Astronomy - telescopes

Astronomy - Telescopes

telescope magnification:
- telescope magnification = telescope objective focal length / telescope eyepiece focal length
- total telescope magnification = Barlow magnification x telescope magnification
- where Barlow magnification = magnification of any Barlow lens or extender if used (usually 2 or 3, if no Barlow, then = 1)
- maximum useable magnification is 2 to 2.5 x aperture in mm (ie. 200x for 80mm, 400x for 150mm) or 50x per inch
- it is a general assumption that the higher the magnification of a telescope, the farther and better it can see. This is true only to a certain point. The aperture becomes much more important once the effects of atmospheric refraction set in.
- planetary observation:
  - "seeing" conditions impose the greatest limitation on a telescope's usable magnification & resolution, and at times of average seeing conditions which is most of the time, the resolution of planets will be as good in a 5" as a 16", it is only on those handful of rare nights of excellent seeing that a 16" can be used to its fullest.
  - in addition, the lack of a guided telescope such as by an equatorial mount with motor drive, limits useful magnification to 200-250x as you will otherwise need to be continuously moving the telescope by hand creating vibrations. This applies to Dobsonian mounts in particular.
  - optimum magnifications for planetary viewing start at about 20-25x the telescope's aperture in inches (eg. 160x for 8"), then increase magnification by using smaller eyepieces until no further detail appears, then drop back to the previous magnification
  - refractors give the best contrast and resolution for a given aperture, and for the main planets, brightness is not usually an issue so the larger aperture of the Newtonians is less important than the higher contrast, better optics of the refractor
  - maximum useful magnification depends on seeing conditions, telescope aperture, quality & optical alignment but is usually about 300-500x for most 6-8" scopes (max. of 75x per inch aperture if excellent optics and good seeing)
  - given the smallest eyepieces are ~6mm focal length, the maximum visual magnification of a 1200mm focal length telescope is 1200/6 = 200x, although use of a 2x Barlow lens could potentially double this
  - for photography, film image size needs to be at least 1.5-3mm on 35mm film, thus with mars, it needs to be at least 12 arc-secs & use eyepiece projection
  - examples:
    - mars at opposition (angular diameter 14-25 arc-secs) with colour filter usage:
      - the minimum magnification needed is 80x but probably will need 200-300x to see good detail ie. focal length 1200mm and aperture 5"-6" minimum
      - 4" reflector, poor seeing @150x and 25 arc secs, vague dark markings
      - 4-6" reflectors or 3" refractors: polar caps, large surface features
      - 6-10" reflectors or 5-6" refractors:
        
        variations of surface features; seasonal cloud activity; violet clearing
        
        photography using f150-f200 and 64-200ASA colour film possible but not easy
      - 12" reflectors:
        
        professional level observations
        
        quality photography using f60-f200 and 64-200ASA colour film or b&w with filtration possible
    - jupiter at opposition (angular diameter ~50 arc-secs):
      - 4-6" reflectors or 3" refractors: 2-3 bands visible, 4 moons
      - 6-10" reflectors or 5-6" refractors: red spot, more detail; photography reasonable
- deep sky:
  - the ideal magnification for general viewing of faint objects is 10-15 x telescope aperture in inches (5x aperture in cm):
    - objects become too dispersed if magnification is higher
    - sky brightness intrudes if magnification is lower
    - however, many say that for a 10" SCT, 50-60x magnification is most useful with occasional use of 100x
  - NB. there is no significant advantage to magnifying point sources such as stars other than to be able to detect binaries
  - observing deep sky objects such as faint galaxies and nebulae requires dark skies with excellent sky transparency and wide apertures of at least 8-10" as light-gathering power is especially important in determining the ability to see faint objects such as distant stars, nebulae & galaxies, thus there are three other major factors which come into play here:
    - sky transparency/brightness - this is more important than aperture as excessive light pollution will place substantial limits on ability to visually detect faint objects which will then not have sufficient contrast with the background sky no matter what aperture you use.
    - object brightness
    - object size
    - telescope threshold contrast
    - telescope light-gathering power
  - a useful tool to determine whether a given telescope in given sky brightness will display a given object is the freeware software program written by Mel Bartels called Optimum Detection Magnification (ODM)
  - a good CCD camera with autoguider ($3000) on a good mount ($2000) can overcome urban light pollution issues and take good pics of deep sky objects but requires software manipulation.
- solar:
  - poor day time seeing means that maximum apertures of 4-6" should be used
- terrestrial:
  - maximal useful magnification for terrestrial objects is ~70x due to atmospheric interferences
telescope resolving power:
- the ability to distinguish close objects such as resolving binary stars, rings on saturn
- this is dependent on:
  - aperture diameter (ie. proportional to the diameter)
  - optical alignment of the system (poorly aligned optics impairs viewing)
  - optical quality
  - "seeing" conditions which impose the greatest limitation on a telescope.
- under good seeing conditions, Dawe's limit of telescope resolving power in arc seconds = 116 / telescope objective diameter in mm
  - actually, in arc seconds = 2270000 x wavelength of light / telescope objective diameter in mm
- eg. 25mm = 4".64; 100mm = 1".16; 150mm = 0".77; 200mm = 0".58; 5000mm = 0".02;
- need a 10" for good resolution of globular clusters
- need an 8" (or 6" refractor) for most galaxies
- effective resolution for apertures > 4" is usually limited by seeing
  - For 1 arcsecond seeing, the effective aperture is 0.138 meters or 5.45 inches and for 4 arcsecond seeing, it's 0.0346 meters or 1.36 inches. In other words, the effective resolution capability of large telescopes is that of a 5 1/2-inch instrument, or likely, even smaller. This is especially the case in solar viewing, where the Sun's energy creates significant atmospheric turbulence and seeing in daytime degrades to the 2 to 4+ arcsecond range. Since large telescopes are larger than our seeing limitation, their greatest benefit over smaller telescopes is their light gathering capability, an important night-time advantage. It should also be pointed out that when viewing with larger apertures, there might be brief moments of near diffraction limited resolution. However, when used photographically, seeing will usually be the limiting resolution.
  - Some manufacturers of small aperture telescopes would like you to believe that they can routinely outperform larger aperture telescopes because of atmospheric turbulence (poor seeing conditions). Occasionally this may be true on planets and the moon (you can stop down the larger aperture simply with cut-out masks to alleviate this problem), but it is never true on deep sky objects (nebulae, galaxies and star clusters) where maximum aperture is needed.
telescope light-gathering power:
- the ability to funnel light into a small point for viewing is proportional to the area of the aperture (ie. square of its radius)
- when compared to the naked eye with an effective aperture of approx. 1/4 " (ie. light-gathering power = 1), telescopes with the following effective apertures will have light-gathering powers of:
  - 2" = 64x; 3" = 144x; 4" = 256x; 5" = 400x; 6" = 576x; 8" = 1024x; 10" = 1600x; 16" = 4096x; 32" = 16384x;
telescope threshold contrast:
- unlike light-gathering power, telescopes of increasing aperture quickly approach a limit to its threshold contrast - the ability to display an object of given brightness on a given background sky brightness
- see see http://www.mapug-astronomy.net/AstroDesigns/MAPUG/VisualDet.htm
- an 8" aperture telescope has nearly 200x better threshold contrast than the naked eye,
- a 16" is approx. 300x, ie. only 50% better than a 8"
- a 64" is 1000x better than naked eye but only 5x better than an 8"
- a 2048" is ~3000x better than naked eye but only 15x better than an 8" despite being 256x larger!

the stellar magnitude brightness of the faintest object visible
under good seeing conditions and excellent sky transparency:
- telescope limiting magnitude = 1.96 + 5log₁₀(telescope objective diameter in mm)
- eg. 25mm = 9.0 magnitude; 100mm = 12.0 magnitude; 150mm = 12.8 magnitude; 200mm = 13.5mm; 5000mm = 20.5 mag.
astro-photographic limiting magnitude is usually some 2-3 magnitudes smaller than visual as time exposures can be used.
telescopes with diameters greater than 100mm may be too bright for terrestrial viewing and thus may need to have their aperture reduced by placing a disk in the front of it.
photographic brightness is dependent on the optical system's f ratio (see astrophotography)

Aperture	Resolving Power	Light Gathering Power	Maximum Visible Magnitude
50mm	2.32"	51x	10.3
60mm	1.93"	73x	10.7
80mm	1.45"	131x	11.3
90mm	1.29"	165x	11.5
100mm	1.16"	204x	11.8
125mm	0.93"	319x	12.3
150mm	0.77"	459x	12.7
200mm	0.63"	816x	13.3
235mm	0.49"	1127x	13.6
280mm	0.4"	1600x	14.5
355mm	0.3"	2500x	15

effect of telescope optic quality and degree of obstruction on image quality given very good seeing:
- A central obstruction such as a secondary mirror, affects the image in two ways:
  - 1. Causes a light loss due to the blocking of light entering the telescope.
    - the best human eye can just detect a difference of 0.1 magnitudes, so with obstructions less than 30 percent of
      the aperture diameter (9 percent of the area), the actual light loss caused by just the blockage is essentually undetectable visually. Indeed, many people have trouble seeing a magnitude difference of 0.2 magnitudes, so for
      obstructions of less than 41 percent of the aperture (16.8 percent of the area), the light loss due to the obstruction is not all that noticable.
  - 2. Introduces diffraction effects which can cause a slight loss of both light and contrast for high power images if the secondary is too large.
    - The obstruction from the secondary and its cell slightly alters the disk and ring diffraction pattern of stars, taking a little light out of the central Airy disk and putting it into the rings (mostly the first ring out from the Airy
      disk for common-sized obstructions). If the secondary is large enough, this energy redistribution can result in a slight reduction in the contrast of fine detail for high power images of the moon and planets.
    - In practice, if the secondary obstruction is less than 20 percent of the main mirror's diameter, the effect on the image is negligible.
    - Overall optical quality is more important in the long run than is how small a secondary mirror your telescope uses. A quarter wave of spherical aberration has about as much effect on the overall energy in the Airy disk of
      an imaged star as a nearly 33 percent central obstruction does.
    - The "modified" Schmidt-Cassegrain telescope needs a much larger secondary, often obstructing 33 to 35 percent of the primary mirror's diameter. This does cause a visible loss in contrast for high power images and a slight
      reduction in limiting magnitudes for stars, but overall, the telescope still performs adequately. Indeed, many planetary observers do successfully use SCTs. The tradeoff is in contrast verses telescope compactness.

Telescope accessories:

telescope mounts
motor drive:
- power driven drive that continuously moves the telescope to keep an object in view despite the effects of the earth's rotation
- requires an equatorial mount or computer-driven drive
- necessary for long exposure photography (more than a few seconds)
eyepieces
eyepiece filters:
- for viewing mars:
  - orange or red filters work best to show the markings as these become darker whilst the orange-red deserts become lighter
  - green or blue filters will enhance the polar caps & bring out any fog, haze or clouds in it's thin atmosphere
- to decrease light pollution effects:
  - see Light Pollution
- deep yellow (#12):
  - enhances lunar features
  - enhances orange/red features of Jupiter's belts & useful for studying polar regions
  - improves detail of neptune & uranus on scopes bigger than 11"