Spectroscopy for Astronomy
Spectrum: intensity of radiation as a function of wavelength (“dispersed light”)Continuum (e.g., blackbody radiation) and Line Emission
Continuum occurs at all wavelengths: e.g., Bλ(T)
Line emission occurs at specific wavelength: λ = hc/(E2-E1)
Radiation: Continuum & Line Emission
Continuum emission:
Blackbody Radiation (e.g., stellar radiation)
Synchrotron Radiation (e.g., accelerator)
Thermal Free-Free Radiation (= Bremsstrahlung)
Line emission:
Atomic Transition (e.g., H I lines)
Molecular Transition (e.g., OH, CO lines)
Solid-State Feature (e.g., aerosol, …)
Line Emission/Absorption: e.g., Hydrogen
H series (mostly in the visible bands)
e.g. H transition: n = 3 → 2 transition at 656.3 nm.
R: Rydberg constant for hydrogen.
Observed stellar radiation = continuum + line emission (mostly absorption)
Spectrum: intensity of radiation as a function of wavelength (“dispersed light”)Continuum (e.g., blackbody radiation) and Line Emission
Galaxy Spectra: examples
Galaxy: numerous stars and gas clouds
Mixture of continua, absorption, and emission lines
Spectrum: Example for absorption and emission
(in addition to the continuum)
(no continuum)
(no line emission)
Assumptions:
[1] hot source is a pure continuum emission source;
[2] gas is a pure line emission source.
Star: let’s assume it to be a pure continuum source
Gas cloudContinuum source through gas cloud
Colored bars: gas cloud emission lines
Continuum source
Assumptions:
[1] Star is a pure continuum source.
[2] Gas cloud has no continuum emission.
White bars: gas cloud absorption lines
Depending on the relative positions of the sources and observers, spectra appear differently.
Spectrum: Example for absorption and emission
Stellar Spectra
Can you identify any lines?
Temperature (= spectral type) is critical to determine the shape of the stellar spectra.
Stellar Spectra
Stellar Spectra
How do we obtain spectra?
We need to disperse the light. How?
We need a dispersing element.What are the two common dispersing elements?
Spectrograph and Spectroscopy: Dispersing Elements
Prism: based on the wavelength dependence of the index of refraction n()
Grating (= a plate with many grooves): based on the wavelength dependence of the diffraction & interference
Basic Spectrograph Structure
Prism (or Grating)
Slit
Collimator
Dispersing Element
Camera
Detector
The slit spectroscopy is basically imaging the slit along the wavelength. Think about this.
Photons of different wavelengths arrive at the different positions on the detector (e.g., CCD, photographic plate).
So you can tell the wavelengths of the photons.
The slit spectroscopy is basically imaging the slit along the wavelength. Think about this.
Basic Spectrograph Structure
Spectrograph: Prism Spectroscopy
Where are the foci of the lenses?
Spectrograph: Diffraction Grating
Let’s recall the diffraction pattern of a telescope first to refresh …
Single slit
Double slitsDouble slit diffraction pattern: interference of two single slit diffraction complicated, narrower!
Diffraction grating = assembly of numerous slits (=ruled grooves)
Spectrograph: Diffraction Grating
Three slits
Four slits
Slit number more complicated interference pattern
Use the interference to distinguish the wavelength!
Spectrograph: Diffraction Grating
m: order of the principal maxima
Interference of diffractions from multi-slits
Different wavelengths have their maxima at different locations for the same orders!
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Note that the pattern of only two different wavelengths are shown!
This corresponds to the reflection.
Spectrograph: Diffraction Grating
Diffraction Grating (ruled grooves): Multi-slit Interference
IntensityDiffraction Pattern
Interference Pattern
N: number of slits
a: half slit size
d: slit distance
Spectrograph: Diffraction Grating
Wavelength dependence
Transmission grating
Reflection grating
Spectrograph: Diffraction Grating
Diffraction Gratings:Ruled Grooves (= multi slits)
Spectrograph: Diffraction Grating
Grating geometry
transmission
reflection
: incidence angle
b: diffraction angle
: wavelength
q: blaze angle
s: groove spacing
, b: opposite signs at opposite sides
transmission
reflection
Path difference between the incident wavefront and diffracted wavefront? = s (sin + sin b) = mfor constructive interference, m is integer
s
Grating geometry
Grating equation:s (sin + sin b ) = m, m = integer
transmission
reflection
Grating geometry
Grating equation:s (sin + sin b) = m, m = integer
m = 0: = -b (Secular reflection)m > 0: - < bm < 0: - > b
Diffraction gratings
For m = 0, all wavelengths fall at the same place, and thegrating acts as a simple mirror.
Typically higher orders will give weaker spectra: most ofthe power is put into the lower orders.
The separation of wavelengths is greater at higher orders:spectral resolving power increases at higher orders.
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• A grating diffracts light into many orders; one order contains only a fraction of the light
• Rule the grating facets so that the direction of reflection off the facet coincides with the desired order of diffraction.
• Up to 90% of the light can be concentrated into the desired spectral order.
• Most spectrographs use reflection gratings: easier to produce and blaze
“Blaze” a grating
Sawtooth profile (= blazed grating) for high grating efficiency for certain wavelengths and orders
Grating: Angular Dispersion
s
s (sin + sinb) = m
sin b = m/s – sin
A (angular dispersion)
= db/d
= m/(s cosb)
= (sin + sinb) / ( cosb)
Angular dependence of the dispersed light along the wavelength.(db/d)
Grating: Angular Dispersion
s (sin + sinb) = m
A (angular dispersion)
= db/d
= m/(s cosb)
= (sin + sinb) / ( cosb)
: incidence angle
b: diffraction angle
: wavelength
q: blaze angle
s: groove spacing
Angular dispersion is a function of m and s. High groove density ( 1/s) and high spectral order (= m) produce high spectral density (= large angular dispersion).
For given s and , large m is achieved with large and b.
is usually fixed.
How photons of different wavelengths will disperse on the camera focal plane (= detector)?
Linear Dispersion = (Angular Dispersion = A) ×(Camera Focal Length = f2)
(Δff/Δ)?
Focal length of the camera
Grating: Linear Dispersion
Slit at the collimator focal plane
Detector at the camera focal plane
Large linear dispersion → high spectral resolving power; coarse velocity measurement
Small linear dispersion → low spectral resolving power; precise velocity measurement
Grating: Linear Dispersion
So photons of different wavelengths will appear on the different pixels of the detector. “Spectrum”
= reciprocal linear dispersion(or plate factor)
Spectroscopy: Slit Imaging
Spectroscopy: Slit Imaging
White (non-dispersed) light
Colored (dispersed) light
Spectroscopy: Slit Imaging
Spectroscopy: Slit Imaging
Spectroscopy: Slit Imaging
2D Detector
Spectral Direction (= Dispersion Direction)
Spat
ial D
ire
ctio
n
Slit image on the detector along the wavelength
Linear dispersion
Slit spectroscopy is imaging the input slit on the detector along the wavelength
Narrow slits give high spectral resolving power
Reimaging Optics
Input image plane Re-imaged
plane
Collimator lens
Camera lens
Collimator and camera pair forms a reimaging system.
Magnification = (Re-imaged size) / (Input size)
= (Camera focal length) / (Collimator focal length)
= fcam / fcoll
Spectroscopy: Slit Imaging
fcoll
fcam
Projected Slit Width
= [Input Slit Width] × [Grating Magnification] × [fcam / fcoll]
r = (collimated
diffracted beam) /
(collimated incident
beam)
= cosβ/cosα 1
Anamorphic magnification
Spectroscopy: Spectral Resolving Power
R is spectral resolving power;
δ is the spectral resolution element (= projected slit width at the wavelength)
Grating Resolving Power and Rayleigh Criteria
The images formed in two wavelengths that are barely resolved must be separated by q. The light of wavelength + must form its principal maximum of order m at the same angle as that for the first minimum of wavelength in that order.
Nd cosq (= projected grating size) determines the angular separation.
Grating Resolving Power and Rayleigh Criteria
Spectroscopic Resolving Power
Spectrograph: Example
• b from the grating equation (b=21.644°, 23.132°; b=1.488°)
• camera plate scale = 1.75 mm/degree
• linear distance between the 3800 and 4000 Å lines = 1.4881.75 = 2.603mm
• reciprocal dispersion (= plate factor) = 200 Å/2.603 mm (or 76.8 Å/mm)
• focal length ratio = 10.16/39.4 = 0.258; projected slit width = 0.010 mm or 0.77 Å
• CCD of 1024 15-μm pixels: 1 pixel resolution = 0.015 × 76.8 = 1.15 Å/pixel and the wavelength coverage is 1.15 × 1024 = 1180 Å
What will be the plate factor and projected slit width? ( = 5°, = 3800-4000 Å, m = 2; 2 pixels per resolution element)