1. Introduction to Spectroscopy

2. Physical Applications
Spectroscopy provides a host of information not attainable from imaging, including:
Line profiles
broadening mechanisms (thermal, collisional, rotational)
velocity dispersions
outflows
Spectral types of stars (temperature, surface gravity)
Elemental abundances
Radial velocities (redshifts)

3.
P Cygni profile

4.
P Cygni profile

5. Lyman-alpha Forest

6. Stellar types

7. Stellar types
burro.astr.cwru.edu/cassie/323/jan22p6.jpg

8. Elliptical galaxy

9. Elliptical galaxy

10. Physical Applications
M57
Physical Applications
nebula M57 2D 1D
Emission line source

11. Basic Spectrograph
Slit: isolates portion of sky that is imaged (not required)
Collimator: makes the beam parallel
Dispersive element: disperses light in wavelength
Camera: focus light on detector, where the spectrum is recorded.
The important characteristics of a spectrograph are the dispersion and resolution.

12. Basic Spectrograph Dispersion: d/d
How widely the light is spread (arcsec/Å or inverse)
In physical detector units,
dx = dfcam , so
dx/d = d/d fcam
This is the linear dispersion of the spectrograph (mm/Å).
Typical to quote inverse of linear dispersion (Å /mm)

13. Basic Spectrograph Dispersion: d/d
Typical to quote inverse of linear dispersion (Å /mm)
“Low” dispersion: ~ Å /mm (spectral types)
“Medium” dispersion: ~ Å /mm (radial velocities)
“High” dispersion: < Å /mm(line profiles)

14. Basic Spectrograph Spectral resolution, or resolving power
Defined as R= (you saw this before with imaging filters).
The optical system images the telescope focal plane on to the spectrograph detector plane.
If a slit is used, the ratio of image scale at the slit vs. the detector plane is

15. Tradeoff: Narrower slit gives higher resolution, but more light lost.
Basic Spectrograph
In order to limit the spreading of light of a single wavelength in the dispersion direction, a slit is usually employed at the telescope focal plane to mask the light from the object.
To first order the possible spectral resolution will be set by the projected width, , (in the dispersion direction) of the image or the slit, on the detector as imaged in the spectrograph.
The wavelength resolution is thus given by ddx
Must also include diffraction limit,/D
min = fcam /D
Tradeoff: Narrower slit gives higher resolution, but more light lost. 

16. Dispersive Elements Prisms First surface disperses the light
Simple dispersive elements
Based upon refraction (Snell’s law)
First surface disperses the light
Second surface disperses further
At this surface different wavelengths also have different angles of incidence

17. Dispersive Elements Diffraction Gratings b a
Use diffraction rather than refraction to disperse light b
A= separation between slits
B=slit width a
a: slit separation
b: slit width

18. Dispersive Elements Diffraction Gratings
Use diffraction rather than refraction to disperse light
Angular separation of interference peaks is wavelength dependent
N is the number of slits
d is the separation of the slits
2a is the width of the slits

19. Diffraction Grating m = sinsin) GN FN Grating equation
GN: Grating Normal
FN: Face Normal
B: Blaze Angle
: Incident Angle
: Diffraction Angle
: Grating Constant
Light from successive grooves in phase only when path difference integral # of wavelengths
m = sinsin)
Grating equation
m is grating order

20. Angular Dispersion
For a fixed incident angle, , differentiating grating equation, m = sinsin), we get angular dispersion:
A grating working at as low as 1st or 2nd order, small , or fine grooves are required
A grating working at high order, large , or coarse grooves are needed
High angular dispersion require large angles of ,  !
Littrow condition: , then

21. Spectral Resolving Power with a Diffraction Grating
W sin    GN W
W sin  d2 d1
Diffraction-limited: =/d2

22. Theoretical Grating Resolution
N is the total number of grooves
 Spectral resolution is proportional to order number, m, and total number of grooves
 Resolution of a grating is simply the number of waves that fit into path difference
In terms of angles:

23. Grism: Combination of a Grating and Prism m = sin(+b)-nsina)
Grating Equation GN FN
m = sin(+b)-nsina)
Undeviated center wavelength
Spectral resolving power
The most important feature for grism is it allows combination of spectroscopy and imaging in a camera

24. Cross-dispersed spectral format
Spectral Format for an Echelle Spectrometer
Either doing order filtering or cross-dispersion
Cross-dispersed spectral format
23- 10
24- 11
Cross-disperser

25. Lick Hamilton Cross-dispersed Echelle Spectrograph
Collimator
Echelle
Schmidt Corrector
Prism Cross-disperser
Schmidt Mirror
Detector
Entrance Slit

26. Echelle Spectrum with the Lick Echelle Spectrograph
The preferred choice for modern 2-D array detectors

27. Multiobject Spectrographs
Multi-slit Spectrographs
Series of different slits targeting multiple objects simultaneously

28. Multiobject Spectrographs
Multi-slit Spectrographs
Series of different slits targeting multiple objects simultaneously

29. Multiobject Spectrographs
Multifiber spectrograph
Place fiber optic cables at locations of objects in the focal plane.
Can be done either with a plate (as for multislit) or robotic positioning of the fibers
Each fiber then feeds the
light from the object to the
spectrograph.
Right: 2dF spectrograph,
showing fibers out the plate (

30. Multiobject Spectrographs
Individual fibers on 2dF spectrograph.
Multifiber spectrograph
Place fiber optic cables at locations of objects in the focal plane.
Can be done either with a plate (as for multislit) or robotic positioning of the fibers
Each fiber then feeds the light from the object to the spectrograph. (

31. Multiobject Spectrographs
Individual fibers on 2dF spectrograph.
Multifiber spectrograph
Place fiber optic cables at locations of objects in the focal plane.
Can be done either with a plate (as for multislit) or robotic positioning of the fibers
Each fiber then feeds the light from the object to the spectrograph. (