Table of Contents

Telescopes
Terminology
Purpose
Atmospheric Nomenclature
Questions

Intro to Astronomy
Misconceptions

Archaeoastronomy
Equitorial Coordinates
Understanding the Seasons

1. To Gather Light: Simplistically, a telescope could be defined as a light bucket. The amount of light gathered by a lens or mirror in comparison to the eye can be expressed as 16D², where D is the aperture of the lens or mirror expressed in inches. This equation does not take into consideration light losses due to transmission or reflection, which may be considerable. A more realistic approach might be 9D². The following table lists the light gathering capabilities of various apertures.
   

   	Aperture (in)		9D²	16D²
   (6.4 mm)	¼	human eye		1
   	2	small refractor	36	64
   	4		144	256
   	8		576	1024
   	12		1300	2300
   (3 m)	96	Hubble, USA	83,000	147,000
   (5 m)	200	Hale, USA	360,000	640,000
   (10 m)	400	Keck, USA	1,440,000	2,560,000

   
   

   Note that as the aperture doubles, the light grasp quadruples.
2. Magnification: The ability to make an image appear larger than its apparent unaided dimension.
   1. Magnification: focal length of telescope / focal length of eyepiece.
   2. The longer the focal length of the system, the higher the potential is for magnification. A 6 inch, F/12 (fl = 72 inches) telescope will produce a higher magnification than a 10 inch, F/5 system (fl = 50 inches) using the same eyepiece.
   3. Limits of Useful Magnification: 6X to 60X per inch.
      1. Upper Limits: An image of an extended object, such as the sun, moon, or a planat, can be said to be composed of a structure of tightly packed dots -- diffraction disks -- similar to a newspaper or magazine photograph. If a newspaper picture is positioned across the room from an observer, a certain amount of detail is perceived in the image. As the observer approaches the picture, it appears larger or magnified over its original dimensions, and more detail can be seen. A position will be reached, however, where there will be no more increase in the amount of information seen in the image. At this point, any further magnification is empty. If the observer continues to decrease his/her distance to the photo, even though the magnification increases, the detail in the image will suffer.
      2. Lower Limits: The diameter of the emerging light cone coming from the eyepiece (called the exit pupil) becomes larger as the magnification of the system decreases. If the exit pupil diameter exceeds the aperture of the eye's pupillary diameter, then the observer is not utilizing the full capabilities of the optics which he/she is employing. The lowest magnification used on a telescope should be governed by the largest exit pupil size which the eye can fully accept. For middle-aged individuals, who do not smoke, 5 mm is generally considered the acceptable value. Mathematically, the exit pupil is defined as the aperture divided by the magnification.
   4. Magnification and Aperture: A telescope with a larger aperture will produce an image composed of smaller diffraction disks (dots) and therefore will allow a higher magnification to be applied to that image before deterioration sets in.
   5. Doubling the Magnification will cause the field of view and image brightness to decrease to one quarter its orginial value. One can literally magnify an image beyond its level of detection by the human eye.
3. Resolution: The ability of an optical system to separate objects of close angular measure so that they may be seen by the observer.
   1. Angles: A circle contains 360 degrees, each of which can be broken into 60 parts called minutes. Each minute of arc can be further divided into 60 seconds. Therefore, a circle contains over one million seconds of arc (1,296,000 seconds exactly).
   2. Mathematically, resolution may be expressed by two basic formulae:
      1. Rayleigh Criterion: 5.45 seconds of arc / aperture in inches. The Rayleigh criterion is based upon theoretical concerns dealing with the physics of light.
      2. Dawes' Limit: 4.56 seconds or arc / aperture in inches. Dawes' Limit is based upon the subjective observations of W. R. Dawes, a 19th century British astronomer.
   3. Resolution potentials of various apertures:
      
      

      	Aperture (in)		Rayleigh	Dawes'
      (6.4 mm)	¼	human eye	21.8	18.24
      	2	small refractor	2.73	2.28
      	4		1.36	1.14
      	8		0.68	0.57
      (3 m)	96	Hubble, USA	0.057	0.048
      (5 m)	200	Hale, USA	0.0273	0.023
      (10 m)	400	Keck, USA	0.014	0.011

      The best resolution of the human eye is about two minutes of arc. Normally, it is about five minutes.

   4. One second of arc resolution on the moon equals about a one mile separation on the lunar surface. A resolution of one half second represents the practical limit of resolution for large aperture telescopes due to atmospheric turbulence (called seeing). It also exemplifies the importance of operating large instrumentation above the earth's atmosphere, where full resolution capabilities can be obtained.
   5. The relationship of magnification of extended objects to resolution: It is important to realize that the number representing the resolution in seconds of arc also specifies the angular size of the diffraction disks which compose the image. Applying this reasoning to magnification, it can be seen that the smaller the aperture, the coarser the dot structure of the image will become. Higher magnifications will be less successful with smaller aperture scopes.
   6. Resolution as it applies to diffraction disks: The resolution of a system also dictates the minimum angular separation, or the angular proximity to which detail can be separated into its individual components. As an example, the following series of dots illustrates an exaggerated, but scaled appearance of the same double star system as viewed through three telescopes of different apertures. The two stars have an angular separation of 1.2 seconds of arc. Note that as the aperture increases, the diffraction disks become smaller, eventually revealing the double as two distinct objects. At this point the system is said to be fully resolved.
      1. 1-inch aperture (4.56 sec. of arc res.) Double appears as one object through the eyepiece.
      2. 2-inch aperture (2.28 sec. of arc res.) Image of double appears to be elongated.
      3. 4-inch aperture (1.14 sec. of arc res.) Image is fully resolved.
4. Contrast: A telescope with good contrast characteristics will allow the observer to differentiate between the various subtle shadings of gray within an astronomical image. The diffraction disks are the key to understanding contrast. The diffraction disks are, in actuality, composed of a disk surrounded by a series of concentric rings of decreasing intensity.
       The contrast of an image is dependent upon the amount of light which is contained in the central disk versus the surrounding rings. The light which falls into the rings is wasted and does not go into the formation of the image, but merely serves to "haze" the picture. Contrast is reduced. Again, the analogy of the newspaper photograph is appropriate. The small dots of various shades of gray form the image. The contrast of the photo would be enhanced if the picture were printed on whiter paper and reduced if printed on grayer paper. In the latter case, the detail in the picture would still be there, but it would present more of a challenge to discern, because of the lack of contrast. The contrast of an image can be improved if the greatest amount of light possible is concentrated into the center disk. A reduction in contrast simply means that the telescope is putting more light into the rings surrounding the diffraction disks which compose the image.
   1. Perfect contrast: Under ideal conditions no more than 84% of the light will fall into the diffraction disk. Sixteen percent of the light will therefore be found in the rings.
   2. Conditions which may reduce the contrast performance of a telescope:
      1. The optical perfection of the system: The lower the quality, the lower the contrast.
      2. The size of an obstruction in the optical path of a telescope reduces contrast. These normally include the secondary mirror, as well as any support structures holding that mirror. As light passes the opaque surface of an obstruction, it is bent slightly causing more light to fall into the rings surrounding the diffraction disk. This phenomenon is called diffraction.
5. Definition: The sharpness of the image. Definition is a function of the optical accuracy of the system. The more precise the optical accuracy, the finer the definition will become.
   1. Astronomically acceptable telescope: The maximum tolerance for an astronomically acceptable image is 1375 Angstroms of deviation of the optical wave front at the image plane. This is compared to a wavelength of sodium light which has a separation of 5500 Å, which equals one wave. Therefore the minimum rating for a telescope which would produce acceptable images is ¼ wave. One Angstrom equals 0.00000001 cm (10-8 cm) or 0.000000004 inch (4 x 10-9 inch). To be astronomically acceptable, a telescopic system must produce an image with an deviation of no more than 0.000000004 inch / Å x 1375 Å = 0.0000055 inch or 5 / 1,000,000th of an inch (5.5 x 10-6 inch).
   2. Comparing resolution and definition: Very often the terms resolution and definition are considered to be the same. This is not true. A 2-inch refractor of superb optical quality will produce images of exceptional clarity and contrast, but it will only resolve objects with a minimum separation of 2.28 seconds of arc. The instrument will still be rather poor with respect to resolution because this is a factor of aperture. A large, optically flawed instrument will give poor definition, but may be fairly adequate with respect to resolution. It will probably not reach the theoretical performance as suggested by Rayleigh or Dawes.
6. Field of View: The area of the sky visible through the telescope eyepiece. Generally speaking, the higher the magnification, the smaller the field of view. Since magnification is directly related to focal length, one could also say that the longer the focal length of the telescope, the narrower will be the field of view as witnessed through similar eyepieces.
   1. Mathematically, field of view = apparent field of eyepiece / magnification
   2. The apparent field of the eyepiece represents the measure of the angle of the light cone which the field lens of the eyepiece is producing within the eyepiece barrel. The field lens is the lens of the eyepiece which first intercepts the light cone being formed by the optical system of the telescope. The eye lens of an eyepiece is closest to the eye when looking into an eyepiece.