Spectroscopic Data

ASTR 3010

Lecture 16

Textbook Ch. 11

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

Dispersive spectroscopy

• Dispersion

λ

θ

dθ

angular dispersion = dθ / dλ

λ + dλ

Dispersive spectroscopy

• Dispersion

λ

θ

dθ

angular dispersion = dθ / dλ

dxλ + dλ

linear dispersion =

Dispersive spectroscopy

• in real life, we are limited by a resolution (imperfect instrument, diffraction, etc.)

λ

dθdx

λ + dλ

dλ δλ: minimum separable wavelength gap

Resolving Power

Typical astronomical spectrometers haveR values in the range of 10-100,000

Dispersing Optical Elements

• prism• gratingo amplitude gratingo blazed gratingo volumetric phase grating

• echelles• objective prism• grism

Prism

• Angular dispersion

• Difficultyo weight o low transmission in UVo low dispersion at long λo non-linear variation of angular

dispersion with λ

α

A

Grating• Using interference of diffracted light

• path length difference b/w beam1 and beam2Δτ = 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 thelight will constructively interfere.

For constructive interference,

σ

θ

α

AB

C

D

beam1

beam2

Grating

σ : grating constant (or groove spacing)

typically, 1/σ is used in astronomical grating100-3000 lines per millimeter

since θ changes only slowly with λ, the angulardispersion of a grating is roughly constant with λ.

σ

θ

α

AB

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 multiplewavelengths coexist.

free spectral range = the range wherethere is no order overlapping.

Need to use “order blocking filters”

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

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 β1=β2

σ

θ β1

Facetnormal

gratingnormal

ε

ε β2

α

AB

A’B’

β1=β2=β

α = β + εθ = 2π + ε – βα + θ = 2ε

condition for constructive interference is the same as the amplitude grating.

β + ε = α and (ε - β) = θ

σ

θ β1

ε

ε β2

α

AB

A’B’

• 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

θ β1

ε

ε β2

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°).

• common echells in astronomyσ is 10-100 lines per mmm is 25-150.

• 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.

echellecro

ss-disp

erse

r

detector

echellogram

Volume Phase Holographic grating

• Periodic change of refraction index instead of rulings.

wavelength (nm)300 900

Effici

ency

80%

40%

VPH

Surface relief

echelle

Objective Prism

• 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.

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