image at: www.telescopes.net/doc/30200
image at: www.mpifr-bonn.mpg.de/public/eff_e.html
image at: www.mpifr-bonn.mpg.de/public/eff_e.html
Technical Data of the Effelsberg Radio Telescope
Reflector Diameter
100 m
Aperture
7,850 m²
Number of Surface Elements (Panels) 2,352
Accuracy of Surface
<0.5 mm
Focal Length in Prime Focus
30 m
Secondary Mirror Diameter
6.5 m
Resolution (Beam Width)
21cm (1.4 GHz)
9.4' (arc min)
3cm wavelength (10 GHz)
1.15'(arc min)
3.5mm wavelength (86 GHz)
10" (arc sec)
Setting Accuracy of Track
+/- 0.25 mm
Maximum Rotation Speed
32°/min.
Maximum Tilt Speed
16°/min.
Total Weight
3,200 t
Construction Period
1968-1971
Computer-generated image of an Airy disk. The outer rings
of the Airy pattern have been enhanced in intensity.
From Wikipedia
Full width at half
maximum
FWHM
FWHM
=1.03 /R
Computer-generated
image of an Airy disk.
The outer rings of the
Airy pattern have been
enhanced in intensity.
From Wikipedia
/R
1.22/R
/R
image at: www.telescope-optics.net/telescope_resolution.htm
1.22/R
/R
Resolution
Angular Resolution
Resolving Power
*
* Focus
*
All stars are so far away that all rays from the same star
effectively parallel
* are
Harry Kroto 2004
*
*
*
*
The angular resolution  is determined by the
angle between two just-resolved objects and is
interference limited i.e. = (/R)
Harry Kroto 2004

*
*

R
d>
*
*
Essentially the opposite side of the triangle
d >  or ideally 1.22 
Harry Kroto 2004

*
*
= (/R)
R

*
*
The angular resolution  is determined by the angle
between two just resolved objects and is interference
limited i.e. = (/R)
Harry Kroto 2004

d


Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0. 12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
at: www.nasaimages.org/luna/servlet/detail/nasaNA...
1.22/R
/R
image at: www.telescope-optics.net/telescope_resolution.htm
image at: www.telescope-optics.net/telescope_resolution.htm
Computer-generated image of an Airy disk. The gray scale
intensities have been adjusted to enhance the brightness of
the outer rings of the Airy pattern.
The total project costs of about 34 million DM were essentially covered by a foundation
(Volkswagen-Stiftung). Additional financing was provided by the state of Nordrhine-Westfalia and
the Max-Planck-Gesellschaft. The federal ministery for science and technology (
Bundesministerium für Bildung und Forschung paid for some special parts of the equipment.
Technical Data of the Effelsberg Radio Telescope
Reflector Diameter100 m
Aperture7,850 m²
Number of Surface Elements (Panels)2,352Shape
Accuracy of Surface< 0.5 mm
Focal Length in Prime Focus30 m
Secondary Mirror Diameter (Gregory-Reflector)6.5 m
Aperture Stop - in Prime Focusf/0.3- in Secondary Focusf/3.85Angular
Resolution (Beam Width) - at 21cm wavelength (1.4 GHz)9.4' (arc minutes)at 3cm wavelength (10 GHz)1.15' (arc minutes)at 3.5mm wavelength (86 GHz)10" (arc seconds)
Azimuth Track Diameter64 m
Setting Accuracy of Track+/- 0.25 mm
Azimuth Range480°
Maximum Rotation Speed32°/min.
Power Output of the 16 Azimuth-Drives17.5 kW each
Radius of Elevation Gear Track28 mElevation Movementfrom 7° to 94°
Maximum Tilt Speed16°/min.
Power Output of the 4 Elevation-Drives17.5 kW each
Total Weight3,200 t
Construction Period1968-1971
Height of Track above Sea Level 319m
Commencement of OperationAugust 1st, 1972
The total project costs of about 34 million DM were essentially
covered by a foundation (Volkswagen-Stiftung). Additional financing
was provided by the state of Nordrhine-Westfalia and the MaxPlanck-Gesellschaft. The federal ministery for science and
technology ( Bundesministerium für Bildung und Forschung paid for
some special parts of the equipment.
Technical Data of the Effelsberg Radio Telescope
Reflector Diameter100 m
Aperture7,850 m²
Number of Surface Elements (Panels)2,352Shape
Accuracy of Surface< 0.5 mm
Focal Length in Prime Focus30 m
Secondary Mirror Diameter (Gregory-Reflector)6.5 m
Resolution (Beam Width) - at 21cm wavelength (1.4 GHz)9.4' (arc
minutes)at 3cm wavelength (10 GHz)1.15' (arc minutes)at 3.5mm wavelength (86 GHz)10" (arc seconds)
Setting Accuracy of Track+/- 0.25 mm
Maximum Rotation Speed32°/min.
Maximum Tilt Speed16°/min.
Total Weight3,200 t
Construction Period1968-1971
image at: www.telescope-optics.net/telescope_resolution.htm
image at: www.telescope-optics.net/telescope_resolution.htm
Computer-generated image of an Airy disk. The outer rings
of the Airy pattern have been enhanced in intensity.
From Wikipedia
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
From Wikipedia, the free encyclopedia
(Redirected from Airy pattern)
Longitudinal sections through a focused beam with (top) negative, (center) zero,
and (bottom) positive spherical aberration. The lens is to the left.
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best
focused spot of light that a perfect lens with a circular aperture can make, limited
by the diffraction of light.
The diffraction pattern resulting from a uniformly-illuminated circular aperture has
a bright region in the center, known as the Airy disk which together with the
series of concentric bright rings around is called the Airy pattern. Both are named
after George Biddell Airy, who first described the phenomenon. The diameter of
this pattern is related to the wavelength of the illuminating light and the size of
the circular aperture.
The most important application of this concept is in cameras and telescopes.
Due to diffraction, the smallest point to which one can focus a beam of light using
a lens is the size of the Airy disk. Even if one were able to make a perfect lens,
there is still a limit to the resolution of an image created by this lens. An optical
system in which the resolution is no longer limited by imperfections in the lenses
but only by diffraction is said to be diffraction limited.
The Airy disk is of importance in physics, optics, and astronomy.
HOMEWORK Consider the resolution
= (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
HOMEWORK Consider the resolution
= (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
0.25
NB
 (rad)
2.1x10-3
 (o)
0.12
1200
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.
 or 
R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
NB
R(cm)
/R
 (rad)
 (o)
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120 GHz ≡  = 3x1010/120 x 109 cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120GHz ≡  = 3x1010/120x109cm = 0.25 cm
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120GHz ≡  = 3x1010/120x109cm = 0.25 cm
Harry Kroto 2004
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120GHz ≡  = 3x1010/120x109cm = 0.25 cm
Harry Kroto 2004
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120GHz ≡  = 3x1010/120x109cm = 0.25 cm
Harry Kroto 2004
Harry Kroto 2004
Consider the resolution = (/R) of:
a) The Bonn 100m Radio Telescope operating at the 21cm H spin flip
line
b) Kitt Peak 12m Radio Telescope operating at the J=1 - 0 rotational
line of CO at 120 GHz
c) Galileo's 2cm optical telescope observing Saturn in the visible at
500nm.

R
 (cm)
R(cm)
/R
21cm
100m
21
10000
21/104
120GHz
12m
500nm
2cm
0.25
500x10-7
NB
1200
2
0.25/12x102
5x10-5/2
 (rad)
 (o)
2.1x10-3
0.12
2.1x10-4
0.012
2.5x10-5
0.0014
= c = 3x1010 cm
thus 120GHz ≡  = 3x1010/120x109cm = 0.25 cm
Harry Kroto 2004
Harry Kroto 2004