Spectrographs

Literature:

Astronomical Optics, Daniel Schroeder

Astronomical Observations, Gordon Walker

Stellar Photospheres, David Gray

Spectral Resolution

d

1 2

Consider two monochromatic beams

They will just be resolved when they have a wavelength separation of d

Resolving power:

d = full width of half maximum of calibration lamp emission lines

R = d

R = 15.000

= 0.73 Å

R = 100.000

= 0.11 Å

R = 500.000

= 0.022 Å

Spectral Resolution

The resolution depends on the science:

1. Active Galaxies, Quasars, high redshift (faint) objects:

R = 500 – 1000

2. Supernova explosions:

Expansion velocities of ~ 3000 km/s

d/ = v/c = 3000/3x105 = 0.01

R > 100

R = 3.000

R = 30.000

35.0000.160100000

60.0000.09130000

100.0000.05310000

140.0000.046000

200.0000.0283000

Rth (Ang)T (K)

3. Thermal Broadening of Spectral lines:

3000001K

1000003G0

1200025F5

375080F0

2000150A0

R1Vsini (km/s)Sp. T.

4. Rotational Broadening:

1 2 pixel resolution, no other broadening

5. Chemical Abundances:

Hot Stars: R = 30.000

Cool Stars: R = 60.000 – 100.000

Driven by the need to resolve spectral lines and blends, and to accurately set the continuum.

6 Isotopic shifts:

Example:

Li7 : 6707.76

Li6 : 6707.92

R> 200.000

7 Line shapes (pulsations, spots, convection):

R=100.000 –200.000

Driven by the need to detect subtle distortions in the spectral line profiles.

Line shapes due to Convection

Hot rising cell

Cool sinking lane

•The integrated line profile is distorted.

• Amplitude of distortions ≈ 10s m/s

R = 200.000

R > 500.000

8 Stellar Radial Velocities:

RV(m/s) ~ R–3/2 ()–1/2 wavelength coverage

R (m/s)100 000 1 60 000 3 30 000 7 10 000 40 1 000 1200

collimator

Spectrographs

slit

camera

detector

corrector

From telescope

Anamorphic magnification:

d1 = collimator diameter

d2 = mirror diameter

r = d1/d2

slit

camera

detector

correctorFrom telescope

collimator

Without the grating a spectograph is just an imaging camera

A spectrograph is just a camera which produces an image of the slit at the detector. The dispersing element produces images as a function of wavelength

without disperser

without disperser

with disperser

with disperser

slit

fiber

Spectrographs are characterized by their angular dispersion

d

d

Dispersing element

ddA =

f

dl

dd

dld = f

In collimated light

S

dd

dld = S

In a convergent beam

Plate Factor

P = ( f A)–1

= ( f )–1

dd

P = ( f A)–1

= (S )–1

dd

P is in Angstroms/mm

P x CCD pixel size = Ang/pixel

w

h

f1

d1

A

D

f

d2

w´

h´

D = Diameter of telescope

d1 = Diameter of collimator

d2 = Diameter of camera

f = Focal length of telescope

f1 = Focal length of collimator

f2 = Focal length of camera

A = Dispersing element

f2

w

h

f1

d1

A

D

d2

f

w´

h´

f2

w = slit width

h = slit height

Entrance slit subtends an

angle and ´on the sky:= w/f

´= h/f

Entrance slit subtends an angle

and ´on the collimator:= w/f1

´= h/f1

w´ = rw(f2/f1) = rDF2

h´ = h(f2/f1) = ´DF2

F2 = f2/d1r = anamorphic magnification due to dispersing element = d1/d2

w´ = rw(f2/f1) = rDF2

This expression is important for matching slit to detector:2 = rDF2 for Nyquist sampling (2 pixel projection of slit).1 CCD pixel () typically 15 – 20 m

Example 1:

= 1 arcsec, D = 2m, = 15m => rF2 = 3.1

Example 2:

= 1 arcsec, D = 4m, = 15m => rF2 = 1.5

Example 3:

= 0.5 arcsec, D = 10m, = 15m => rF2 = 1.2

Example 4:

= 0.1 arcsec, D = 100m, = 15m => rF2 = 0.6

5000 A

4000 An = –1

5000 A

4000 An = –2

4000 A

5000 An = 2

4000 A

5000 An = 1

Most of light is in n=0

b

The Grating Equation

m = sin + sin b 1/ = grooves/mm

dd =

m cos =

sin + sin cos

Angular Dispersion:

Linear Dispersion:

ddx

dd=

ddx

=1fcam

1

d/d

dx = fcam d

Angstroms/mm

Resolving Power:

w´ = rw(f2/f1) = rDF2

dx = f2 dd

f2 dd

rDF2

R = /d = Ar

1

d1

D

=rA

D

d1

For a given telescope depends only on collimator diameter

Recall: F2 = f2/d1

D(m) (arcsec) d1 (cm)

2 1 10

4 1 20

10 1 52

10 0.5 26

30 0.5 77

30 0.25 38

R = 100.000 A = 1.7 x 10–3

Adaptive Optics corrects for the atmospheric motion and allows one to achieve near

diffraction limit

What if adaptive optics can get us to the diffraction limit?

Slit width is set by the diffraction limit:

=

D

R = r

A D

d1

D=

Ar

d1

R d1

100000 0.6 cm

1000000 5.8 cm

For Peak efficiency the F-ratio (Focal Length / Diameter) of the telescope/collimator should be the same

collimator

1/F 1/F1

F1 = F

F1 > F

1/f is often called the numerical aperture NA

F1 < F

d/

1

But R ~ d1/

d1 smaller => must be smaller

Normal gratings:

• ruling 600-1200 grooves/mm

• Used at low blaze angle (~10-20 degrees)

• orders m=1-3

Echelle gratings:

• ruling 32-80 grooves/mm

• Used at high blaze angle (~65 degrees)

• orders m=50-120

Both satisfy grating equation for = 5000 A

Grating normal

Relation between blaze angle , grating normal, and angles of incidence and diffraction

Littrow configuration:

= 0, = =

m = 2 sin

A = 2 sin

R = 2d1 tan D

A increases for increasing blaze angle

R2 echelle, tan = 2, = 63.4○

R4 echelle tan = 4, = 76○

At blaze peak + = 2

mb = 2 sin cos

b = blaze wavelength

3000

m=3

5000

m=2

4000 9000

m=1

6000 14000Schematic: orders separated in the vertical direction for clarity

1200 gr/mm grating

2

1

You want to observe 1 in order m=1, but light 2 at order m=2, where 1 ≠ 2 contaminates your spectra

Order blocking filters must be used

4000

m=99

m=100

m=101 5000

5000 9000

9000 14000

Schematic: orders separated in the vertical direction for clarity

79 gr/mm grating

30002000

Need interference filters but why throw away light?

In reality:

collimator

Spectrographs

slit

camera

detector

corrector

From telescope

Cross disperser

y ∞ 2

y

m-2

m-1

m

m+2

m+3

Free Spectral Range m

Grating cross-dispersed echelle spectrographs

Prism cross-dispersed echelle spectrographs

y ∞ –1

y

Cross dispersion

y ∞ · –1 =

Increasing wavelength

grating

prism

grism

Cross dispersing elements: Pros and Cons

Prisms:

Pros:

• Good order spacing in blue

• Well packed orders (good use of CCD area)

• Efficient

• Good for 2-4 m telescopes

Cons:

• Poor order spacing in red

• Order crowding

• Need lots of prisms for large telescopes

Cross dispersing elements: Pros and Cons

Grating:

Pros:

• Good order spacing in red

• Only choice for high resolution spectrographs on large (8m) telescopes

Cons:

• Lower efficiency than prisms (60-80%)

• Inefficient packing of orders

Cross dispersing elements: Pros and Cons

Grisms:

Pros:

• Good spacing of orders from red to blue

Cons:

• Low efficiency (40%)

Important Data reduction issues:

1. Blaze function

2. Scattered Light

3. Reflections

• „Picket Fence“ or reflected light for Littrow configuration

Spectrum of a White Light Source (Flat Lamp)

Picket fence:

Scattered light

Scattered light is light that is scattered into the interorder spacing of echelle spectrographs. All instruments have scattered light at some level or another. This must be removed in the reduction process. Why?

A cross section across rows of the spectrum of the white light source

Bias level of CCD

To determine the abundance of an element in the stellar spectrum you need to measure the equivalent width

w

Id

Ic

w =Ic – I

Ic

d∫

w

Id + Is

Ic + Is

Is

w =Ic + Is – (I +Is)

Ic + Is

w =Ic – I Ic + Is

Scattered light reduces equivalent width

∫

∫

d

d

Width of a perfectly black line of rectangular profile that would remove the same amount of flux

I

So you want to build a spectrograph: things to consider

• Chose R product– R is determined by the science you want to do– is determined by your site (i.e. seeing)

If you want high resolution you will need a narrow slit, at a bad site this results in light losses

Major consideration: Costs, the higher R, the more expensive

normal

Do I need to tilt the grating to make it fit in my room?

• Reflective or Refractive Camera? Is it fed with a fiber optic?

Camera pupil is image of telescope mirror. For reflective camera:

Image of Cassegrain hole of Telescope

camera

detector

slit

Camera hole

Iumination pattern

• Reflective or Refractive Camera? Is it fed with a fiber optic?

Camera pupil is image of telescope mirror. For reflective camera:

Image of Cassegrain hole

camera

detector

A fiber scrambles the telescope pupil

Camera hole

ilIumination pattern

Cross-cut of illumination pattern

For fiber fed spectrograph a refractive camera is the only intelligent option

fiber

e.g. HRS Spectrograph on HET:

Mirror camera: 60.000 USD

Lens camera (choice): 1.000.000 USD

Reason: many elements (due to color terms), anti reflection coatings, etc.

Lost light due to hole in mirror

• Stability: Mechanical and Thermal?

HARPS

HARPS: 2.000.000 Euros

Conventional: 500.000 Euros

Tricks to improve efficiency:Overfill the Echelle

d1

d1

R ~ d1/

w´ ~ /d1

For the same resolution you can increase the slit width and increase efficiency by 10-20%

Atmospheric Seeing Blurs the Image on Slit

slit

Lost light

R = /d = Ar

1

d1

D

But…

You catch more photons, but a wider slit means lower resolution

Need to turn this

Into this

Tricks to improve efficiency:Image slicing

The slit or fiber is often smaller than the seeing disk:

Image slicers reformat a circular image into a line

A modern Image slicer

Fourier Transform Spectrometer

Interferogram of a monchromatic source:

I() = B()cos(2n)

Interferogram of a two frequency source:

I() = B1()cos(21) + B2(2)cos(22)

Interferogram of a two frequency source:

I() = Bi(i)cos(2i) = B()cos(2)d–∞

+∞

Inteferogram is just the Fourier transform of the brightness versus frequency, i.e spectrum

Words of Advice

If it is too good to be true it probably isn‘t

Lessons learned:

1. „The Phosphorus Stars“

2. „The Lithium Stars“

3. „The non-pulsating, pulsating A stars“

„You have to be careful that you do not fool yourself and unfortunately, you are the easiest person to fool“

- Richard Feynman