1. JGR 19 Apr 2001 1 Basics of Spectroscopy Gordon Robertson (University of Sydney)

2. JGR 19 Apr 2001 2 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

3. JGR 19 Apr 2001 3 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...

4. JGR 19 Apr 2001 4 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.

5. JGR 19 Apr 2001 5 Spectral formats Long-slit spectroscopy Narrow band imaging Echelle Multi-slit Focal-plane mask Multi-fibre Focal-plane fibre feed Integral field Focal-plane IFU spatial cross-disp.

6. JGR 19 Apr 2001 6 Types of spectroscopic observations

7. JGR 19 Apr 2001 7 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

8. JGR 19 Apr 2001 8 Reflection grating geometry   Path difference = a (sin  + sin  ) (  is negative in this case) a a sin  a sin |  |

9. JGR 19 Apr 2001 9 The grating equation   m = a(sin  + sin  ) a m = order of diffraction, most often  1

10. JGR 19 Apr 2001 10 Telescope - slit - collimator f Tel f Coll slit (width s in m) D Telescope objective Collimator b (beam diam) Reduction scale factor = b/D = f Coll /f Tel

11. JGR 19 Apr 2001 11 Reflection grating optics (schematic) grating camera dd collimator ii detector  cc slit b  

12. JGR 19 Apr 2001 12 Spectral resolution of a grating Idealised image of slit at neighbouring wavelengths: Intensity Position on detector +  The observed spectrum is convolved (smoothed) by the line spread function (in practice more Gaussian than rectangular) Wavelength equivalent of slit width

13. JGR 19 Apr 2001 13 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)

14. JGR 19 Apr 2001 14 Resolution and grating ‘depth’ Grating depth = b tan  In Littrow configuration (  =  ): ,  b becomes

15. JGR 19 Apr 2001 15

16. JGR 19 Apr 2001 16 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

17. JGR 19 Apr 2001 17 Grating blaze 0 +1 +2 0 +1

18. JGR 19 Apr 2001 18 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

19. JGR 19 Apr 2001 19 Prisms as dispersive elements (2) 1%

20. JGR 19 Apr 2001 20 Prisms as dispersive elements (3) t b 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)

21. JGR 19 Apr 2001 21 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 Introduction to Volume Phase Holographic (VPH) gratings

22. JGR 19 Apr 2001 22 Note: no antireflection coatings Test of a prototype VPH grating

23. JGR 19 Apr 2001 23 Now we know how to disperse the light - using interference/diffraction or variation of n( ) in glass. What other fundamental constraints apply to spectrographs?

24. JGR 19 Apr 2001 24 The A  product A1A1 A3A3 33 11 E.g. f/8 beam  half- angle = 3.6°, and 1´´ seeing in AAT  Focal spot diam = 0.15 mm  A 1  1 = 0.72 mm 2 deg 2 E.g. f/2.5 camera  half-angle = 11.3°, and 1´´ seeing  Focal spot diam = 0.047 mm  A 3  3 = 0.72 mm 2 deg 2 A2A2 22 E.g. 150mm collimated beam Angular spread = 1´´  D/b = 26´´  A 2  2 = 0.72 mm 2 deg 2 On primary, angular spread = 1´´ and diameter b = 3.89 m  A  = 0.72 mm 2 deg 2 A  is equivalent to entropy of the beam. It cannot be decreased by simple optics. It is also known as etendue

25. JGR 19 Apr 2001 25 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 

26. JGR 19 Apr 2001 26 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

27. JGR 19 Apr 2001 27 Optical design for ATLAS spectrograph (D. Jones, P. Gillingham) focal plane collimator VPH grating camera CCD detector

28. JGR 19 Apr 2001 28 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 10  m rms radius) Adequate sampling at the detector –at least 2 pixels/FWHM, preferably ~3

29. JGR 19 Apr 2001 29 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