Reciprocal linear dispersion - Simon P Driver · – This is roughly linear since cos ......
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1 • continuing with the L.R.T. spectrograph • Usually we quote the RECIPROCAL LINEAR DISPERSION – dλ/dx, in units of Å/mm, so for the 1200 lines/mm grating. – This is roughly linear since cos θ does not change much over usual λ range recorded (~1000 Å) Reciprocal linear dispersion dλ dx = 10 7 249600 = 40 Å/mm r d dx θ λ cos 249600 ≈ • Resolving power is defined as ∴ for a CCD with 20μm pixels, and LRT spectrograph at 40 Å/ mm, we have 0.04 Å/μm or 0.8 Å/pixel. Then the resolving power is – R = 5000 Å / 0.8 Å = 6250 in the optical region. – – Simple calibration procedures can provide Doppler shifts accurate to about 0.1pixel, or 0.08 Å with LRT, giving velocity uncertainty R = λ Δλ Δυ = c Δλ λ = 3 × 10 5 × 0.08 5000 = 4.8 km s –1 . Resolving power and radial velocity
Transcript of Reciprocal linear dispersion - Simon P Driver · – This is roughly linear since cos ......
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• continuing with the L.R.T. spectrograph
• Usually we quote the RECIPROCAL LINEAR DISPERSION
– dλ/dx, in units of Å/mm, so
for the 1200 lines/mm grating. – This is roughly linear since cos θ does not change much
over usual λ range recorded (~1000 Å)
Reciprocal linear dispersion
€
dλdx
=107
249600= 40 Å/mm
rddx
θλ cos249600
≈
• Resolving power is defined as
∴ for a CCD with 20µm pixels, and LRT spectrograph at 40 Å/mm, we have 0.04 Å/µm or 0.8 Å/pixel. Then the resolving power is
– R = 5000 Å / 0.8 Å = 6250 in the optical region. –
– Simple calibration procedures can provide Doppler shifts accurate to about 0.1pixel, or 0.08 Å with LRT, giving velocity uncertainty
€
R =λΔλ
€
Δυ = cΔλλ
= 3×105 ×0.085000
= 4.8 km s–1.
Resolving power and radial velocity
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Examples of stellar spectra at typical resolution ~6000
Hε He
He He
He Hδ Hγ B1 Iab
B2 III Hγ Hδ
Hδ Hγ B2 IV
wavelength nm
Échelle Spectroscopy • échelle ⇔ ladder • used for really high-resolution
spectroscopy, e.g. R ~ 50,000, • 2 dispersing elements split a long
high-resolution spectrum into different orders stacked above each other and recorded by 1 large CCD
Collimator
Slit
Camera
Echelle grating
Cross-dispersing prisms
Detector
Grating normal γ
θi θr
Facet normal
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Échelle Spectroscopy • Set of prisms gives initial dispersed
spectrum • Coarse (~ 80 lines/mm) échelle
grating • used at a large angle for high orders
(m ~ 20-70), with its grooves at right-angles to the incident spectrum - a cross-dispersion grating.
Grating normal γ
θi θr
Facet normal
Collimator
Slit
Camera
Echelle grating
Cross-dispersing prisms
Detector
Example of high-resolution spectroscopy
Lyman-α absoprtion lines at a wide range of redshifts in the spectrum of a quasar.
Resolution R = λ⁄Δλ = 50,000
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An ‘echellogram’ of a solar-type star (from WHT + UES)
wavelength
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gth
OR
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R N
UM
BE
R
Multiple-Object Spectrometerse.g. Two-Degree-Field instrument on AAT (2df)
Up to 400 objects observed simultaneously via 400 optical fibres
www.ast.cam.ac.uk/AAO/2df/gallery.html
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Multi-object spectroscopy via lots of slits cut in a metal plate at precise position in focal plane.
image slicers • image slicers are the newest technology
– very small mirrors separate parts of the image – can be treated like individual slits
• now spectroscopy of objects of any shape… don't need to e.g. pick out star positions in advance
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• example: image slicer for MIRI on future James Webb Space Telescope
10. Multiwavelength Astronomy • NB, (detectable) EM spectrum covers 10-12
to 103 m – huge range of photon energies: need many methods
to detect, and sometimes different kinds of telescope
• ground vs. space instrumentation: choice driven by atmospheric opacity vs. cost/accessibility/resolution issues
