**Basics of Spectroscopy** Gordon Robertson (University of Sydney)

**Outline** • Aims of spectroscopy • Variety of instrumentation - formatting to a 2D detector • Diffraction gratings • Optical setups, Grating equation, Spectral resolution • Prisms • Volume Phase Holographic gratings • The A product • Conclusion

**Science goals of spectroscopy** 1. Elemental composition and abundances 2. Kinematics 3. Redshifts / cosmology i.e. what is it, where is it, what are its internal motions…. For stars, star clusters, nebulae, galaxies, AGN, intervening clouds etc...

**** Aims of spectroscopic observations Ideally…. A data cube, covering a wide range in each of ,, With good …. spatial resolution , , wavelength resolution , and efficiency BUT detectors are 2-dimensional, so the data must be formatted to fit them. Many interesting new ways of dealing with this.

**Narrow band imaging** spatial cross-disp. Spectral formats Long-slit spectroscopy Echelle Multi-slit Focal-plane mask Multi-fibre Focal-plane fibre feed Integral field Focal-plane IFU

**Types of spectroscopic observations**

**Dispersive elements** A grating, prism or grism….. Sends light of different wavelengths in different directions… hence (via the camera) to different positions on the detector. So incident light must be collimated

**Reflection grating geometry** a sin || a sin a Path difference = a (sin + sin ) ( is negative in this case)

**** The grating equation a m = a(sin + sin ) m = order of diffraction, most often 1

**slit** (width s in m) Telescope objective b (beam diam) D Collimator fTel fColl Telescope - slit - collimator Reduction scale factor = b/D = fColl/fTel

**Reflection grating optics (schematic)** collimator slit grating b cc d i detector camera

** + ** Wavelength equivalent of slit width The observed spectrum is convolved (smoothed) by the line spread function (in practice more Gaussian than rectangular) Spectral resolution of a grating Idealised image of slit at neighbouring wavelengths: Intensity Position on detector

**Spectral resolution formula** Where s is the slit angle on the sky (radians). In Littrow configuration ( = ): • Implications: • Larger telescopes (D) need larger spectrographs (b) for same R • If slit width (s) can be reduced, spectrograph size can be contained • The geometric factor is maximised at large deviation angles (fine rulings, high order)

**Resolution and grating ‘depth’** Grating depth = b tan b , In Littrow configuration ( = ): becomes

**Spectral resolution from general texts ** But physics and optics texts give the resolution of a grating as: Where N is the total number of (illuminated) rulings E.g. for the RGO spectrograph, 1200 l/mm gratings in 1st order, this gives R > ~ 180,000 (i.e. ~ 0.03Å)! This assumes perfectly collimated input, i.e. diffraction-limited slit. Astronomers use wider slits, because of atmospheric seeing

**0** +1 -1 +2 +1 0 -1 Grating blaze

**Prisms as dispersive elements (1)** • Advantages: • Can have high efficiency (no multiple orders) • More than one octave wavelength range possible • Disadvantages: • Low spectral resolution • Non-uniform dispersion (higher in blue, less in red) • Size, mass • Requirements for homogeneity, exotic materials, expense

**1%** Prisms as dispersive elements (2)

**Prisms as dispersive elements (3)** b t E.g. D = 3.89 m (AAT); (b = 150 mm); t = 130 mm; s 1.5; = 5500 Å; LF5 glass gives R = 250 ( = 22 Å)

**Introduction to Volume Phase Holographic (VPH) gratings** • Peak efficiency up to ~90% • Line densities from ~100 to (6000) l/mm - 1st order • Wavelength of peak efficiency can be tuned • Transmission gratings - Littrow config. or close to it • DCG layer (hologram) is protected on both sides • Each grating is an original, made to order • Large sizes possible

**Test of a prototype VPH grating** Note: no antireflection coatings

**Now we know how to disperse the light - using** interference/diffraction or variation of n() in glass. What other fundamental constraints apply to spectrographs?

**2** A2 E.g. f/2.5 camera half-angle = 11.3°, and 1´´ seeing Focal spot diam = 0.047 mm A33 = 0.72 mm2 deg2 E.g. 150mm collimated beam Angular spread = 1´´ D/b = 26´´ A22 = 0.72 mm2 deg2 On primary, angular spread = 1´´ and diameter b = 3.89 m A = 0.72 mm2 deg2 E.g. f/8 beam half-angle = 3.6°, and 1´´ seeing in AAT Focal spot diam = 0.15 mm A11 = 0.72 mm2 deg2 A is equivalent to entropy of the beam. It cannot be decreased by simple optics. It is also known as etendue The A product 3 A1 1 A3

**A can be degraded...** Like entropy, A can be increased (degraded): E.g. focal ratio degradation (FRD) in an optical fibre increases while leaving A unchanged. As a result, spectrograph loses some light, or has to be larger and more expensive, or loses resolution. Seeing has degraded A before we get the light. So .. Best if A of the beam is as small as possible, But best if an instrument accepts the largest possible A

**A can be reformatted….** An integral field unit (or other image slicer) can decrease the spread on the ‘wavelength’ axis at the expense of increasing it in the spatial direction. A is conserved, but we end up with better wavelength resolution A can be decreased in an adaptive optics (AO) system, by using information about the instantaneous wavefront. For large telescopes, AO allows good resolution at managable cost

**focal plane** Optical design for ATLAS spectrograph (D. Jones, P. Gillingham) collimator VPH grating camera CCD detector

**A few practical details** In practical spectrograph designs, we have to take account of: • Field size at the focal plane • collimator needs to be larger than ‘b’ • Optical systems must deliver good image quality • aberration broadening < ~1 pixel (eg 10m rms radius) • Adequate sampling at the detector • at least 2 pixels/FWHM, preferably ~3

**Putting it all together….** • The incoming ,, data have to be formatted to 2D detector • resulting in a wide variety of instruments, with different emphases • Principal dispersive elements are gratings • normally in a collimator - grating - camera - detector system • large systems are required, especially with large telescopes • spectral resolution • depends on beam size • is generally much lower than the diffraction-limited maximum • The size and cost of instruments depends on the A that they have to accept • Challenge for the future: feasible systems for 30 - 50 m telescopes