Transmission Gratings

Transmission gratings have been flown on the Einstein [8], EXOSAT [16], and Chandra observatories [2,4]. They generally consist of a grating ring filled with little grating elements. Those rings can be placed into the beam path between the Wolter telescope and the focal plane detector preferably close to the mirror exit, thereby dispersing the focussed light into spectral orders. The ring has to follow a special curvature, called Rowland Torus, to guarantee equal beam paths for all rays traversing any of the grating elements [1]. This avoids third order optical aberrations and resulting degradation of the spectral resolution (Fig. 8.2).

The resolution of a transmission grating spectrometer is given by the grating line density and the angular resolution of the telescope: the dispersion angle corresponding to a given wavelength X is sin a = mX/d, (8.1)

Resolving Powers

Resolving Powers

Fig. 8.1 Resolving power of various spectroscopic instruments (Einstein Observatory-OGS, Chandra Observatory-LETG, Chandra Observatory-HETG, XMM-Newton RGS, XMM-Newton EPIC pn-CCDs, Suzaku XRS)

Fig. 8.1 Resolving power of various spectroscopic instruments (Einstein Observatory-OGS, Chandra Observatory-LETG, Chandra Observatory-HETG, XMM-Newton RGS, XMM-Newton EPIC pn-CCDs, Suzaku XRS)

Fig. 8.2 Chandra Transmission grating spectrometer. Individual grating elements are mounted onto a ring following the "Rowland Torus," a surface with two different curvatures: within the dispersion plane, the radius is half of the distance between grating and focal plane, perpendicular to the dispersion plane, the radius is equal to the distance between grating and focal plane. The image of any (point-) source is "stretched" on both sides of the central order image according to the photon energies, thereby producing a spectrum

Fig. 8.2 Chandra Transmission grating spectrometer. Individual grating elements are mounted onto a ring following the "Rowland Torus," a surface with two different curvatures: within the dispersion plane, the radius is half of the distance between grating and focal plane, perpendicular to the dispersion plane, the radius is equal to the distance between grating and focal plane. The image of any (point-) source is "stretched" on both sides of the central order image according to the photon energies, thereby producing a spectrum with d is the grating spacing and m is diffraction order. Typically, only the first diffraction order is used. Line densities vary between 500 lmm-1 (Einstein Observatory) and 5000 lmm-1 (Chandra Observatory). Resolving powers more than 2000 have been reached. Since gratings perform best at low energies, they are mostly freestanding because any substrate would absorb the soft X-rays. Then the grating bars are held only by a coarse support grid.

Transmission gratings are often produced by using an electroforming process, mostly combined with a replication technique [13]. In a first step, a "master" is produced either by a mechanical (diamond-tip) ruling or by laser interference. From this master, the individual gratings are replicated by a photochemical process. Subsequently, the support grid is added by a similar technique (Fig. 8.3). The typical grating material is gold, because it is well suited for electroforming processes and provides, because of its high-Z, sufficient opacity even with grating bar thicknesses below 1 |im.

The efficiency of a classical amplitude grating (bars completely opaque, slits completely transparent) is given by

with a = slit width between grating bars. In the ideal case with a/d = 0.5, the maximum efficiency for each of the symmetric first orders reaches 1/n2 = 10.1%, and all even orders vanish, a desired effect to prevent spectral line confusing. In reality,

Circular Catwalk Industrial
Fig. 8.3 Electron microscope image of a freestanding transmission grating with 1000 lines per millimeter. The grating bars are held by support grid having a pitch of 25 |m (courtesy DR. JOHANNES HEIDENHAIN GmbH)

Energy [keV]

t 0.0100

0.0010

0.0001

Energy [keV]

t 0.0100

0.0010

0.0001

Fig. 8.4 Diffraction efficiencies of the Chandra Observatory LETG for first to sixth and sum of all higher diffraction orders. The design of the grating (bar/slit ratio = 0.5) suppresses the even (2nd and 4th) orders. With a thickness of ~0.4 |im, the grating bars are partially transparent, and constructive interference enhance the efficiency at the Au-M edge below 10 A. Source: Chandra Proposer's Guide [14]

Fig. 8.4 Diffraction efficiencies of the Chandra Observatory LETG for first to sixth and sum of all higher diffraction orders. The design of the grating (bar/slit ratio = 0.5) suppresses the even (2nd and 4th) orders. With a thickness of ~0.4 |im, the grating bars are partially transparent, and constructive interference enhance the efficiency at the Au-M edge below 10 A. Source: Chandra Proposer's Guide [14]

the grating bars are not completely opaque. Then, waves passing through the bars are absorbed and phase-shifted and interfere with waves coming through the grating slits. Whether this interference is constructive or destructive depends on the bar thickness and the photon energy. For gold wires with a thickness around 0.4 |im, a maximum of constructive interference around 1.5 keV can enhance the first order efficiency for each of both orders up to 25% (Fig. 8.4).

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