JGR 19 Apr 2001 1 Basics of Spectroscopy Gordon Robertson (University of Sydney)

JGR 19 Apr 2001 1

Basics of Spectroscopy

Gordon Robertson

(University of Sydney)

JGR 19 Apr 2001 2

Outline

• Aims of spectroscopy– Variety of instrumentation - formatting to a 2D detector

• Diffraction gratings– Optical setups, Grating equation, Spectral resolution

• Prisms• Volume Phase Holographic gratings • The A product• Conclusion

JGR 19 Apr 2001 3

Science goals of spectroscopy

1. Elemental composition and abundances

2. Kinematics

3. Redshifts / cosmology

i.e. what is it, where is it, what are its internal motions….

For stars, star clusters, nebulae, galaxies, AGN, intervening clouds etc...

JGR 19 Apr 2001 4

Aims of spectroscopic observations

Ideally….

A data cube, covering a wide range in each of ,,

With good ….spatial resolution , , wavelength resolution ,and efficiency

BUT detectors are 2-dimensional, so the data must be formatted to fit them.

Many interesting new ways of dealing with this.

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Spectral formats

Long-slit spectroscopy

Narrow band imaging

Echelle

Multi-slit

Focal-plane mask

Multi-fibre

Focal-plane fibre feed

Integral field

Focal-plane IFU

spat

ial

cross-disp.

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Types of spectroscopic observations

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Dispersive elements

A grating, prism or grism…..

Sends light of different wavelengths in different directions…

hence (via the camera) to different positions on the detector.

So incident light must be collimated

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Reflection grating geometry

Path difference = a (sin + sin )( is negative in this case)

a

a sin

a sin ||

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The grating equation

m = a(sin + sin )

a

m = order of diffraction, most often 1

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Telescope - slit - collimator

fTel fColl

slit (width s in m)

DTelescopeobjective

Collimator

b (beam diam)

Reduction scale factor = b/D = fColl/fTel

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Reflection grating optics (schematic)

grating

camerad

collimator

idetector

cc

slit

b

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Spectral resolution of a grating

Idealised image of slit at neighbouring wavelengths:

Intensity

Position on detector

+

The observed spectrum is convolved (smoothed) by the line spread function (in practice more Gaussian than rectangular)

Wavelength equivalent of slit width

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Spectral resolution formula

αcos

βsintan

θs

D

bR Where s is the slit angle on the

sky (radians).

sθ

αtan 2

D

bR In Littrow configuration ( = ):

Implications:

• Larger telescopes (D) need larger spectrographs (b) for same R

• If slit width (s) can be reduced, spectrograph size can be contained

• The geometric factor is maximised at large deviation angles (fine rulings, high order)

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Resolution and grating ‘depth’

Grating depth = b tan

In Littrow configuration ( = ):sθ

αtan 2

D

bR

,b

becomessθ

(depth) 2

DR

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RGO Spectrograph Resolution vs Wavelength; 25 cm camera; 1.5 arcsec slit

100

1000

10000

100000

3000 5000 7000 9000 11000 Wavelength /A

Res

olu

tio

n

1200/1, bl coll

250/1, bl coll

1200/2, bl cam

1200/1, bl cam

Resolutionin km/s

10

100

1000

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Spectral resolution from general texts

mNR

λ

λ

But physics and optics texts give the resolution of a grating as:

Where N is the total number of (illuminated) rulings

E.g. for the RGO spectrograph, 1200 l/mm gratings in 1st order, this gives R > ~ 180,000 (i.e. ~ 0.03Å)!

This assumes perfectly collimated input, i.e. diffraction-limited slit.

Astronomers use wider slits, because of atmospheric seeing

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Grating blaze

0 +1

+2-1

0

+1

-1

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Prisms as dispersive elements (1)

Advantages:•Can have high efficiency (no multiple orders)•More than one octave wavelength range possible

Disadvantages:•Low spectral resolution•Non-uniform dispersion (higher in blue, less in red)•Size, mass•Requirements for homogeneity, exotic materials, expense

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Prisms as dispersive elements (2)

Derivative of refractive index - LF5 glass

1

10

100

3000 4000 5000 6000 7000 8000 9000 10000

Wavelength /A

dn

/d(l

am

bd

a (

A))

*10

^6

LF 5 Refractive Index

1.56

1.57

1.58

1.59

1.6

1.61

1.62

1.63

1.64

1.65

3000 4000 5000 6000 7000 8000 9000 10000

Wavelength /A

Re

fra

ctiv

e I

nd

ex

1%

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Prisms as dispersive elements (3)

t

b

bD

ddn

bt

R

s

resolution Spectral

E.g. D = 3.89 m (AAT); (b = 150 mm); t = 130 mm; s 1.5; = 5500 Å;

LF5 glass gives R = 250 ( = 22 Å)

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• Peak efficiency up to ~90%• Line densities from ~100 to (6000) l/mm - 1st order• Wavelength of peak efficiency can be tuned• Transmission gratings - Littrow config. or close to it• DCG layer (hologram) is protected on both sides• Each grating is an original, made to order• Large sizes possible

Introduction to Volume Phase Holographic (VPH) gratings

JGR 19 Apr 2001 22

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

400 500 600 700 800 900 1000

Wavelength (nm)

Eff

icie

nc

y

f/2.2

f/1.7

Ralcon 1516 l/mm grating - June 2000

Note: no antireflection coatings

Test of a prototype VPH grating

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Now we know how to disperse the light - using interference/diffraction or variation of n() in glass.

What other fundamental constraints apply to spectrographs?

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The A product

A1

A3

3

1

E.g. f/8 beam half-angle = 3.6°,

and 1´´ seeing in AAT Focal spot diam = 0.15 mm

A11 = 0.72 mm2 deg2

E.g. f/2.5 camera half-angle = 11.3°,

and 1´´ seeing Focal spot diam = 0.047 mm

A33 = 0.72 mm2 deg2

A2

2

E.g. 150mm collimated beamAngular spread = 1´´ D/b = 26´´

A22 = 0.72 mm2 deg2

On primary, angular spread = 1´´

and diameter b = 3.89 m

A = 0.72 mm2 deg2

A is equivalent to entropy of the beam. It cannot be decreased by simple optics. It is also known as etendue

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A can be degraded...

Like entropy, A can be increased (degraded):

E.g. focal ratio degradation (FRD) in an optical fibre increases while leaving A unchanged.

As a result, spectrograph loses some light, or has to be larger and more expensive, or loses resolution.

Seeing has degraded A before we get the light.

So .. Best if A of the beam is as small as possible,But best if an instrument accepts the largest possible A

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A can be reformatted….

An integral field unit (or other image slicer) can decrease the spread on the ‘wavelength’ axis at the expense of increasing it in the spatial direction.

A is conserved, but we end up with better wavelength resolution

A can be decreased in an adaptive optics (AO) system, by using information about the instantaneous wavefront.

For large telescopes, AO allows good resolution at managable cost

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Optical design for ATLAS spectrograph

(D. Jones, P. Gillingham)

focal plane

collimator

VPH grating

camera

CCD detector

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A few practical details

In practical spectrograph designs, we have to take account of:

• Field size at the focal plane– collimator needs to be larger than ‘b’

• Optical systems must deliver good image quality– aberration broadening < ~1 pixel (eg 10m rms radius)

• Adequate sampling at the detector– at least 2 pixels/FWHM, preferably ~3

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Putting it all together….

• The incoming ,, data have to be formatted to 2D detector– resulting in a wide variety of instruments, with different emphases

• Principal dispersive elements are gratings– normally in a collimator - grating - camera - detector system– large systems are required, especially with large telescopes– spectral resolution

• depends on beam size • is generally much lower than the diffraction-limited maximum

• The size and cost of instruments depends on the A that they have to accept

• Challenge for the future: feasible systems for 30 - 50 m telescopes