1. Issues with the use of telescopes
Magnification
Magnification determines how much larger the image is as compared to the size of the source of the light (the object) fo
Magnification = fe
Where
fo is the focal length of the objective
fe is the focal length of the eyepiece

2. Issues with the use of telescopes
Magnification
From the group exercises, most of the object the average observer would look at at actually relatively large.
Magnification is not the most important characteristic of a telescope for a backyard astronomer.
Professional astronomy also requires the examination of deep sky objects, which require a high magnification.

3. Issues with the use of telescopes The crucial issue - RESOLUTION
Magnification
Further problems – if the image produced by the telescope does not accurately represent the source, and high magnification might only magnify the inaccuracies.
The crucial issue - RESOLUTION

4. Issues with the use of telescopes
Resolution
More important (possibly more important) than magnification is resolution.
Resolution – the property of an instrument to identify (resolve) small details.
The smallest angular size identifiable by an instrument is given by 
min = .25 D
Where
 is the wavelength of the EM waves being collected in m (1 m = 10-6 m)
D is the diameter of the aperture (the opening which collects the wave) in meters
The calculated value of  will be in seconds of arc (arc seconds)

5. Issues with the use of telescopes Resolution
min is called the diffraction limited resolution of the telescope

6. Issues with the use of telescopes
Resolution
 (in m )
min (in arc sec) = .25
D (in m)
The ability to resolve small details is determined by the wavelength fo the EM wave and the diameter of the aperture.
For high resolution, one would observe as the shortest wavelength possible and use the largest diameter aperture possible.
For a telescope, the diameter of the aperture is determined by the diameter of the objective.

7. Issues with the use of telescopes Resolution
 (in m )
min (in arc sec) = .25
D (in m)
For the naked eye,
Shortest visible wavelength 400 x 10-9 m = .4 m
Diameter of the aperture (the pupil)  3 mm = 3 x 10-3 m
min  33” = .55’ = .0093o
The average human eye can resolve object with an angular diameter of about a half a minute.
Compare with your estimate from Group Exercise 2

8. Issues with the use of telescopes Resolution
 (in m )
min (in arc sec) = .25
D (in m)
For the Mount Palomar 200 inch optical telescope,
Shortest visible wavelength 400 x 10-9 m = .4 m
Diameter of the aperture (the objective) = 200 in = 5.08 m
min  1.96 x 10-2 “ = 3.2 x 10-5 ‘ = 5.5 x 10-7 degrees
The Mount Palomar telescope can resolve objects about 1700 times smaller than the naked eye

9. Issues with the use of telescopes
Resolution – The Hubble Space Telescope
Hubble works on the same principle as the first reflecting telescope built in the 1600s by Isaac Newton. Light enters the telescope and strikes a concave primary mirror, which acts like a lens to focus the light. The bigger the mirror, the better the image. In Hubble, light from the primary mirror is reflected to a smaller secondary mirror in front of the primary mirror, then back through a hole in the primary to instruments clustered behind the focal plane (where the image is in focus).       
Mirror size Primary mirror: 2.4 m – (94.5 inches) in diameter
Secondary mirror: 0.3 m - (12 inches) in diameter  
Angular resolution Hubble's angular resolution is 0.05 arcsecond. This is the "sharpness" of Hubble's vision. If you could see as well as Hubble, you could stand in New York City and distinguish two fireflies, 1 m (3.3 feet) apart, in San Francisco.

10. Issues with the use of telescopes
Resolution
 (in m )
min (in arc sec) = .25
D (in m)
If the Mount Palomar 200 inch optical telescope recorded radio waves of wavelength 1 meter,
wavelength  1 m = 1 x 106 m
Diameter of the aperture (the objective) = 200 in = 5.08 m
min  4.9 x 104 “ = 820’ = 13.7o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The Mount Palomar telescope would not be able to resolve these objects
It would not be able to “see” the moon !

11. Issues with the use of telescopes
Resolution
 (in m )
min (in arc sec) = .25
D (in m)
For the National Radio Astronomical Observatory Robert C. Byrd Radio Telescope,
wavelength  1 m = 1 x 106 m
Diameter of the aperture (the objective) = 100 m
min  2500” = 41’ = .69o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The NRAO telescope would be able (roughly) to resolve radio sources of these angular diameters
This is the worlds largest fully steerable radio telescope

12. Issues with the use of telescopes
Resolution
 (in m )
min (in arc sec) = .25
D (in m)
For the Arecibo Radio telescope,
wavelength  1 m 1 x 106 m
Diameter of the aperture (the objective) = 305 m
min  819” = 13.7’ = .22o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The Arecibo telescope would easily be able to resolve radio sources of these angular diameters
However, the Arecibo telescope can only “see” object directly above it

13. Issues with the use of telescopes
Refractors
Difficulties:
* Physical size of long focal length objectives
* Absorption of light by the lenses
* Grinding two precision surfaces
* Chromatic and spherical aberrations

14. Issues with the use of telescopes
Reflectors
Advantages:
Compound telescopes with long focal length objectives can be relatively compact
Single ground surface
Disadvantage:
MUST have an obstruction in the path

15. Issues with the use of telescopes
Wide Field Telescopes
Designed in 1930 by Bernhard Schmidt, the Schmidt Camera was the forerunner of the modern Schmidt-Cassegrain telescope. Notwithstanding all of the advances in optical and electromechanical technology over the intervening years, however, the classical Schmidt Camera to this day accomplishes feats of astrophotography that are simply unattainable with any other telescopic lens, telescope, or electronic imager. No other photo-optical instrument permits such extremely wide-field photography at such fast photographic speed and with such an amazingly flat imaging area to the field edge. Unlike the Schmidt-Cassegrain telescope, however, the Schmidt Camera is strictly a photographic instrument and can not be used visually.

16. Issues with the use of telescopes Chromatic Aberrations
Associated with lenses.
The Problem: A lens acts like a prism.
The lens will break visible light into a rainbow, resulting in a different focal length for each wavelength in the incoming wave.

17. Issues with the use of telescopes Chromatic Aberrations

18. Issues with the use of telescopes Chromatic Aberrations
The fix:
Use a second lens to refract the wave in the exact opposite direction as the refraction by the objective. A carefully designed second lens will correct the problem.
Computer aided correction for digital images.

19. Issues with the use of telescopes Chromatic Aberrations

20. Issues with the use of telescopes Spherical Aberrations
Associated with BOTH lenses and mirrors.
The Problem: Light hitting different parts of the lens or mirror will refract or reflect differently than other at other locations.
The lens or mirror will have different focal lengths, depending upon where the incoming wave strike the objective.

21. Issues with the use of telescopes Spherical Aberrations
The fix:
Grind the lens or mirror with more precision to eliminate the multiple focal lengths
Use a second lens to refract the wave in the exact opposite direction as the refraction by the objective. A carefully designed second lens will correct the problem.
Computer aided correction for digital images.

22. Issues with the use of telescopes Spherical Aberrations - HST
When the Hubble Space Telescope first send back images, the results were highly disappointing. It was determined that the telescope suffered from spherical aberrations. The belief is that the mirror was ground, polished, and tested here on earth, but that the constructors did not take adequate provisions for the change is shape of the objective mirror in the lower gravity environment of earth orbit.

23. Issues with the use of telescopes Spherical Aberrations - HST
Manipulations of the digital images were carried out with computers, fixing the problems with spherical aberrations

24. Issues with the use of telescopes
Atmospheric Effects
The atmosphere is, in of itself, a lens. As a result, it refracts EM waves. The refraction becomes complicated by motions or turbulence in the atmosphere, which causes VERY complicated refraction characteristics.
A ground based telescope will simply magnify these effects, causing distorted or blurred images.

25. Issues with the use of telescopes
Atmospheric Effects
This variation in refraction as a result of atmospheric motions is what causes starts to twinkle.
The fix: GET THEE INTO SPACE OR

26. Issues with the use of telescopes
Adaptive Optics
What is Adaptive Optics?
Rays of light from a distant star or galaxy are blurred as they pass through the turbulent air of the earth's atmosphere, preventing a telescope on the surface of the earth from forming sharp images. Instruments using a new method called adaptive optics, can eliminate the blurring effect of the atmosphere. This images formed with the 100-inch telescope plus adaptive optics are as sharp as the images from NASA's Hubble Space Telescope. This is the most revolutionary development in astronomy since Galileo invented the telescope in 1609.
From the Mount Wilson Observatiory

27. Issues with the use of telescopes
Adaptive Optics
How Adaptive Optics Works
Adaptive optics measures the atmospheric distortions in the incoming light from a star or other object and sends electronic signals to a deformable mirror that can change its shape rapidly to correct for the distortions. In the system built for the 100-inch telescope, the light reflected from the telescope mirror is divided into several hundred smaller beams or areas. Looking at the beam of light from a star, the system sees hundreds of separate beams, some of which have been deviated because of atmospheric turbulence. The electronic circuits in the system compute the altered shape of a mirror surface that would realign the separate beams so that they are all going in the same direction. Then a signal is sent to the deformable mirror to change its shape in accordance with these electronic signals, resulting in an undistorted beam.

28. Issues with the use of telescopes
Adaptive Optics
Neptune
Without AO
With AO

29. Issues with the use of telescopes
Adaptive Optics
Upper Left: Io image taken with Keck adaptive optics; K-band, 2.2micron.
Upper Right: Io image based on visible light taken with Galileo spacecraft orbiter.
Lower Left: Io image taken with Keck adaptive optics; L-band, 3.5micron.
Lower Right: Io image taken without Keck adaptive optics.

30. Issues with the use of telescopes
Rotation of the Earth
Problem: When you are looking at an object, the telescope will rotate with the earth. This will cause the object to move out of the field of view.
For high magnifications, this can happen amazingly fast.
Correction: Motor Drives and computer controlled motor drive.
Can be made to fix on a point on the object, and move the telescope to keep the position of the object in the eyepeice fixed.