Spectroscopic Data ASTR 3010 Lecture 16 Textbook Ch. 11

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

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

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

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

Dispersing Optical Elements prism prism grating grating o amplitude grating o blazed grating o volumetric phase grating echelles echelles objective prism objective prism grism grism

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

Grating Using interference of diffracted light Using interference of diffracted light path length difference b/w beam1 and beam2 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, σ α A B C D beam1 beam2

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

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”

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

Disadvantages of Amplitude Gratings 1.If beam1 and beam2 are constructively interfering, then, a beam in the middle of two path (if not blocked) would destructively interfere 2.Using only one order out of many  Inefficiency!

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 β 1 =β 2 σ β1β1 Facet normal grating normal ε ε β2β2 α A B A’ B’

β 1 =β 2 =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 σ β1β1 ε ε β2β2 α A B A’ B’

Blazing is to shift the maximum efficiency of the grating from order 0 to order m. 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 Except for echelles, blazed gratings are usually designed to work in order m=±1 β1β1 ε ε β2β2 α

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°). 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 common echells in astronomy σ is lines per mm m is At a given direction (θ), there can be many (≈100) overlapping orders! At a given direction (θ), there can be many (≈100) overlapping orders! ε θ α -β

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

echellogram

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

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

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. 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.

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