Spectroscopic Data

1. Spectroscopic Data ASTR 3010 Lecture 16 Textbook Ch. 11

2. Spectroscopy in astronomy • spectroscope – an instrument to look through visually • spectrometer – measures a spectrum • spectrograph – records a spectrum • dispersive spectroscopy : difference wavelengths at different positions • non-dispersive spectroscopy : no dispersive element. E.g., Michelson interferometry

3. Dispersive spectroscopy • Dispersion dθ λ + dλ θ λ angular dispersion = dθ / dλ

4. Dispersive spectroscopy • Dispersion dθ λ + dλ θ dx λ angular dispersion = dθ / dλ linear dispersion =

5. Dispersive spectroscopy • in real life, we are limited by a resolution (imperfect instrument, diffraction, etc.) dλδλ : minimum separable wavelength gap λ + dλ dθ Resolving Power Typical astronomical spectrometers have R values in the range of 10-100,000 dx λ

6. Dispersing Optical Elements • prism • grating • amplitude grating • blazed grating • volumetric phase grating • echelles • objective prism • grism

7. Prism • Angular dispersion • Difficulty • weight • low transmission in UV • low dispersion at long λ • non-linear variation of angular dispersion with λ A α

8. Grating • Using interference of diffracted light • path length difference b/w beam1 and beam2 Δτ = AB – CD AB = σ sin (α) CD = σ sin (2π – θ) = -σ sin (θ) Δτ = σ (sinα + sinθ) if Δτ is a integral multiple of λ, then the light will constructively interfere. For constructive interference, beam1 beam2 A B C σ D θ α

9. Grating σ : grating constant (or groove spacing) typically, 1/σ is used in astronomical grating • 100-3000 lines per millimeter since θ changes only slowly with λ, the angular dispersion of a grating is roughly constant with λ. beam1 beam2 A B C σ D θ α

10. Angular dispersion increases by selecting high order or increasing the number of lines per millimeter on the grating. Important characteristics of diffraction gratings is dispersion into multiple orders order overlap! At particular θ, there are multiple wavelengths coexist. free spectral range = the range where there is no order overlapping. Need to use “order blocking filters”

11. Prism versus Diffraction Grating • no order overlap • heavy • no UV transmission • low resolution at large λ • non-linear angular dispersion with λ • works on all wavelengths! • linear dispersion with λ • most light reflected into the 0th order • order overlap

12. Disadvantages of Amplitude Gratings • If beam1 and beam2 are constructively interfering, then, a beam in the middle of two path (if not blocked) would destructively interfere • Using only one order out of many  Inefficiency!

13. Blazed reflection grating phase grating = periodically adjusting the phase of diffracted waves. blazed grating is one of commonly used phase gratings  has a sawtooth-shaped surface Sometimes known as echelle grating Goal is to arrange a tilt so that all rays diffracted from a single facet are in phase.  this will happen if β1=β2 A B B’ A’ σ ε θ grating normal ε β2 β1 α Facet normal

14. β1=β2=β α = β + ε θ = 2π + ε – β α + θ = 2ε condition for constructive interference is the same as the amplitude grating. β + ε = α and (ε - β) = θ A B B’ A’ σ ε θ ε β2 β1 α

15. Blazing is to shift the maximum efficiency of the grating from order 0 to order m. • Except for echelles, blazed gratings are usually designed to work in order m=±1 ε θ ε β2 β1 α

16. Echelles • To produce a large angular dispersion, we need to operating at high order (m) and with dispersed rays nearly parallel to the grating surface (θ≈90°). • common echells in astronomy σ is 10-100 lines per mm m is 25-150. • At a given direction (θ), there can be many (≈100) overlapping orders!  α θ -β ε

17. Echelle spectrograph instead of using order blocking filter, the dispersed light is once again dispersed in the perpendicular direction. echelle cross-disperser detector

18. echellogram

19. Volume Phase Holographic grating • Periodic change of refraction index instead of rulings. VPH 80% Surface relief Efficiency 40% echelle 900 300 wavelength (nm)

20. Objective Prism • Prism placed in front of the objective lens (spectrum of the entire image)

21. grism = grating + prism • a combination of a prism and grating arranged so that light at a chosen central wavelength passes straight through  The advantage of this arrangement is that the same camera (and other optical elements) can be used both for imaging (without the grism) and spectroscopy (with the grism) by only moving the grism in and out.

22. In summary… Important Concepts Important Terms Resolving power grating constant Gratings : amplitude, blazed (phase), echelle grism • Different dispersive elements • Diffraction grating • Pros and cons of prism and grating • Chapter/sections covered in this lecture : Ch. 11