in such a way that a plane wave hits the dispersive component and
  2. after the component, convert the change in angle into a change in position, for detection e.g. on a CCD line or a CMOS sensor.

6.7.1 Grating spectrometer

The optics of these devices will be discussed here using a grating spectrometer.

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Basic structure of a grating spectrometer

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Figure 6.7.1 shows the basic structure of a grating spectrometer. Light from the source to be examined (or from the sample to be examined) is imaged with a condenser lens on a point (spherical lens) or on a line (cylinder lens). A diaphragm (chalk-shaped hole or gap) only lets light through from the area to be examined. Another lens (spherical or cylindrical) is used to parallelize the light from the diaphragm. For this purpose, the diaphragm is in the focal plane of the lens. This parallel light is deflected by the grating, our dispersive element. One of the higher orders (greater than or equal to one), which consists of parallel light, is imaged by a further lens (spherical or cylindrical) on a position-sensitive detector (e.g. a CCD line or a photodiode array).

The parallel rays of the different wavelengths are inclined to different degrees to the optical axis. This means that the foci of the different wavelengths are separated on the detector. The width of a focal point depends on the diffraction phenomena on the lenses, but also on the grating.

The largest object is the grid itself. If it has a lattice constant g (distance between the “bars”) and N lines, it has a width bGrid= Ng, so it is a gap with the width Grid. According to equation (3.7) the diffraction pattern then has the form (see also Figure 6.7.1)

(6.1)

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Diffraction at a grating with the grating constanteg = 20λ and n = 6 grating periods, i.e. a width of 120λ.

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The smallest structure is the single line, which we want to assume here as a gap of width a ≤g. We can use a fill factor sf Define and write:

(6.2)

The diffraction pattern of a single grating line is modeled as a gap (see also Figure 6.7.1):

(6.3)

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Diffraction at a single slit with the width g ∕ sf= 20 ∕ 2λ = 10λ.

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Finally, a lattice creates a periodic structure at the angles (see also Figure 6.7.1)

(6.4)

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Position of the grating orders, shown with the diffraction images of the entire grating with diffraction at a single slit with the width g = 20λ n = 6 and sf= 2.

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These three components then result in the diffraction pattern of a real grating. The amplitudes must be added in the correct phase. We assume here that one component is dominant at each of the locations of the diffraction maxima, so that as a first approximation we can neglect the phases and add the intensities. The widest component is the one with the smallest structure size, i.e. the single gap. This results in the envelope.

The narrowest component is the gap, which represents the entire grid. This diffraction pattern is repeated at every diffraction order of the grating.

Together this results in the diffraction pattern of the grating

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Diffraction pattern of a grating with the width g = 20λ, n = 6 and sf= 2.

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The following figure 6.7.1 shows the influence of diffraction on a single grating element.

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Diffraction pattern of a grating with the width g = 20λ, n = 6 and sf= 3 with a grid with the width g = 20λ, n = 6 and sf= 10.

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Finally, Figure 6.7.1 shows the effect of the number of illuminated grid elements.

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Diffraction pattern of a grating with the width g = 20λ, n = 6 and sf= 3 with a grid with the width g = 20λ, n = 20 and sf= 3.

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From Figure 6.7.1 it can be seen that a larger number of illuminated grid lines reduces the line width on the detector. It is therefore important to always fully illuminate a grid. This can be achieved with an upstream optic.

From Figure 6.7.1 it can be observed that the amplitude of the first diffraction maximum depends on the shape and diffraction at a grating period.

Each grating has a usable spectral range. If the second order of one wavelength is superimposed on the first of another wavelength, these two spectral components can no longer be separated.

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Figure 6.7.1 shows the same structure as Figure 6.7.1, but with a prism as the dispersive element. The reasoning behind the optical structure is the same as for the grating spectrometer.

Prism spectrometers have advantages over grating spectrometers

  1. In contrast to a grid, there is only one, deflected order.
  2. There is no mixing of different orders, and therefore potentially a very large free spectral range.
  3. By choosing the material, the dispersion and thus the wave separation can be adjusted.
  4. Prisms are less prone to surface damage such as grids.
  5. The diffraction at the lens apertures or at the prism limits the possible resolution

But prism spectrometers also have disadvantages:

  1. Light passes through matter, which means that the material properties such as absorption limit the possible wavelengths
  2. In the case of gratings, the dispersion can be adjusted over a very wide range via the grating spacing g. This is not possible with prisms.
  3. The wavelength resolution can be improved by using higher orders.

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Schematic representation of a grating reflection spectrometer. The lamp and lens in front of the entrance slit are to be understood symbolically and represent the source.

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Both structures discussed in Figures 6.7.1 and 6.7.1 use lenses as optical elements. The problems of absorption, as mentioned for lenses, also apply to lenses, of course. This is why many spectrometers use mirrors and reflecting gratings, as shown schematically in Figure 6.7.1.

Light enters the spectrometer through an entrance slit that is in the focus of a spherical mirror. The upper mirror therefore generates parallel light that is diffracted and reflected by a re fl ection grating. The first order is suppressed by the shape of the grid (see Blaze grid in Section 3.12.1). The grid now directs different colors in different directions. The lower mirror now focuses the plane waves with different directions on the plane of the exit slit. Only a small wavelength range, given by the width of the exit slit, is admitted to the detector. This detector can be a photodiode, an avalanche diode [Mar09, 3.3.5.1, pp. 176-177] or a photomultiplier [Mar09, 4.2.5.1, pp. 317-318]. The wavelength is now selected by rotating the grating.

Spectrometers like the one shown in Figure 6.7.1 contain no dispersive elements apart from the grating and, since only re fl ection is used, initially also no absorptive components. The absorption in air (e.g. by water) can be avoided by evacuating the spectrometer. This type of spectrometer can also be used in the ultraviolet or in the far infrared, even for terahertz radiation.

The grating spectrometer shown above is ideally suited to determine the intensity at a wavelength with the highest temporal resolution. Spectra, on the other hand, take a long time, but can be measured with sources that are constant over time and have a very high signal-to-noise ratio.

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Schematic representation of a grating reflection spectrometer. The lamp and lens in front of the entrance slit are to be understood symbolically and represent the source. This is a modification of the spectrometer from Figure 6.7.1.

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In the spectrometer in Figure 6.7.1, the exit slit (see Figure 6.7.1) has been replaced by a line detector (e.g. a camera chip). As in the spectrometers in Figures 6.7.1 and 6.7.1, the spectrum can be measured as a whole. The grating is now fixed, or it is only rotated to select the wavelength range.

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A commercial grating spectrometer as used in the laboratory of the Institute for Experimental Physics at the University of Ulm.

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This type of grating spectrometer can also be manufactured in a highly integrated manner.

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Schematic representation of an integrated grating reflection spectrometer. This is a modification of the spectrometer from Figure 6.7.1.

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The spectrometer from Figure 6.7.1 has the same structure as that from Figure 6.7.1. Everything is applied to a glass block, the outer walls of which are structured as a mirror (with metal vapor deposition) or as a grid (also with metal vapor deposition). Light is fed in with an optical fiber. Their opening is the entry opening. The line detector is also attached directly to the glass body. The whole structure can be potted if desired.



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