Optical Telescope
Faint Light
• Astronomical objects are
distant and faint.
– Effectively at infinity
• Light collection is more
important than
magnification.
– Refraction
– Reflection
• The Andromeda Galaxy
(M31) subtends 3°.
– 6 times the moon
– Only visible to the unaided
eye in very dark conditions
Refraction
i   r
i
r
• Light is bent at the surface
between two media.
– Index of refraction n
t
ni sin i  nt sin t
n
c
v
• Refraction is governed by
Snell’s law.
Radius of Curvature
• Lenses shaped like parts
of spheres are easy to
make.
R
f
– Easy to calculate rays
• Use Snell’s Law on a
small part of a sphere.
R
 (n  1)
f
– Radius of curvature R
– Focal length f
– Index for air is 1
Refracting Telescope
• A refracting telescope is designed to concentrate light from
a distant object.
– Object light rays nearly parallel
– Final image rays also parallel
objective
focal point
eyepiece
Aperture
• Lenses collect and concentrate light.
• The diameter (D) of the objective lens is the aperture.
– Measured in m or mm
– Larger apertures for fainter objects
• The light gathering power (LGP) is related to the area of
the lens.
– Circular lens: A = (D2)/4
– Intensification relative to eye aperture 5 mm: LGP = D2/(5 mm)2
F-Stop
• The brightness of an image is measured by the
focal ratio of the focal length to the aperture.
– F-number or f-stop = f/d
– Dimensionless quantity
– Denoted by f/
• Lower f-numbers are “faster” and need shorter exposure
times.
Fraunhofer Diffraction
• A single narrow slit
creates diffraction.
– No minimum for m = 0
a sin   m
m  1,2,
Airy Disk
• Fraunhofer patterns are
symmetric around the
opening.
• A circular hole produces
rings around a central
maximum.
– 84% of energy in center
Angular Resolution
• The limit of resolution is
set by the aperture.
• The Rayleigh criterion is
calculated from the first
minimum of the Airy disk.
– Aperture radius a
– Wavenumber k
– Bessel function J1
 2 J1 (ka sin  ) 
I ( )  I 0 

 ka sin  
J1 ( x)  0
sin  

x  0,3.83,7.02...
3.83 3.83


 1.22
ka
2a
D
1.22
D
Tube Length
• The intermediate image at the focal point is a real image.
– Long tube accommodates long focal length
– Parallel ray image related to the focal length
MO  
siO
f
 O
soO
so
objective
focal point
eyepiece
Magnification
• The eyepiece magnifies the
intermediate image.
• The total magnification is
the product from both
lenses.
objective
ME  
siE
s
 i
soE
fE
M  MOM E  
focal point
eyepiece
fO
fE
Yerkes Refractor
• The world’s largest refractor is in Wisconsin.
– 40 inch aperture, f/19
– 63 foot tube
Yerkes 40 inch
Chromatic Aberration
• The index of refraction
depends on the
wavelength.
– Longer wavelengths - lower
indexes
– Blue light bends more than
red
• Air n(589 nm) =1.00029
• Crown glass 1.52
• Flint glass
1.66
• Compound lenses can
compensate for chromatic
aberration.
Spherical Aberration
f
• A spherical surface does
not focus all parallel lines
to the same point.
• Aspheric lenses can be
used to correct the
aberration .
Curved Mirror
• Light that begins at one
focus of an elliptical
mirror converges at the
other focus.
focus
focus
– A parabola for a focus at
infinity
Parabolic Mirror
• A perfect parabolic mirror has a focal length like a lens.
• All wavelengths are focused to the same point.
– No chromatic aberration
• The size of the mirror dish is the aperture.
focal length
focal point
Newtonian Reflector
• For viewing ray should be parallel on exit.
– Combined primary mirror and eyepiece
• The reflecting telescope is cheaper, because a mirror is
easier to make than a lens for a given size.
secondary diagonal mirror
primary mirror
eyepiece
Schmidt-Cassegrain Reflector
• A Cassegrain focus uses a flat mirror to make the tube up
to three times longer.
– Spherical aberration from extra mirror
– Aspheric Schmidt lens corrects aberration
Schmidt corrector lens
eyepiece
Keck Reflector
• World’s largest reflector is in Hawaii.
– 400 inch aperture, f/1.75
– Focal length 57.4 feet.
– Telescope height 81 feet.
Keck Observatory
Coma
• Parabolic mirrors focus
precisely for rays parallel
to the central axis.
• The distortion for off axis
objects is called coma.
– Greatest for low f-numbers
• Lenses can correct for the
coma.
Starizona.com
Atmospheric Absorption
• The atmosphere absorbs radiation, except at visible light,
infrared, and radio frequencies.
Adaptive Optics
• The moving atmosphere disturbs images.
– Wavefront distortions
• Real time corrections are made by feedback to a
deformable mirror.
– Sample wavefront from beam splitter
– Measure distortion
– Compute necessary compensation for mirrors
Telescope Advantages
•
•
•
•
REFRACTOR
Superb resolution
Good for detail
Rugged alignment
Transports well
•
•
•
•
REFLECTOR
Inexpensive optics
Large aperture
Good for dim objects
Uniform treatment of colors
SCHMIDT-CASSEGRAIN
• Portable size
• Combines best optical qualities
• Good for photography
Altazimuth Mount
• Telescope mounts should permit two directions of motion.
• Altazimuth mounts directly control altitude and azimuth.
altitude control
azimuth control
Equatorial Mount
• Altazimuth mounts do not track with the star’s movement.
• Equatorial mounts are oriented to the pole.
• Allows control of declination and right ascension.
declination axis
polar axis
Charge-Coupled Device
• The CCD is an array of
photosensitive
semiconductor capacitors.
– Charge stored proportional
to light intensity
– Transfers charge as a shift
register
– Amplifier on last capacitor
converts charge to voltage
Hammamatsu.com
Telescope CCDs
• CCDs are sensitive to light
from ultraviolet to
infrared.
• Sensitivity to thermal
noise and cosmic rays can
blur an image.
• CCDs are very efficient.
• Multiple exposures are
averaged to get correct
image.
– Can be sensitive to
individual photons
– Dark frame closed shutter
Hubble Space Telescope
•
•
•
•
The Hubble is an orbiting reflector telescope.
It has no atmosphere to peer through.
The onboard computer gives it enhanced optics.
There are four different
cameras for different views.
Infrared and Ultraviolet
• Infrared is absorbed by
water vapor.
– Observe at high altitude
• Satellite telescopes avoid
the atmosphere.
– IRAS (1983) - first
evidence of planets around
other stars
– Spitzer Space Telescope
(2003-9).
• Ultraviolet is largely
absorbed by the
atmosphere.
– Requires satellites
– HST, GALEX
M81 from GALEX