CHAPTER 1 Optical Telescope I. Reflective and Refractive Telescopes

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CHAPTER 1 Optical TelescopeI. Reflective and
Refractive Telescopes

• Telescopes serves three main functions (1) they
  are light collectors. The simplest telescopes
  simply focus light rays to a small area. (2)
  Resolve light so that finer details can be seen
  (3) Magnification making objects look bigger
  (closer)
• As we are observing objects at very large
  distances, light can be assumed to come from
  infinity and can be represented as parallel rays
• Two main types refractive and reflective

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1. Light wavefront from a source is in shape of a
spherical surface
3. A small fraction of the wavefront will be
intercepted by the telescope aperture.
2. After travelling long distance, incoming light
wavefront from a source will be plane parallel.
Adapted from Astrophysics by Judith A. Irwin
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Tiny amount of light intercepted

• E.g. Fraction amount of light collected from the
  Sun with a 2m diameter telescope on Earth
• Distance from the Sun to Earth 1 Astronomical
  Unit (AU) 1.5x1011 m
• Light spread over a surface area 4p(1.5x1011)2
• Light collecting area p(1)2
• Fraction of light collected p(1)2/4p(1.5x1011)2
  1.1x10-23!
• Need bigger telescopes to collect more light
  (refer to Chapter 2)
• Limits cost, mechanical structure, seeing,

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Basic Refractor
(Convex lens)
fo focal length of objective
real image formed here
Basic Reflector
Concave
fo focal length of primary
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Optics Review

• Lens Formula
• where o object distance from lens (ve on
  left)
• i images distance from lens
  (ve on right)
• f focal length of lens (ve for
  convex)
• Linear magnification m
• where m gt 0 if the image is erect,
• mgt1 if enlarged
• Reference Optics by Hecht and Zajac
  (Addison-Wesley)

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• For research telescopes or astro-photography, we
  place the analyzer (e.g. CCD camera,
  spectrometer) at the focal plane
• Normal human eye is most relaxed when it is
  focused on distant objects, i.e., on incoming
  parallel light.
• For visual observations, we need an eyepiece to
  properly collect the light through the objective
  lens or the primary mirror into the eye

fo
fe
Adapted from Telescope and Technique by C.R
Kitchin
Note Focal point of objective and eyepiece
coincide
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II Telescope Optics

• One of the most important number that
  characterize a telescope is its focal ratio (or,
  f/ number)
• E.g. Telescopes aperture diameter 5 cm
• Focal length of primary
  25cm
• Focal ratio 25cm/5cm 5 (a f/5
  telescope)

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• FAST telescope (or, fastscope)
• Small focal ratio (or, small f/ number lt 6)
• So, short telescope for fixed aperture
• Wide field of view (with same eyepiece)
• Bright images for quick recording, but aberration
  a problem
• Excel at low magnification (large image scale)
  views of deep sky objects, e.g. galaxies, or open
  star clusters

Adapted from http//www.absolutebeginersastronomy
.com/
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• SLOW telescope (or, slowscope)
• Large focal number (f/ gt 8)
• Narrow field of field (with same eyepiece)
• Images are less bright but aberration less an
  issue.
• Good for high magnification (fine image scale),
  small field observing, e.g. planets, double stars
• Most large research telescopes are slow, e.g.
  Hubble Space Telescope (f/24)

Adapted from http//www.absolutebeginersastronomy
.com/
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Magnification

• For visual observation with a telescope, the
  objective lens forms a real image at the focal
  plane while the eyepiece forms a virtual image at
  infinity.
• The angle at which these rays enter the eye
  defines the angular size of the virtual image.
• Magnification (M) is the ratio of the observed
  angular size (aIM) to the actual angular size of
  the object (aOB)

Adapted from Observational Astronomy by Andrew
Norton
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Exit Pupil

• The image of the objective lens as seen through
  the eyepiece is called the Exit Pupil
• Properties 1. All light passing through the
  objective must also pass through the exit pupil
  2. the beam emerging from the eyepiece will have
  minimum diameter at exit pupil.

fo fe
fe
Adapted from Telescope and Technique by C.R
Kitchin
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Exit pupil
Adapted from Optics by Hecht and Zajac
Eye relief

• Eye Relief distance between eyepiece and exit
  pupil
• This is where the pupil of the observers eye
  should be placed
• If the size of the exit pupil is larger than the
  pupil of the eye, then some of the available
  light will be lost.
• On the other hand, if the size of the exit pupil
  is much smaller than the eyes pupil, then only a
  fraction of the center of the eyes retina will
  be used and the eye wont see clearly.

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• Suppose D diameter of primary/objective
• d diameter of exit pupil

For astronomical telescopes, usually fo gtgt fe ,
therefore we have Practical Information
Diameter of human pupil 7 mm Comfortable eye
relief 6 10 mm We generally want to roughly
match the size of the exit pupil with the human
pupil, thus constraining the focal length of
eyepiece to be used.
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III Optical Aberrations

• Any deviation from perfection of an image not due
  to diffraction are known as aberrations
• There are six primary aberrations Spherical
  aberration, Coma, Astigmatism, Distortion, Field
  Curvature, Chromatic aberration
• All, except the last one, affect both refractive
  and reflective telescopes. Chromatic aberration
  affects only refractive telescopes.

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1. Spherical Aberration
Adapted from Hyper Physics concepts http//hyperp
hysics.phy-astr.gsu.edu/hbase/hph.html

• For lenses and mirrors made with spherical
  surfaces, rays which are parallel to the optic
  axis but at different distances from the center
  fail to converge to the same point.
• Effect is usually a 1, or larger, difference in
  focal length
• For mirrors, effect can be totally removed if the
  mirror is parabolic instead of spherical
  (However, it is difficult to grind parabolic
  shape!)

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2. Coma
Adapted from Observational Astrophysics by
Robert C. Smith

• For light rays entering the lens at an angle
  (off-axis)
• Coma is an effect where images of off-axis
  objects are displaced by increasing amount away
  from optical axis.
• Create trailing "comet-like" blur directed away
  from axis.
• May produce a sharp image in the center of the
  field, but become increasingly blurred toward the
  edges.

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Demonstration of Coma Aberration
Circular stars
Comet-shaped stars
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3. Astigmatism
Adapted from Telescope and Techniques by C. R.
Kitchin
Adapted from Hyper Physics concepts http//hyperp
hysics.phy-astr.gsu.edu/hbase/hph.html

• Different curvature in horizontal and vertical
  planes
• Only important for wide-field imaging

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4. Distortion
Adapted from Hyper Physics concepts http//hyper
physics.phy-astr.gsu.edu/hbase/hph.html

• Usually seen in thick double convex lenses.
• Differential transverse magnification for
  different distances of image away from optical
  axis
• Explain why there is a practical limitation in
  the magnification achievable from a simple
  magnifier.

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5. Field Curvature
Adapted from Hyper Physics concepts http//hyperp
hysics.phy-astr.gsu.edu/hbase/hph.html

• The focal plane is not a plane, but a curved
  surface
• Flat detectors, e.g. CCD, will not be in focus
  over its entire region

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6. Chromatic Aberration

• First, recall the physics of refraction (Snells
  Law)
• where n1, n2 are the index of refraction of the
  two media

Medium 1
Medium 2
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• Index of refraction for most transparent
  materials are wavelength dependent, i.e. n is a
  function of l

q2,blue lt q2,green lt q2,red lt q1 n2,blue gt
n2,green gt n2,red gt n1

• Chromatic aberration is the visual effect of the
  wavelength dependent refraction
• BUT, light reflects all wavelengths of light
  identically.

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• Chromatic aberration greatly reduced (10 times)
  by multiple lens system, e.g. achromatic doublet
• Usually, two lens have same curvature and are
  cemented together
• Note Same focal length for two wavelengths so
  that they can be corrected simultaneously

High dispersion glass
Low dispersion glass
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Summary of aberrations
Corrections Most of the aberrations can be
reduced (but never totally removed) by using
multi-lens system.
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IV. Telescope Configuration (Refractors)

• Aberration overcome by having achromatic
  objective lens and multi-lens eyepiece
• Biggest refractor built 1 m diameter (Yerkes)
• Limitations for building bigger refractors
• Light absorption and chromatic aberration
• Objective lens has to be supported at the edges
  and they sag under their own weight (glass is a
  fluid!)
• To achieve large f/ number, telescope will be
  long and requires massive support and domes

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IV. Telescope Configuration (Reflectors)

• The biggest optical telescopes (10 m diameter,
  Keck) built in the world are reflectors
• Major advantages
• No chromatic aberration
• No spherical aberration (parabolic mirrors)
• Mirror can be supported at the back, no huge
  support structure needed
• Improved technique on making big mirrors
  (Aluminium-on-glass, recoating needed)

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Newtonian

• The first working reflector (1668, 1 inch
  diameter)
• Eyepiece moved to the side of the telescope

Adapted from Telescope and Technique by C.R
Kitchin
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Cassegrain
Paraboloidal
Hyperboloidal
Adapted from Tumbling Stone general
dictionary http//spaceguard.ias.rm.cnr.it/tumblin
gstone/dict.htm

• Basic configuration for most large research
  telescopes (e.g. Hubble, Keck 10m, VLT 8.2m)
• Secondary mirror produces narrow cone of light
• Can have large focal length compared to the
  physical length of telescope (telephoto
  advantage)
• Small field of sharp focus (few arcminutes)

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Ritchey-Chretien
Hyperboloidal
Hyperboloidal
Adapted from Tumbling Stone general
dictionary http//spaceguard.ias.rm.cnr.it/tumblin
gstone/dict.htm

• Variation of the Cassegrain
• Remove coma aberration in addition to spherical
  aberration
• Good quality images over a larger field-of-view
  (10-20 arcminutes)
• Example HKU OGS 0.4m (16 inch) telescope

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Combined Refractor and Reflector Schmidt Camera
(Thin)
Adapted from Tumbling Stone general
dictionary http//spaceguard.ias.rm.cnr.it/tumblin
gstone/dict.htm

• Advantage Wide field-of-view (6-10 degree), good
  for sky surveying work
• Two major ones Palomar, Siding Spring (1.2m)
• Disadvantage telephoto disadvantage (long
  telescope length versus focal length)

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Schmidt-Cassegrain
Thin
Spherical
Adapted from Tumbling Stone general
dictionary http//spaceguard.ias.rm.cnr.it/tumblin
gstone/dict.htm

• Compact design compromise of large field-of-view
  and long focal length
• Popular design for small telescopes, especially
  for astro-photography

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Maksutov-Cassegrain
Spherical primary mirror
Spherical corrector lens
Spherical mirror

• Two spherical mirrors and a lens in front
  (spherical surfaces are easier to manufacture)
• Secondary mirror is formed by aluminizing a spot
  on the inside of the lens

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New developments of optical telescopes

• Segmented primary mirrors
• Large equivalent light collecting area

Adapted from Telescope and Technique by C.R
Kitchin
36 mirror segment (1.8m) equivalent of a single
10m mirror
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Very Large Telescope Primary mirror (8.2 m)
Adapted from Very Large Telescope project

• Adaptive Optics Telescope can correct for any
  deviation from its desired shape by active
  real-time mechanical control from behind the
  mirror

A total of 175 controlled actuators
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Large Zenith Telescope Primary mirror (6 m)
Adapted from Large Zenith Telescope project

• Liquid Mirror
• Spin up liquid Mercury on parabolic surface
• Advantage 10 times cheaper than conventional
  mirror.
• Disadvantage 1. Can only point straight up!
  (that explains the name) 2. Mercury is toxic

Rotate at period of 8.5 second to get a thin
(2mm) layer of Mercury
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V. Telescope Mount

• Function Support the optical components, point
  them to a required position, and track the object
  as it moves
• Two components telescope tube, support for the
  tube (mounting)
• Actually, most research telescopes contain no
  tube (open frame)

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Very Large Telescope
Secondary mirror
Primary mirror
Adapted from Very Large Telescope project
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Mounting

• A stable and rigid mounting is very important for
  observations
• Two main types equatorial and alt-azimuth

• Angle of this axis with respect to the ground is
  fixed
• Size of angle depends on the site

Adapted from http//www.astro.ufl.edu/oliver/ast
3722/ast3722.htm
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Equatorial Mounting

• Two axes Polar axis (parallel to Earths
  rotation axis) and Declination axis (which is
  perpendicular to polar axis)
• Once telescope is pointed at a star, tracking can
  be done with only one constant-speed motor
  rotating in opposite direction of earths
  rotation along polar axis. Steady image can be
  recorded.
• Disadvantage expensive to build for large
  telescopes, asymmetry gravity effects

Adapted from Telescope and Technique by C.R
Kitchin
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NASA Infrared Telescope Facility (3 m) (English
mount)
2.5 m Issac Newton Telescope (polar disc
equatorial mount)
Question Along what directions are the polar and
declination axes of these mounts?
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Alt-azimuth (Alt-az) mounting

• Used by all big (gt4m) telescopes recently built
• Allow motions in altitude (vertical) direction
  and azimuth (horizontal) direction
• Symmetric gravity effects, cheaper to build
• Disadvantages 1. To track objects in the sky,
  need two axes rotating at different speed 2.
  Rotation of image during tracking need to be
  overcome (by rotating cameras!) 3. Dead-zone
  near zenith

Adapted from Telescope and Technique by C.R
Kitchin
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Gemini (Hawaii Chile, 8.1m)
Subaru (Hawaii, 8.3m)
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VI. Observatory and Observatory site

• All telescope can be benefited by placing in an
  observatory (sometimes known as the dome)
• Classic design a hemispherical roof with a open
  slot, rotating on a circular wall
• Choosing good sites means that majority of
  worlds largest telescopes are located in a few
  places, e.g. Hawaii, Chile, Arizona, Canary
  Island
• Criteria away from light pollution, clean
  atmosphere (low dust and water), height,
  accessibility, steady atmosphere,