Slitless Spectrograph

If a dispersive element is located before the focal plane of a telescope, the processor is called a slitless spectrograph.

• Objective grating: If a concave reflective grating is substituted to the primary mirror of a small telescope, one obtains the basic form of slitless spectroscopy with an objective grating. For an object at infinity and given a wavelength, the design with a paraboloid reflective grating working at a normal diffraction angle is rigourously stigmatic on the axis; similarly a stigmatic solution is also obtained with a spherical reflective grating and variable spacing lines. For an object point at finite distance, there always exists a conicoid grating shape providing a stigmatic image for a wavelength diffracted perpendicularly to the grating vertex, sometimes called normal diffraction mounting. Because gratings are not available in very large size, other alternatives have been developed for objective spectroscopy.

• Normal field objective prisms: If a prism pair is designed to cancel the deviation at wavelength A0 but still provides a dispersion, the processor is known as Fehrenbach prisms or normal field objective prisms. For the determination of stellar radial velocities, such prism pairs have been pioneered by Fehrenbach in 1944 [56] and developed up to 0.6 m aperture diameter (Fehrenbach et al. [57]) as telescope input pupil components. Exposures are taken with the prism-pair at 0° and then with inplane rotation of 180°, thus providing two counter-dispersed spectra of 5° sky field as for the Schmidt telescope at Haute Provence Observatory [58]. Let nd,1 and nd,2 be the d-yellow hydrogen line refractive indices of prisms with small wedge angles A1 and A2, respectively. If the wedges are opposite such as A2 = -A1 = A, then the beam deviation angle of the two prisms - which form a parallel plane plate - is a = (nd,1 - nd,2) A.

By choosing a glass pair such as nd,2 = nd,1 = nd the deviation is cancelled, a = 0. Introducing the Abbe number vd = (nd -1)/ (nF — nC), the dispersion angle between the F-blue and C-red hydrogen wavelengths is, from the above relation,

From the Schott (nd, vd) diagram of glasses, one can see that the dispersion of these two wavelengths is ~ 2.3-times larger for the glass pair SK14-F5 (nd = 1.603) than for the glass pair BK6-LLF6 (nd = 1.531). The design of Fehrenbach normal field prisms for a given central wavelength X0 sometimes requires the glass manufacturer to elaborate a special glass.

It must be noticed that Fehrenbach normal field prisms have the highest throughput compared to any slitless dispersion system. Instead of being installed at the telescope input, they also can be located at a reimaged pupil of a large telescope. For galaxies at extremely large distances, this should allow efficient detections of large redshifted spectra - typically z — 7 - such as the Lyman cutoff observed in the near infrared region.

• Grism: If the processor is a simple A-shaped prism, the beam is turned through a deviation angle but the dispersion is less than from a transmission grating. Therefore, if a transmission grating is bonded to the prism such as the resulting deviation cancels at wavelength X0, then the beam is still dispersed. Such a combination is called a grism or Carpenter prism and is usually located before a telescope focus for objective spectroscopy.

• Grens: If the surface of a prism - which is not bonded to the grating - is given some power to act as a lens, the processor is sometimes called a grens. For instance, wide-field correctors equipped with a grens were designed by Richardson [127,128] for objective spectroscopy at the prime focus of large telescopes (Fig. 1.35).

Fig. 1.35 Richardson objective grens at Cfht prime focus. The wedge of the third lens is 1.1° with a 45 </mm grating giving 1,000 A/mm dispersion on a focal plane tilted 0.38° (after Richardson [127])

1.12.8 Multi-Object Spectroscopy with Slits or Fiber Optics

If a spectrograph simultaneously disperses objects whose positions in the field are discrete, the process is called multi-object spectroscopy. Two classical alternatives are with multi-slit masks or optics fibers.

Dispersed Giens focal field

• Multi-slit mask: From the spectrograph imaging mode, the coordinates of the objects are selected in a rectangular field and a multi-slit mask is then made as input of the spectrograph mode. The spectra are generally obtained on a rectangular detector and have homothetical positions to those of the objects in the telescope field. This technique is well adapted for a typical 5-7 arcmin field. Accurate multi-slit masks are generated by high-power Yag lasers which, in addition to rectangle slits, allow curvilinear-slit cuts of constant width in the dispersion direction for arch-like object studies (Di Biagio et al. [14]).

• Fiber optics: Optics fibers have the advantage of selecting objects whatever their location in a small field (5-7 arcmin) or a large field. The fiber output ends feed the long slit of one or several spectrographs. However, optics fibers suffer from focal ratio degradation (Frd) so that the collimator of the spectrograph must have a somewhat faster f-ratio than that of the emerging telescope beams. Some examples of large field instruments are the galaxy and quasar surveys 2dF (400 fibers, 2° field at 4 m AAT), Sdss (640 fibers, 2 x 1.5° field at 2.5 m extended field R-C), 6dF(150 fibers, 6° field at 1.2 m UK Schmidt) and next Lamost (4000 fibers, 5° at 4 m Schmidt) (cf. Table 1.1). For a large sky scale and low object density, each fiber input can be motorized.

1.12.9 Integral Field Spectrographs

If a spectrograph allows the entrance of all N2 contiguous subareas of a field area (Sx, Sy) subdivided into N x N elements, the arrangement is an integral field spectrograph (Ifs). The data recording process (Sx, Sy, A), then called 3-D spectroscopy, allows obtaining simultaneous spectra of all the field image elements of the seeing size. The basic constraints for acquiring three-dimensional information -the so-called "data cube" - with two-dimensional detectors was discussed by Monnet [109].

If an arrangement allows integral field spectroscopy when placed in series with a classical spectrograph, this is called an integral field unit (IFU).

G. Courtes showed in 1952 [40] that the detection of extended objects is greatly increased by use of fast camera optics. Such systems which then reduce the efl of a telescope are called focal reducers. Usually, the dispersor - grism, Fabry-Perot, colored or interference filters - is introduced in the afocal beams before the camera optics. Sometimes it can be very efficient to use an interference filter in convergent beams (Courtes [41]). An interesting instrumental concept - which is not really a spectrograph but a simultaneous multi-bandpass imager or multi-bandpass photometer - consists of reimaging several spectral zones of a dispersed image of the telescope pupil on individual regions of a detector or on several detectors (Courtes [40]); the optical design is facilitated by use of a white pupil mounting [11]. These multi-bandpass photometers are efficient systems for the determination of faint astronomical objects having a large redshift.

We may distinguish several alternatives for Ifs, all using collimating optics, disperser or scanning interferometer, and camera optics.

• Bundle fiber and lenslets: A bundle fiber with the output fiber ends feeding a long slit provide a simple arrangement for an Ifu. However, the light losses because of the gaps between the cores of the fibers can be avoided by use of a 2-D microlens array which images the telescope pupil on the fiber input. This requires re-arranging the entrance bundle fiber, also in number N2, into a cartesian frame such as proposed by Courtes [42] and developed by Allington-Smith et al. [4]. At the fiber output, a

1-D microlens array may also be used for a sharp re-imaging of the field of view elements on one or several long-slit spectrographs.

• Lenslets: A mostly transparent Ifs consists to form the telescopic image on a

2-D microlens array, or lenslet, which images the telescope pupil into N2 sub-pupils on a mask. The mask has N2 holes, much smaller than the microlenses, which allow all the light to enter the spectrograph. This provides a simple arrangement for an Ifu. After the beam collimation a grism must be appropriately oriented about the axis of the camera optics in order to optimize the 2-D filling of the spectra on the detector area (Courtes [43]). Depending on the spectral dispersion, the filling of the N2 spectra on the detector area requires an optimization involving the microlens size, the detector size, and the grism orientation with respect to the lenslet. The well-defined hole- or slit-function and optical etendue of this system (Jacquinot [81]) provide a uniform spectral resolution for stellar or extended objects.

• Scanning Fabry-Perot: For an N2 high sampling of contiguous subareas, another alternative is to use a scanning Fabry-Perot instead of a classical disperser. As shown by Caplan [25] and Bland-Hawthorn [16], this requires the data processing of a more complex point spread function, the Airy function, than with a grating spectrograph. The temporal fluctuation of the sky during the integration makes it difficult to obtain an accurate intensity ratio of two distant spectral lines unless rapid scanning is used (Caplan [25]). Some accounts on these instruments are given by Le Coarer, Amram et al. [35], Georgelin, Comte et al. [67] and Tully [163].

• Fourier transform spectrometer: With the advent of 2-D infrared detectors,

3-D or imaging Fourier transform spectrometers (FTS) have been designed and built for the near infrared by Maillard [99], who proposed an option for the JW Space Telescope. The state-of-the-art of detector technology only allows a moderate N2 number for the far infrared, however the Spire Fts, with optics designed by Dohlen et al. [47], is one of the two imaging spectrometers installed on the Her-schel Space Telescope for observations from the L2 Lagrange point of the Sun-Earth system.

• Image slicer: Bowen [20] introduced the first image slicer (IS) to avoid the light loss at the narrow slit of high-resolution stellar spectrographs. This uses a 1-D plane-facet array of k facets which by appropriate orientation reflects at 90° the telescope image of a square area N2a2 of N2 elements into k rectangular elements of area (Na/k) x (Na). Richardson [126, 129] introduced a new IS concept with two concave mirrors of equal curvature whose centers of curvature are on their reciprocal vertices. Each mirror is separated in two halves - the slit mirrors and the aperture mirrors - to form a straight slot, and the two slots are arranged in orthogonal directions. The starlight enters the IS through a cylindric lens which produces two mutually perpendicular line images: the first image line is at the slot of the aperture mirrors and the second line coincides with the slot of the slit mirrors. These later mirrors allow the central part of the light to directly pass through whilst the reflected light goes back to the aperture mirrors. Slight tilts of all four mirrors provides the next sliced subfield elements after even numbers of reflections, thus requiring efficient coatings. A lens located at the slit images the telescope pupil on the spectrograph grating. The sliced subfields are in odd number k and symmetrically distributed end-to-end from the central subfield. The gain in detection is obtained by superposing all the k spectra; this is achieved by a cylindric lens located after the camera optics of the spectrograph (cf. also the account by Hunter [79]). In the Walraven IS [164], the beam propagates by multiple internal reflections into a plane parallel glass plate which is in contact with a triangular area of a prism to allow the light to emerge. Starting from a modified-Walraven IS, Diego [46] added to this system input and output prisms of same wedge, thus obtaining k sliced images all co-focused side-to-side at the same axial position.

Multiple reflections can be avoided with the Lemaitre IS [94] which is designed from two spherical concave mirrors. The slicing transformation of a square field into k rectangular subfields is achieved by uniform rotation of k element areas of each mirror around a lateral axis, so the facets are distributed along helices. If the radii of curvature of the facets are 2R for the field mirror array, R for the pupil mirror array, and their axial separation is R, the sliced subfields are reim-aged by the pupil mirror with transverse magnification M = -1. In the stellar mode for high spectral resolution, the reimaged subfields are just superposed (Fig. 1.36-Up). Therefore, the Etendue or Lagrange invariant expressed by (1.34) immediately entails that a square section of the telescope beam of aperture angle u is transformed into an anamorphosed section whose linear semi-apertures are u'x = ku and u'y = u in accordance with the output Etendue (N2a2/k) x (4ku2). The emerging beam is given a square section at the spectrograph pupil - i.e. the grating -by inserting a cylindrical field lens near the slit. In the integral field spectroscopy mode, the subfields must be arranged end-to-end to feed a long-slit spectrograph. This requires a second rotation of the facets of the pupil mirror array around the other lateral direction (Fig. 1.36-Down), so this mirror is much more difficult to build since it is not directly generated by differential rotations of parallel slice elements from a continuous mirror surface. This mode, developed with the Content IS [37] for Ifus, uses an additional 1-D optics array located at the slit array to reimage the pupil at a correct position in the spectrograph. Transverse magnifications differing from -1 are obtained by changing the curvature of the pupil mirror.

When the slice number k becomes large, one may encounter efficiency difficulties due to the amount of diffracted light from the small mirror elements, so a compromise must be adopted by appropriate scaling of the IS.

Fig. 1.36 Principle of the helix image slicer. The pupil is imaged by the field mirror array on the pupil mirror array. The reimaging of the sliced subfields by the pupil mirror is here shown with magnification M=—1. (Up): Classical mode for superposed spectra, (Down): Long slit mode for Ifus (after Lemaitre [94] and Content [37])

Fig. 1.36 Principle of the helix image slicer. The pupil is imaged by the field mirror array on the pupil mirror array. The reimaging of the sliced subfields by the pupil mirror is here shown with magnification M=—1. (Up): Classical mode for superposed spectra, (Down): Long slit mode for Ifus (after Lemaitre [94] and Content [37])

1.12.10 Back-Surface Mirrors

The large mirrors in telescopes are always front-surface mirrors, but for small mirrors there are advantages with back-surface mirrors. A common example is a right-angle deviation prism. In that case no metal coating is required because the reflection at the diagonal is by internal reflection. If the angle of incidence of the light is lower than the critical incidence angle it is necessary to have a reflective coating on the outside of the back surface, such as in a bathroom mirror. This reflective surface can be well protected against corrosion and dust.

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