Astronomical Spectroscopy
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Basic Spectrograph Optics
Objective Prism Spectrographs
Slit Spectrographs
Spectrograph
Real Spectrographs
Spectrometer
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Spectroscope
Grating Spectrographs
Spectrogram
IR Spectrographs
Spectrum
Echelle Spectrographs
Fiber & Multi-Object Spectrographs
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)
Refraction
Diamond
• 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)
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air: n = 1.0003
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)
C
Prisms
• 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
A
A’
glass
air
C’
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
Diffraction Gratings
• Multi-slit diffraction
• reflection gratings and
transmission gratings
• most astronomical
gratings are reflection
gratings
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)
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
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
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)
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
Why use a slit?
• to increase resolution
– 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
Collimator
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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
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
Camera Types
• reflecting camera
(schmidt 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
a
Spectrograph Math
b
• 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:
b
b  sin b
1
 sin b
1 n
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
l  sin b l
 sin b / b l
cos b d
The Math (cont’d):
b
1 n

l cos b 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
Throughput Matters
• The higher the throughput, the better
• Limitations:
– slit width (get a bigger collimator or better
seeing)
– efficiency of
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mirror coatings
grating
lens transmission
detector
(typical)
GoldCam
Spectrograph, KPNO
2.1m Telescope
Coude light path
KPNO 2.1m Telescope
coude = elbow
large, fixed spectrograph
high resolution spectroscopy
2.1-m Coude Spectrograph
IR spectrometers
Phoenix
•IR array detectors, 1-5 microns
•spectrograph must be cooled to
reduce thermal background
Now on
Gemini
South
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
KPNO 4-m
Echelle
Spectrograph
•Compact Cassegrain
instrument
•Resolution ~ 4 x 104
•Originally designed for
photographic plates, image
tubes, now used with CCDs
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
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
Solar Spectrum