1. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Instrumentation Concepts Ground-based Optical Telescopes Keith Taylor (IAG/USP) Aug-Nov, 2008 Aug-Sep, 2008 IAG-USP (Keith Taylor)

2. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Imaging Fourier Transform Spectrographs (IFTS) FTS = Michelson Interferometer: IFTS = Imaging IFTS over solid angle, . Beam-splitter produces 2 arms; Light recombined to form interference fringes on detector; One arm is adjustable to give path length variations; Detected intensity is determined by the path difference,  x, between the 2 arms.

3. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ IFTS theory (simple version) Given that frequency, = 1/ (unit units of “c”): Phase difference between two mirrors = 2  x So recorded intensity, I, is given by: I xx 2 (, ) 1 2 = [1 + cos(2  x)] Now, if we vary x in the range:   x/2  , continuously then:   -- I (x) = B ( ).(1 + cos2  x).d   -- B ( ) = I (x).(1 + cos2  x).dx and These represent Fourier Transform pairs. Spectrum B ( ) is obtained from the cosine transformation of the Interferogram I (x)

4. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ IFTS reality (simple version) At x = 0: the IFTS operates simply as an imager; White light fringes – all wavelengths behave the same At all other x-values, a subset of wavelengths constructively/destructively interfere For a particular, the intensity varies sinusoidally according to the simple relationship: I ) 1 2 ( = [1 + cos(2  x)] In reality, of course, x goes from 0   x max which limits the spectral resolving power to: R 0 =  = 2  x max eg: if  x max = 100mm and = 500nm then: R 0  1.10 5

5. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ IFTS in practice Since we are talking here about an imaging FTS then what is it’s imaging FoV? Circular symmetry of the IFTS is identical to the FP and hence: 2  l.cos  = m And also: R  >> 2  limited only by the wavelength variation, , across a pixel: However, in anaolgy to the FP  Phase-correction is required in order to accommodate path difference variations over the image surface.

6. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Pros & Cons of an IFTS Advantages: Arbitary wavelength resolution to the R limit set by  x max ; A large 2D field of view; A very clean sinc function, instrumental profile cf: the FP’s Airy Function A finesse N = 2  /  which can have values higher than 10 3 Disadvantages: Sequential scanning – like the FP. However, the effective integration time of each interferogram image can be monitored through a separate complementary channel, if required; Very accurate control of scanned phase delay is required Especially problematic in the optical At all times, the detector sees the full spectrum and hence each interferogram receives integrated noise from the source and the sky This compensates for the fact that all wavelengths are observed simultaneously which is why there is no SNR advantage over an FP; Also sky lines produce even more noise, all the time.

7. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Michelson Interfermeter (N = 2 interference ; n >>1)

8. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Hybrid and Exotic Systems Examples of this are: Integral Field Units (IFUs). These can use either: Lenslets Fibres Lenslets + Fibres Mirror Slicers FP & IFTS are classical 3D imaging spectrographs ie: Sequential detection of images to create 3D datat cubes: FP = Wavelength scanning IFTS = Phase delay scanning There are, however, techniques which use a 2D area detector to sample 2D spatial information with spectral information, symultaneously. These we refer to as: Hybrid Systems

9. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Integral Field Spectroscopy Extended (diffuse) object with lots of spectra Use “contiguous” 2D array of fibres or ‘mirror slicer’ to obtain a spectrum at each point in an image SIFS Tiger MPI’s 3D

10. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Lenslet array (example) Used in SPIRAL (AAT) VIMOS (VLT) Eucalyptus (OPD) LIMO (glass) Pitch = 1mm Some manufacturers use plastic lenses. Pitches down to ~50  m

11. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Tiger (Courtes, Marseille) Technique reimages telescope focal plane onto a micro-lens array Feeds a classical, focal reducer, grism spectrograph Micro-lens array: Dissects image into a 2D array of small regions in the focal surface Forms multiple images of the telescope pupil which are imaged through the grism spectrograph. This gives a spectrum for each small region of the image (or lenslet) Without the grism, each telescope pupil image would be recorded as a grid of points on the detector in the image plane The grism acts to disperse the light from each section of the image independently So, why don’t the spectra all overlap?

12. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Tiger (in practice) Enlarger Lenslet arrayCollimator Grism Camera Detector

13. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Avoiding overlap The grism is angled (slightly) so that the spectra can be extended in the -direction Each pupil image is small enough so there’s no overlap orthogonal to the dispersion direction -direction Represents a neat/clever optical trick

14. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Tiger constraints The number and length of the Tiger spectra is constrained by a combination of: detector format micro-lens format spectral resolution spectral range Nevertheless a very effective and practical solution can be obtained Tiger (on CFHT) SAURON (on WHT) OSIRIS(on Keck) True 3D spectroscopy – does NOT use time-domain as the 3 rd axis (like FP & IFTS) – very limited FoV, as a result

15. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Tiger Results (SAURON – WHT)

16. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Fibres in Astronomy Optical fibre technology offers the astronomical spectrograph designer vast opportunities. Astronomical Spectroscopy is the art of recording spatial and spectral information simultaneously onto a 2D area detector. In other words it requires the re-formatting of information to suit the detector and the astronomical goals. If we could arbitrarily define the geometry of our detectors (even to make them 3D!) then none of the sophisticated optical design would be necessary. This is where fibres come into their own … They are the “perfect” image re-formatters, taking any shape of object and re- forming it into a spectrograph slit.

17. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Types of Fibre Generally used for astronomy (dia >50  m) Special case for Adaptive Optics (dia ~10  m) Operates by total internal reflections Protective buffer Fiber operates as an optical wave-guide

18. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Focal Ratio Degradation (FRD) Input f-ratio = Output f-ratio (A  is preserved) But not, unfortunately, in a fibre Note central obstruction Note: Input f-ratio is not preserved; F in (slower) > F out (faster) Central obstruction is filled in A  in < A  out ; to compensate, R decreases or d increases

19. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Numerical Aperture (NA) Protective buffer nfncn0nfncn0 Note: tan  max = 1/2 F in = NA, the numerical aperture: NA ~ 0.22 ( F in is slower than > 2.3) for normal fibres For the fibre to operate as an optical waveguide, total internal reflection (TIR) has to be maintained throughout the passage of light along the fibre. TIR then requires:  n 2 f  n 2 c n0n0 sin  max =

20. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Using Fibres to link Telescopes to Spectrographs. Advantages Spectrograph independent from telescope. Bench Spectrographs, no weight or volume restrictions. High spectral stability. Fibres are easy to use and install (once prepared!) Possibility to perform two-dimension spectroscopy with fibre bundles. Drawbacks Transmission losses. Focal Ratio Degradation. Circular aperture losses. Poor sky subtraction. Fixed “slit aperture”. Difficult to prepare if not proper tools are available. Fragile!

21. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Fibre slicer (the simplest approach) A simple fibre re-formatter from sky to spectrograph slit 2D array of fibres at the telescope focal plane Re-formatted onto a long- slit of the spectrograph

22. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Fibre slicer attributes and examples Captures light over a full seeing disk (and more) without degrading the intrinsic resolving power of the spectrograph; Facilitates spatially resolved spectroscopy; No requirement to centre a point object on a slit; No requirement to match slit width to the seeing; Effectively detaches spectral and spatial information; Facilitates spatially integrated spectroscopy Integral field spectroscopy (IFS) Supplies robust spectrophotometry Objects aligned along the slit Examples: F.I.S. (on AAT - 1981)100 fibres SILFID (on CFHT - 1988)400 fibres HEXAFLEX (on WHT – 1991) 61 fibres 2D-FIS(on WHT – 1994)125 fibres

23. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Fibre Spectral Image 400 individual fibres All wavelengths are aligned

24. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ … and now some numbers! Clearly for a fibre diameter,  fibre, each individual fibre aperture (  fibre ) on the sky is given by:  fibre DF fibre  fibre = where F fibre is the input focal ratio of the fibre. Example: Take  fibre =0.5” ; D = 8m and F fibre = 5   fibre ~80  m This integral field unit (IFU) fibre can be retro-fitted to existing long-slit spectrographs, however there are 3 problems: 1.Focal ratio degradation (FRD) which requires fast f-ratios 2.Collimator speeds which are matched to normal Cassegrain f-ratios, which require slow f-ratios 3.Spatial information is lost in the inter-fibre gaps

25. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Coupling fibres with micro-lenses Micro-lens array Lenslet/fibre coupling If  = spatial sampling on sky (subtended by micro-lens), then  fibre = .D T. F fibre  lens = .D T.F Tel

26. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ The SIFS IF courtesy C&L de Oliveira, (LNA) ‏

27. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Down-side of lenslet/fibre coupling F spec F in F in (slower) > F spec (faster) because of FRD The fibre But fibre receives light from micro-lens significantly faster than F in (where: F fibre (faster) < F in (slower) - see red rays) F fibre Take:  fibre = dia. of fibre  lens = dia. of micro-lens  lens  fiber 1 + F in F fibre = therefore Conclusion – don’t make  lens too small Use macro-lenses (!)

28. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Mirror Image Slicers Pioneered by MPI (3D) (Gensel) Compact Efficient Slicer of choice but … Cannot be retrofitted to existing spectrographs

29. Aug-Nov, 2008 IAG/USP (Keith Taylor) ‏ Slicer Promo (The End)