1. Astronomical Spectroscopy
Basic Spectrograph Optics
Objective Prism Spectrographs
Slit Spectrographs
Real Spectrographs
Grating Spectrographs
IR Spectrographs
Echelle Spectrographs
Fiber & Multi-Object Spectrographs
Spectrograph
Spectrometer
Spectroscope
Spectrogram
Spectrum

2. Vocabulary Spectral resolution, Resolving Power: R = l/Dl
l is the wavelength of interest
Dl is the smallest wavelength interval that can be resolved
“low” resolution 10<R<1000
“moderate” resolution 1000<R<10,000
“high” resolution R>10,000, R>100,000
Dispersion – Dl/pixel or Dl/Å (informal)

3. Diamond
Refraction
The speed of light in a dense medium (air, glass…) is (usually) slower than in a vacuum
Index of refraction (ratio of speed of light in a vacuum to the speed in the medium)
air: n =
water: n= 1.33
fused quartz: n=1.46
salt: n=1.53
The speed of light in a material depends on wavelength – “dispersion” (another use of that word)

4. Prisms Prisms disperse light by refraction
air
glass A C A’ C’
Prisms disperse light by refraction
When a beam of white light passes from one medium into another at an angle, the direction of the beam changes due to refraction
Different colors of light are bent at different angles
Generally, red light is bent less, blue light is bent more

5. Objective Prism Spectroscopy
Prism installed at the top of the telescope
24” diameter, about 10 degree wedge
Each point source produces a spectrum
Low resolution, useful for surveys
KISS Images/Burrell Schmidt

6. Diffraction Gratings Multi-slit diffraction
reflection gratings and transmission gratings
most astronomical gratings are reflection gratings

7. d (sina + sinb) = nl (the grating equation)
Reflection Gratings
light reflecting from grooves A and B will interfere constructively if the difference in path length is an integer number of wavelengths.
The path difference is dsina + dsinb (where d is the distance between facets on the grating), so
d (sina + sinb) = nl (the grating equation)
n is the “spectral order” and quantifies how many wavelengths of path difference are introduced between successive facets or grooves on the grating)

8. The Grating Equation d (sina + sinb) = nl
The groove spacing d is a feature of the grating
The angle of incidence, a, is the same for all wavelengths
The angle of diffraction, b, must then be a function of wavelength
sin b = nl/d – sin a

9. Sample Problem
sin b = nl/d – sin a
You are working with a grating with 1000 grooves per millimeter.
The angle of incident light (a) is 15º
At what angle will light of 400 nm be diffracted in 1st order (n=1)?
500 nm? 600 nm?
Careful: express wavelength and groove spacing in similar units

10. Multiple Grating Orders
sin b = nl/d – sin a
multiple spectra are produced by a diffraction grating, corresponding to different orders (n=1,2,3…)
For a grating of 1000 grooves/mm and 15º incident angle, what wavelength of light will be diffracted to an angle of 14º in second order?
(for this figure, m=n)

11. Slit Spectrographs
Entrance Aperture: A slit, usually smaller than that of the seeing disk
Collimator: converts a diverging beam to a parallel beam
Dispersing Element: sends light of different colors into different directions
Camera: converts a parallel beam into a converging beam
Detector: CCD, IR array, photographic plate, etc.
Image from CSIRO

12. Why use a slit? to increase resolution blocks unwanted light
by narrowing the slit
also decreases throughput
blocks unwanted light
from the sky
other nearby sources
sets a reference point
A decker offers a range of slit widths

13. Collimator
The collimator converts the diverging beam of white light from the slit to a parallel beam
The focal ratio of the collimator must be matched to the effective focal ratio of the telescope
The diameter of the collimator determines the diameter of the light beam in the spectrograph
The size of the collimator affects the size of the “slit image” on the detector
Bigger, longer focal length cameras reduce the size of the slit image, and increase the resolution of the spectrograph

14. Reflection Grating Efficiency
Problem: A grating diffracts light into many orders; one order contains only a fraction of the light
Fix: 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
easier to blaze
“Blaze” a grating
C. R. Kitchin, Optical Astronomical Spectroscopy

15. Camera Types reflecting camera (schmidt camera) transmission camera
broad wavelength coverage
on- of off-axis (central obstruction?)
transmission camera
lenses
generally on-axis, no central obstruction
broad wavelength coverage requires multiple elements

16. Spectrograph Math based on the grating equation d (sin a + sin b) = nl
“a” is the angle from the slit to the grating normal and “b” is the angle from the grating normal to the camera. a is usually fixed.
The “angular dispersion” of a spectrograph is given by db/dl:

17. The Math (cont’d): The resolution varies as
the order number (higher=more resolution)
the grating spacing (more rulings = smaller spacing = more resolution)
the camera-collimator angle (as b increases, cos b gets smaller and resolution increases)
The effective resolution of a spectrograph is a function of
the grating resolution
the size of the slit image (collimator and camera focal lengths: (slit size x fcam/fcol)
the pixel size

18. Throughput Matters The higher the throughput, the better Limitations:
slit width (get a bigger collimator or better seeing)
efficiency of
mirror coatings
grating
lens transmission
detector
(typical)

19. GoldCam Spectrograph, KPNO 2.1m Telescope

20. Coude light path KPNO 2.1m Telescope
coude = elbow
large, fixed spectrograph
high resolution spectroscopy

21. 2.1-m Coude Spectrograph

22. IR spectrometers Phoenix Now on Gemini South
IR array detectors, 1-5 microns
spectrograph must be cooled to reduce thermal background
Now on
Gemini
South

23. Limitations for High Dispersion
Problem: detector size, shape
generally square or 1x2 format
a conventional grating spectrograph produces a very LONG high dispersion spectrum that won’t fit on a CCD
Solution: the echelle grating
works in high orders (n=100)
a second dispersing element spreads the light in a perpendicular direction

24. KPNO 4-m Echelle Spectrograph
Compact Cassegrain instrument
Resolution ~ 4 x 104
Originally designed for photographic plates, image tubes, now used with CCDs

25. Echelle Gratings
To increase spectral resolution, increase the order at which a grating is used
For high orders, must increase a and b in the grating equation (to ~50-75o)
The spectral range for each order is small so the orders overlap
Separate the orders with a second disperser (cross disperser) acting in a perpendicular direction.
C. R. Kitchin, Optical Astronomical Spectroscopy

26. Multi-object Spectroscopy
Observing one star at a time is inefficient
when many stars are available in a field (say, a star cluster) use multi-object spectroscopy
put an optical fiber at locations of stars to take spectra.
Feed the optical fibers into a spectrograph.

27. WIYN’s Hydra MOS ~85 fibers Full degree FOV
Wonderful for star clusters, globular and galactic!
blue and red fibers
R from a few x 102 to 2 x 104

28. Solar Spectrum