Lecture 02: Astronomical Telescope and Optical Design

Lecture 02:
Astronomical Telescope and
Optical Design
Wenda Cao
Big Bear Solar Observatory
New Jersey Institute of Technology
Big Bear Solar Observatory
Last Week ….
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Object and Image
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1.5 m GREGOR
Ray and Wave optics
Geometrical Optics
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Paraxial and Gaussian optics
 Lenses
 Stops, Pupils and f-numbers
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Mirrors
Physical Optics
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Diffraction
 Fourier optics: PSF, OTF & MTF
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Textbook: “OPTICS”,
Eugene Hecht, Chap. 5 & 10
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Outline
Mt. Wilson, 100 inch, 1917
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GMT, 24.5 m
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Fundamental Optics
Telescope Functions
Telescope Aberrations
General Types of
Telescopes
Optical System of AllReflecting Telescope
Next Generation Large
Solar Telescopes
Refer to materials at
www.telescope-optics.net
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1. Telescope Functions
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Astronomical telescopes
make objects from space
appear as bright, contrasty
and large as possible
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Classical Telescope
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Modern Telescope
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Light gathering power
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Telescope resolution
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Telescope magnification
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1.1 Classical Telescopes
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The astronomical telescope is composed of an objective
lens and an eyepiece lens.
Objective lens: gathers the light and bends it into focus.
Focus: incoming light is bent into a bright point.
Eyepiece lens: brings the bright image from the focus and
magnifies it to the size of your eye’s pupil.
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1.2 Modern Telescopes
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Mirrors vs lenses
Large primary mirror vs small
objective lens
Secondary mirror and multiple
folding mirrors vs eyepiece
CCD camera vs eyes
On-axis/off-axis complicated
optical system vs simple system
$100,000,000 vs $100
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1.3 Light Gathering Power
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Aperture diameter D: effective diameter of the
telescope primary mirror
eye
SDO/HMI
Hinode
NST
ATST
KECK
6mm
14cm
50cm
1.6m
4m
10m
1
5.4×102
6.9×103
7.1×104
4.4×105
2.7×106
D 2
2
( )
2   D 
d
 ( ) 2  6 mm 
2
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Light Gathering Power
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Light Transmission T
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Mirror (reflection):
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Fresh aluminum coating ~ 10% loss for
visible; Dielectric coating reduce loss to a
fraction of percent
Lens (refraction):
2
R  (ni cos  i  n cos  ) /( ni cos  i  n cos  )
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Estimate light loss when it normally passes
through a thin crown glass lens (n = 1.5)
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R ~ 1% for AR coating surface
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Lens absorption A ~ 4% per inch in glass
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~ 4% plus absorption for coated doublet
Central obstruction:
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0.15 ~ 0.4D, resulting in ~ 2 -16 % loss
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1.4 Telescope Resolution
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Diffraction
J1 ( x)  0 at x  3.83, 7.02, 10.17 ...
q1  R sin   1.22 f

D
 1.22f #
q1

1   1.22
f
D
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Telescope Resolution
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Rayleigh criterion: angle
defined as that for which the
central peak of one PSF falls
upon the first minimum of the
other
 ( m)

 (" )  0.25
 (rad )  1.22
D ( m)
D
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Sparrow criterion: angular
separation when the combined
pattern of the two sources has
no minimum between the two
centers

 (rad ) 
D
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Telescope Resolution
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Angular resolution: can be quantified as the smallest angle
between two point sources for which separate recognizable
images are produced


 (rad )  1.22
 (rad ) 
D
1 rad  206265"
D
1 "  725 km on the Sun
eye
SDO/HMI
Hinode
NST
ATST
KECK
6mm
14cm
50cm
1.6m
4m
10m
1
5.4×102
6.9×103
7.1×104
4.4×105
2.7×106
> 60”
0.74”
0.21”
0.06”
0.03”
0.01”
43500 km
534 km
150 km
47 km
19 km
< 8 km
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1.5 Telescope Magnification
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Magnification: is given by a ratio of the image size produced
on the retina when looking through a telescope, versus retinal
image size with the naked eye.
 tan  h ' / f e f o
MT  
 '

 tan  h / f o f e
MT 
fo D
D
 
f e d d eye
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Telescope Magnification
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The effective focal length of McMath-Piece Telescope is 86 m.
Angular diameter of the Sun is about 32’ (arcminute), could
you find the physical size of the Sun on its focal plane?
h  f eff 
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Telescope Terms
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Clear Aperture (or Aperture Stop)
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Effective focal length
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Focal ratio or f-number
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f  number  f #  N 
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Fast beam: small f-number, short exposure time
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Slow beam: large f-number, long exposure time
Image scale:

1
(rad/mm)
h f
206265
s" 
(" /mm)
f
3438
s' 
(' /mm)
f
s

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f
D
2. Optical Aberrations
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Ideal and real optical system
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Optical Aberrations
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Chromatic aberration
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Monochromatic aberrations
Monochromatic aberrations
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Spherical aberration
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Coma
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Astigmatism
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Field curvature
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Image distortion
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2.1 Ideal and Real Optics
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Ideal optics (Gaussian optics) produce an exact point-to-point
conjugated correspondence between the source and its image.
Ideal optics take effect under first-order theory or paraxial optics
3 5 7
sin     

 ...
3!
cos   1 
2
2!
5!

4
4!
7!

6
6!
 ...
sin    , cos   1
3
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Third-order theory: sin    
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Aberrations are departures of the performance of an optical
system from the predictions of paraxial optics.
Aberration occurs when light from one point of an object after
transmission through the system does not converge into a single
point.

3!
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2.2 Telescope Aberrations
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Perfect optics and aberrated optics
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Aberrations: any deviation of the wavefront formed by an optical
system from perfect spherical (or from perfect flat).
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Aberrations disturb optimum convergence of the energy to a pointimage, with the result being degradation of image quality.
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Aberrations: forms
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Wavefront aberrations: measured at the wavefront itself, as a
deviation from the perfect reference sphere.
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Wavefront error (P-V or RMS), phase error
Geometric aberrations: measured at the focal point, as a linear or
angular deviation of rays projected from the wavefront.
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Ray spot diagram
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Aberrations: causes
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Intrinsic telescope aberration: are those inherent to conical
surface, to glass medium, and those resulting from fabrication errors
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Chromatic aberrations
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Monochromatic aberrations:
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Spherical aberration
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Coma
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Astigmatism
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Field curvature
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Image distortion
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Fabrication error
Induced telescope aberrations: caused by (1) alignment errors, (2)
forced surface deformations due to thermal variations, gravity and
improper mounting, and (3) atmosphere turbulence.
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2.3 Chromatic Aberration
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Chromatic aberration: is present only in refractive systems
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Chromatic aberration occurs because lenses have a different
refractive index for different wavelengths of light
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Refractive index decreases with increasing wavelength
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Red light is refracted to the greatest extent followed by blue and
green light
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Solution to CA: (1) achromatic doublet, (2) reflecting system
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Spherical Aberration
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Spherical aberration (SA): rays issuing from a source at infinity
on axis do not all converge at the same point
The marginal rays have a shorter focus
The paraxial rays have a longer focus
Only form of monochromatic axial aberration
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Spherical Aberration
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Spherical and paraboloidal mirrors
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Solutions
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Spherical PM: Large N
Parabolic PM
SA  N
3
D 3
( )
f
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2.4 Coma
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Coma: rays issuing from an off-axis source do not all converge at
the same point in the focal plane
This creates a blur which resembles a comet
Off-axis aberration: it occurs either due to the incident wavefront
being tilted, or decentered with respect to the optical surface
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Coma
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Coma: either affects off-axis image points or the result of axial
misalignment of optical surface
It is the dominant aberration in off-axis telescope: NST, ATST
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Solutions
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Limit field of view
Use large N
Coma  N
2
D 2
( )
f
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2.5 Astigmatism Aberration
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Astigmatism: off-axis point aberration caused by the inclination of
incident wavefronts relative to the optical surface
Astigmatism: results from the projectional asymmetry onto surface
Astigmatism: the focus of
rays in the plane containing
the axis of the system and
off-axis source (the
tangential plane) is different
from the focus of rays in the
perpendicular plane (sagittal
plane)
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Astigmatism Aberration
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Either affects off-axis image points or the result of axial
misalignment of optical surface
It is the dominant aberration in off-axis telescope: NST, ATST
Solutions
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Limit field of view
Use large N
AA   N
2
1
D
 ( )
f
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2
Field Curvature and Distortion
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Field curvature: occurs when the images does not form on a
“plane”, but on a curved surface
FC   N
2

1
D
 ( )
f
2
Distortion: plate scale is not perfectly constant but varies both with
the field angle and the direction
OD   3
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Fabrication Error: deviations of an actual optical surface from the
perfect reference surface due to fabrication process
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3. General Types of Telescopes
 Refracting Telescopes (objective is a lens)
 Reflecting Telescopes (objective is a mirror)
 Newtonian telescope
 Gregorian telescope
 Cassegrain telescope
 Catadioptric Telescopes
 Use mirrors and lenses
 Schmidt-Cassegrain
 Maksutov-Cassegrain
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Refractors
 Easy to use and reliable
 Supply wide field of view
 High contrast images with no
secondary mirror or diagonal
obstruction.
 Sealed optical tube reduces
image degrading air currents
and protects optics.
 Low stray light
o More expensive per inch of
aperture
o Heavier, longer and bulkier than
equivalent aperture reflectors
o Small apertures
o Low spatial resolution
o Chromatic aberration
The Coronal Solar Magnetic Observatory (COSMO)
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Reflectors
 Low in optical aberrations
 Lowest cost per inch of
aperture, allow us to build
large telescopes
 Cover wide spectral range
from EUV to NIR
 Large relative aperture:
reasonably compact and
portable
 Offer multiple foci
o Open optical tube design allows
image degrading air currents
and air contaminants
o Require high polishing accuracy
o Subject to temperature variation
and telescope flexure
o Slight light loss due to 2nd
obstruction
o On-axis telescope have more
stray lights
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Catadioptric Telescopes
 Best all-around, all-purpose telescope design.
Combines the optical advantages of both
lenses and mirrors while canceling their
disadvantages.
 Sharp images over a wide field (3-7 degrees).
 Refracting Corrector plate.
 Reflecting Primary and Secondary mirrors.
 Closed tube design reduces image degrading
air currents.
 Most are extremely compact and portable.
 Large apertures at reasonable prices and less
expensive than equivalent aperture refractors.
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Newtonian Telescope Optics
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Most commonly used of the amateur telescopes
Ease of construction, portability, insensitivity to alignment and cheap
Primary mirror placed at the bottom of telescope tube
Secondary mirror: small elliptically shaped flat mirror
An alternative: “Folded Newtonian” provides high magnification with
a long focal length
Main drawback: coma aberration at the edge of the field of view
A disadvantage is the extra obscuration caused by the circular flat
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Cassegrain Telescope Optics
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Most commonly used of the astronomical night-time telescopes
Longer effective focal length and higher magnification
Concave PM with a hole at its center: placed at the bottom of tube
Convex SM with a small aperture: placed near the top of telescope
Classical Cassegrain: a parabolic PM with a hyperbolic SM
Dall-Kirkham system: an under-corrected parabolic PM with a
spherical SM for direct viewing with small field of view
Ritchey-Chretien (RC) system: overcorrected hyperbolic PM and
SM for a wide field with a coma free
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Gregorian Telescope Optics
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Most commonly used of the solar telescopes
Prime focus for installation of solar heat stop
Concave PM: placed at the bottom of the
telescope structure
Concave SM with a small aperture: placed
near the top of telescope
Optics: a parabolic PM with a elliptical SM
A disadvantage for on-axis Gregorian
telescope is the extra obscuration caused by
the SM and support structure
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Nasmyth Telescope Optics
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A derivative of the Cassegrain and
Gregorian telescopes
Small flat mirror in front of PM deliver
the focus to the side of telescope
Nasmyth foci of very large astronomical
telescopes provide access to
professional, bulky and heavy
instrumentations
8 m Subaru Telescope
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