1 / 40

Spectroscopy principles

Spectroscopy principles. Jeremy Allington-Smith University of Durham. Contents. Reflection gratings in low order Spectral resolution Slit width issues Grisms Volume Phase Holographic gratings Immersion Echelles Prisms Predicting efficiency (semi-empirical). Generic spectrograph layout.

Mia_John
Download Presentation

Spectroscopy principles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Spectroscopy principles Jeremy Allington-Smith University of Durham

  2. Contents • Reflection gratings in low order • Spectral resolution • Slit width issues • Grisms • Volume Phase Holographic gratings • Immersion • Echelles • Prisms • Predicting efficiency(semi-empirical)

  3. Generic spectrograph layout Camera Collimator Focal ratios defined as Fi = fi / Di

  4. Grating equation n1 n2 A B b a A’ B’ a • Interference condition:  path difference between AB and A'B' • Grating equation: • Dispersion: f2 dx db

  5. "Spectral resolution" dl l • Terminology (sometimes vague!) • Wavelength resolutiondl • Resolving power • Classically, in the diffraction limit, Resolving power = total number of rulings x spectral order I.e. • But in most practical cases for astronomy (c < l/DT), the resolving power is determined by the width of the slit, so R < R* Total grating length

  6. Spectral resolution • Spectral resolution: • Projected slit width: Conservation of Etendue(nAW)    Image of slit on detector Camera focal length

  7. Resolving power Size of spectrograph must scale with telescope size • Illuminated grating length: • Spectral resolution (width) • Resolving power: • expressed in laboratory terms • expressed in astronomical terms since and Collimator focal ratio Physical slitwidth Grating length Angular slitwidth Telescope size

  8. Importance of slit width • Width of slit determines: • Resolving power(R)since Rc = constant • Throughput (h) • Hence there is always a tradeoff between throughput and spectral information • Functionh(c) depends on Point Spread Function (PSF) and profile of extended source • generally h(c) increases slower than c+1whereas R c-1 so hR maximised at small c • Signal/noise also depends on slit width • throughput ( signal) • wider slit admits more sky background ( noise)

  9. Signal/noise vs slit width • For GTC/EMIR in K-band (Balcells et al. 2001) SNR falls as slit includes more sky background Optimum slit width

  10. Anamorphism dispersion Output angle • Beam size in dispersion direction: • Beam size in spatial direction: • Anamorphic factor: • Ratio of magnifications: • if b < a, A > 1, beam expands • W increases  R increases • image of slit thinner  oversampling worse • if b > a, A < 1, beam squashed • W reduces  R reduces • image of slit wider  oversampling better • if b = a, A = 1, beam round • Littrow configuration Input angle

  11. Generic spectrograph layout Camera Collimator Fi = fi / Di

  12. Blazing b = active width of ruling (b  a) • Diffracted intensity: • Shift envelope peak to m=1 • Blaze condition specular reflection off grooves: also  since Interference pattern Single slit diffraction F = phase difference between adjacent rulings q = phase difference from centre of one ruling to its edge

  13. Efficiency vs wavelength • Approximation valid for a > l • lmax(m) = lB(m=1)/m • Rule-of-thumb: 40.5% x peak at (large m) • Sum over all orders < 1 • reduction in efficiency with increasing order 2 3 4 5 6 (See: Schroeder, Astronomical Optics)

  14. Order overlaps Effective passband in 1st order Don't forget higher orders! Intensity 1st order blaze profile m=1 First and second orders overlap! m=2 Passband in 2nd order Zero order matters for MOS 2nd order blaze profile Passband in zero order m=0 Wavelength in first order marking position on detector in dispersion direction (if dispersion ~linear) 1st order 0 lL lC 2lL lU 2lU (2nd order) 0 lL lU

  15. Order overlaps dispersion Detector 1st order To eliminate overlap between 1st and 2nd order • Limit wavelength range incident on detector using passband filter or longpass ("order rejection") filter acting with long-wavelength cutoff of optics or detector (e.g. 1100nm for CCD) • Optimum wavelength range is 1 octave (then 2lL = lU) • Zero order may be a problem in multiobject spectroscopy Zero order 2nd order

  16. Predicting efficiency • Scalar theory approximate • optical coating has large and unpredictable effects • grating anomalies not predicted • Strong polarisation effect at high ruling density (problem if source polarised or for spectropolarimetry) • Fabricator's data may only apply to Littrow (Y = 0) • convert by multiplying wavelength by cos(Y/2) • grating anomalies not predicted • Coating may affect grating properties in complex way for largeg (don't scale just by reflectivity!) • Two prediction software tools on market • differential • integral

  17. GMOS optical system CCD mosaic (6144x4608) Mask field (5.5'x5.5') Detector (CCD mosaic) Science fold mirror field (7') Masks and Integral Field Unit From telescope

  18. Example of performance • GMOS grating set • D1 = 100mm, Y = 50 • DT = 8m,c = 0.5" • m = 1, 13.5mm/px • Intended to overcoat all with silver • Didn't work for those with large groove angle - why? • Actual blaze curves differed from scalar theory predictions

  19. Grisms • Transmission grating attached to prism • Allows in-line optical train: • simpler to engineer • quasi-Littrow configuration - no variable anamorphism • Inefficient for r > 600/mm due to groove shadowing and other effects

  20. Grism equations • Modified grating equation: • Undeviated condition: n'= 1,b = -a = f • Blaze condition: q=0lB = lU • Resolving power (same procedure as for grating) q = phase difference from centre of one ruling to its edge

  21. Volume Phase Holographic gratings • So far we have considered surface relief gratings • An alternative is VPH in which refractive index varies harmonically throughout the body of the grating: • Don't confuse with 'holographic' gratings (SR) • Advantages: • Higher peak efficiency than SR • Possibility of very large size with highr • Blaze condition can be altered (tuned) • Encapsulation in flat glass makes more robust • Disadvantages • Tuning of blaze requires bendable spectrograph! • Issues of wavefront errors and cryogenic use

  22. VPH configurations • Fringes = planes of constant n • Body of grating made from Dichromated Gelatine (DCG) which permanently adopts fringe pattern generated holographically • Fringe orientation allows operation in transmission or reflection

  23. VPH equations • Modified grating equation: • Blaze condition: = Bragg diffraction • Resolving power: • Tune blaze condition by tilting grating (a) • Collimator-camera angle must also change by 2a  mechanical complexity

  24. VPH efficiency Barden et al. PASP 112, 809 (2000) • Kogelnik's analysis when: • Bragg condition when: • Bragg envelopes (efficiency FWHM): • in wavelength: • in angle: • Broad blaze requires • thin DCG • large index amplitude • Superblaze

  25. VPH 'grism' = vrism • Remove bent geometry, allow in-line optical layout • Use prisms to bend input and output beams while generating required Bragg condition

  26. Limits to resolving power • Resolving power can increase as m, r and W increase for a given wavelength, slit and telescope • Limit depends on geometrical factors only - increasing r or m will not help! • In practice, the limit is when the output beam overfills the camera: • W is actually the length of the intersection between beam and grating plane - not the actual grating length • R will increase even if grating overfilled until diffraction-limited regime is entered (l > cDT) Grating parameters Geometrical factors

  27. Limits with normal gratings • For GMOS with c= 0.5", DT= 8m,D1 =100mm, Y=50 • Rand l plotted as function of a • A(max) = 1.5 since D2(max) = 150mmR(max) ~ 5000 Normal SR gratings Simultaneous l range

  28. Immersed gratings • Beat the limit using a prism to squash the output beam before it enters the camera: D2 kept small while W can be large • Prism is immersed to prism using an optical couplant (similar n to prism and high transmission) • For GMOS R(max)~ doubled! • Potential drawbacks: • loss of efficiency • ghost images • but Lee & Allington-Smith (MNRAS, 312, 57, 2000) show this is not the case

  29. Limits with immersed gratings • For GMOS with c= 0.5", DT= 8m,D1 = 100mm • R and l plotted as function of a • With immersion R ~ 10000 okay with wide slit Immersed gratings

  30. Echelle gratings • Obtain very high R(> 105) using very long grating • In Littrow: • Maximising g requires large mr since mrl= 2sing • Instead of increasing r, increase m • Echelle is a coarse grating with large groove angle • R parameter = tang (e.g R2  g= 63.5) Groove angle

  31. Multiple orders • Many orders to cover desired ll: Free spectral range Dl = l/m • Orders lie on top of each other: l(m) =l(n) (n/m) • Solution: • use narrow passband filter to isolate one order at a time • cross-disperse to fill detector with many orders at once Cross dispersion may use prisms or low dispersion grating

  32. Echellette example - ESI Sheinis et al. PASP 114, 851 (2002)

  33. Prisms • Useful where only low resolving power is required • Advantages: • simple - no rulings! (but glass must be of high quality) • multiple-order overlap not a problem - only one order! • Disadvantages: • high resolving power not possible • resolving power/resolution can vary strongly with l

  34. Dispersion for prisms • Fermat's principle: • Dispersion:

  35. Resolving power for prisms Angular width of resolution element on detector • Basic definitions: • Conservation of Etendue: • Result: • Comparison of grating and prism: Angular dispersion Angular slitwidth Beam size Telescope aperture Disperser 'length' 'Ruling density'

  36. Prism example A design for Near-infrared spectrograph* of NGST • DT = 8m, c= 0.1", D1 = D2 = 86mm, 1 <l< 5mm • R 100 required Raw refractive index data for sapphire Collimator Slit plane Double-pass prism+mirror Detector Camera * ESO/LAM/Durham/Astrium et al. for ESA

  37. Prism example (contd) • Required prism thickness,t: • sapphire: 20mm • ZnS/ZnSe: 15mm • Uniformity in dl orR required? • For ZnS: n2.26  a=75.3 f= 12.9

  38. Appendix: Semi-empirical efficiency prediction for classical gratings

  39. Efficiency - semi-empirical • Efficiency as a function of rl depends mostly on g • Different behaviour depends on polarisation: P - parallel to grooves (TE) S - perpendicular to grooves (TM) • Overall peak at rl = 2sing (for Littrow examples) • Anomalies (passoff) when light diffracted from an order at b = p/2  light redistributed into other orders • discontinuities at (Littrow only) • Littrow: symmetry m 1-m • Otherwise: no symmetry (rl depends on m,Y) double anomalies • Also resonance anomalies - harder to predict

  40. Efficiency - semi-empirical (contd) Different regimes for blazed (triangular) grooves g < 5 obeys scalar theory, little polarisation effect (P S) 5 <g < 10S anomaly at rl  2/3, P peaks at lowerrl than S 10 < g < 18various S anomalies 18 < g < 22anomalies suppressed, S >> P at large rl 22 < g < 38strong S anomaly at P peak, S constant at large rl g > 38S and P peaks very different, efficient in Littrow only NOTE Results apply to Littrow only From: Diffraction Grating Handbook, C. Palmer, Thermo RGL, (www.gratinglab.com) rl a=b

More Related