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Why only take 2 interferograms? Why not take 2* N ?

Why only take 2 interferograms? Why not take 2* N ?. The birth of the TAURUS concept. Note: A single interferogram only contains (1/ N ) th of in spatial information Scanning the FP across a full FSR is a natural way to: Recover ALL of the spatial information

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Why only take 2 interferograms? Why not take 2* N ?

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  1. IAG/USP (Keith Taylor)‏ Why only take 2 interferograms?Why not take 2*N ? The birth of the TAURUS concept • Note: A single interferogram only contains (1/N)th of in spatial information • Scanning the FP across a full FSR is a natural way to: • Recover ALL of the spatial information • Resolve the fundamental ambiguity in the individual interferograms • Scanning can be achieved in 3 ways: • Changing : - by tilting the FP or by moving the image across the fringes • as in photographic interferograms (to partially resolve ambiguity) • Changing : - by changing the pressure of a gas in the FP gap • as in 0th dimensional scanning with eg: propane • Scanning d: - by changing the physical gap between the plates • very difficult since need to maintain parallelism to /2N, at least TAURUS = QI etalons + IPCS … c1980

  2. IAG/USP (Keith Taylor)‏ Queensgate Instruments (ET70)

  3. IAG/USP (Keith Taylor)‏ Piezo transducers (3) CS100 controller Queensgate Instruments (Capacitance Micrometry) FP etalons • Construction • Super-flat /200 base • Centre piece (optical contact) • Top plate • Capacitors • X-bridge • Y-bridge • Z-bridge (+ stonehenge) Scanning d over 1*FSR m  (m-1) ; d  d + (/2)

  4. IAG/USP (Keith Taylor)‏ } Imperial College, London  QI etalons + CS100 University College, London  IPCS TAURUS  16 Mbyte datacubes Alec Boksenberg and theImage Photon Counting System (IPCS) Perfect synthesis …

  5. IAG/USP (Keith Taylor)‏ How big a field? From before, Jacquinot central spot given by: R = 2 or: R ~ 82/2 ~ 82(d/DT)2/J2, where J is the angle on the sky. However, given an array detector, we can work off-axis: So, how far? Answer: Until the rings get narrower than  ~2 pixels (the seeing disk) Now, from the Airy Function we obtain: d/d = -1/0.sin() The full TAURUS field, F is then: F = 22(d/DT)2/R F/J ~ 20, typically or ~400 in 

  6. IAG/USP (Keith Taylor)‏ TAURUS Datacube • Recalling the phase delay equn: • m = 2l.cos • For small values of : •  goes as [1 – (2/2)] • where   tan-1[(y-y0]/[x-x0]) • and (x0,y0) = centre of FP fringes • (x1,y1) is shifted in z-dirn w.r.t. (x0,y0) and this -shift is thus ~parabolic in  It is also periodic in “m”. We thus refer to this shift as a “Phase-correction” So the surface of constant  is a “Nested Parabola” Cut through a “Nested Parabola and you get a set of rings and these rings are the FP fringes.

  7. IAG/USP (Keith Taylor)‏ Wavelength Calibration(converting z to ) As shown, surfaces of constant , as seen in an (x,z)-slice are defined by a set of nested parabolæ, equally spaced in z. Any (x,y)-slice within the cube cuts through these nested paraboloids to give the familiar FP fringes (rings). Now -calibration requires transforming z   where: l(z) = l(0) + az a is a constant of proportionality. Constructive interference on axis (x0,y0) gives: az0 = m0/2 - l(0) but an off-axis (x,y) point transmits the same 0 at (z0 + pxy) where: apxy = l(z0).(secxy – 1)

  8. IAG/USP (Keith Taylor)‏ z I0(z)   z z Phase corrected I0() at (x1,y1) at (x2,y2) Phase Correction The 2D phase-map, p(x,y), can be defined such that: p(x,y) = mz0(sec – 1) The phase-map, p(x,y), can be obtained from a -calibration data-cube by illuminating the FP with a diffuse monochromatic source of wavelength, . Note: Phase-map is discontinuous at each z

  9. IAG/USP (Keith Taylor)‏ The Phase-Map The phase-map is so called since it can be used to transform the raw TAURUS cube, with its strange multi-paraboloidal iso-wavelength contours into a well-tempered data cube where all (x,y)-slices are now at constant wavelengths. The process is called phase-correction since it represents a periodic function of period, z. ie: If the z-value (z’) of a phase-shifted pixel exceeds the z-dimensions of the data-cube, then the spectra is simply folded back by one FSR to (z’ - z). It will be noted that the phase-map (as defined previously) is independent of  and hence in principle any calibration wavelength, cal, can be used to phase-correct an observation data-cube at an arbitary obs, remembering that:   2 & z = /2 But also, the phase-map can be expressed in -space as: xy = 0(1 - cos) and hence is also independent of gap, l, and thus applicable to all FPs at all .

  10. IAG/USP (Keith Taylor)‏ (1  2)  m2 m1 = z2 – z1 z 1 m1 2 2 Order (m) and gap (l) determination The periodicity of the FP interference fringes makes -calibration non-trivial. The paraboloidal mapping from z   doesn’t exactly help, either! Nevertheless, using 2 calibration wavelengths: Say: 1 and 2, peak on-axis at z1 and z2 The trick is to find m1 (and hence m2), the order of interference. From m we can infer the gap, l , and hence obtain a -calibration where: az0 = m0/2 - l(0) Then: If m1 can be estimated (from manufacturers specs or absolute capacitance measures) then we can search for a solution where m2 is an integer. This can be an iterative process with several wavelength pairs. Clearly the further 1 and 2 are apart, the more accuracy is achieved.

  11. IAG/USP (Keith Taylor)‏  = 0 { } (z  z0) + 1 m0z0 Wavelength Calibration If m1 can be estimated (from manufacturers specs or absolute capacitance measures) then we can search for a solution where m2 is an integer. This can be an iterative process with several wavelength pairs. Clearly the further 1 and 2 are apart, the more accuracy is achieved. Once the interference order, m1, for a known wavelength, 1, has been identified then wavelength calibration is given by:

  12. IAG/USP (Keith Taylor)‏ FPP in collimated beam • Interference fringes formed at infinity: • Sky and FP fringes are con-focal • Detector sees FP fringes superimposed on sky image IF FP

  13. IAG/USP (Keith Taylor)‏ FPI in image plane • Interference fringes formed at infinity: • Sky and FP fringes are not con-focal • Detector sees FP plates superimposed on sky image • ie: No FP fringes seen on detector • FP is not perfectly centred on image plane (out of focus) to avoid detector seeing dust particles on plates. FP IF

  14. IAG/USP (Keith Taylor)‏ FP (or Interference Filter)in image plane The FP still acts as a periodic monochromator but the angles into the FP (or IF) must not exceed the Jacquinot criteria, which states that: 2 < 82/R (or R = 2) At f/8:  = 2.tan-1(1/16) ~7.2º, so R < 500 At f/16:  = 2.tan-1(1/32) ~3.6º, so R < 2,000 Note: the FoV is determined not by the width of the fringes but by the diameter of the FP. Also, an IF is simply a solid FP ( ~2.1) with very narrow gap.

  15. IAG/USP (Keith Taylor)‏ Data-cube science

  16. IAG/USP (Keith Taylor)‏ • FP observations of NGC 7793 on the 3.6m. • Top left: DSS Blue Band image. • Top right: Spitzer infrared array camera (IRAC) 3.6μm image. • Middle left: Hα monochromatic image. • Middle right: Hα velocity field. • Bottom: position-velocity (PV) diagram.

  17. IAG/USP (Keith Taylor)‏ • FP observations of NGC 7793 on the 36cm. • Top left: DSS Blue Band image. • Top right: Spitzer IRAC 3.6μm image. • Middle left: Hα monochromatic image. • Middle right: Hα velocity field. • Bottom: PV diagram.

  18. IAG/USP (Keith Taylor)‏ ADHOC screen shot (Henri)

  19. IAG/USP (Keith Taylor)‏ ADHOC screen shot (Henri)

  20. 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.

  21. IAG/USP (Keith Taylor)‏ [1 + cos(2x)] I     B() = I(x) = I(x).(1 + cos2x).dx B().(1 + cos2x).d - - and x 1 (, ) = 2 2 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: Now, if we vary x in the range:   x/2  , continuously then: These represent Fourier Transform pairs. Spectrum B() is obtained from the cosine transformation of the Interferogram I(x)

  22. IAG/USP (Keith Taylor)‏ ) I ( = [1 + cos(2x)] 1 = R0 = 2  2xmax   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/dsitructively interfere • For a particular , the intensity varies sinusoidally according to the simple relationship: In reality, of course, x goes from 0  xmax which limits the spectral resolving power to: eg: if xmax = 100mm and  = 500nm then: R0  1.105

  23. 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.

  24. IAG/USP (Keith Taylor)‏ Pros & Cons of an IFTS Advantages: • Arbitary wavelength resolution to the R limit set by xmax; • 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 103 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.

  25. IAG/USP (Keith Taylor)‏ Michelson Interfermeter(N = 2 interference ; n >>1)

  26. IAG/USP (Keith Taylor)‏ Hybrid and Exotic Systems • FP & IFTS are classical 3D imaging spectrographs • ie: Sequential detection of images to create 3D datat cubes: • FP = Wavelength scanning • IFTS = Phase delay scanning Examples of this are: Integral Field Units (IFUs). These can use either: • Lenslets • Fibres • Lenslets + Fibres • Mirror Slicers 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

  27. 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 Tiger SIFS MPI’s 3D

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

  29. 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?

  30. IAG/USP (Keith Taylor)‏ Tiger (in practice) Enlarger Detector Camera Lenslet array Collimator Grism

  31. IAG/USP (Keith Taylor)‏ Avoiding overlap -direction • 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 Represents a neat/clever optical trick

  32. 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 3rd axis (like FP & IFTS) – very limited FoV, as a result

  33. IAG/USP (Keith Taylor)‏ Tiger Results (SAURON – WHT)

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