Terminology and Calculations For The Telescope And Eyepiece

Knowledge of some related terminology, some leading to a few easy calculations is necessary as the first step in eyepiece acquisition. In addition other key attributes of image quality are given to help judge the quality of the eyepiece.
Aperture: The diameter of the objective lens or mirror.
  • The larger the aperture the greater the light gathering and hence the greater the detail
Resolution: The ability to distinguish two objects from one another.
  •  An optical system such as the telescope has an inherent maximum resolution which does not change. The observable resolution of an optical system, does change with magnification but only to the point where the inherent maximum resolution of the system is attained. Beyond this point additional magnification will have no positive affect on the observable resolution. The purpose of magnification is to provide image enlargement making it easier to see detail and is useful only to the point that it fulfills the resolution capabilities of the optical system. Once the maximum resolution is observably fulfilled, additional magnification is pointless as an aid to revealing further detail. Beyond this point the image will start to look “blurry”.
Focal Length: The distance between the lens and the focal point, measured along the optical axis.
  • Measured in millimetres (mm) and written on the eyepiece and the telescope
  • Used to calculate the resultant magnification 0f the telescope-eyepiece optical system
  • An eyepiece of smaller focal length and wider field of view is better than one with a larger focal length and a smaller field of view because it will reveal fainter stars and more general detail
  • The largest focal-length eyepiece you can use with your telescope is easy to calculate: multiply the focal ratio (the focal length of your scope divided by its aperture) by 7.
Magnification: The ability to make visually smaller objects look larger.
Magnification = Telescope Focal Length / Eyepiece Focal Length
  • A function of the telescope – eyepiece system, which uses the  telescope objective lens to create an image of a distant object and then making that image look larger by the use of an eyepiece lens.
  • Maximum magnification should be about 50 to 60 times the aperture in inches
  • Magnifying the image beyond a certain amount does not reveal more but instead renders less detail –  “empty magnification”
  • Realistically, the atmosphere will usually limit your planetary observing to a maximum magnification of about 300x, no matter how large your telescope aperture
  • It has been said that the realistic maximum magnification is about 300x, no matter how large aperture of the scope due to atmospheric limitations.
  • Increasing the magnification makes the image larger, dimmer and field of view smaller
  • The bigger the telescope aperture, the more magnification can be used
  • For low-power viewing of large objects, or to use your telescope as a low-power finder, you will want an eyepiece that delivers close to the maximum possible true field of view.
  • Low magnification is used to find objects initially as well as to view larger objects, while higher magnifications are used for the optimum contrast and resolution when viewing planets and double stars.
Focal Ratio: The ratio between the focal length and the aperture of the telescope.
Focal Ratio = Telescope focal length / Telescope Aperture
  • Related to buying eyepieces, a faster focal ratio scope of say F5 or less requires better quality eyepieces. A telescope of F10 to F15 has less stringent requirements. This is due to the precision of the eyepiece optics required and to take advantage of the wider field of view potentially provided for by a faster scope.
  • The focal ratio (f) of a telescope is a measure of the “speed” of the instrument to capture images in astrophotography.
  • Fast f/4 to f/5 focal ratios are generally best for lower power wide field observing and deep space photography. Slow f/11 to f/15 focal ratios are usually better suited to higher power lunar, planetary, and binary star observing and high power photography. Medium f/6 to f/10 focal ratios work well with either.
  • Barlow lenses can be used to make a “fast” scope “slower” and reducer lenses can make a “slow” scope “faster”.
  • A telescope having half the focal ratio of another telescope will allow imaging to take place in 1/4 of the time. The resultant image will however be half as large.
Field Stop:The Field Stop is the metal ring inside the eyepiece barrel that limits the field size and is a fixed property of the eyepiece. It defines the edge of the field of view.
  • The field stop limits the Apparent Field of View (AFOV) and True Field of View (TFOV) of an eyepiece
Apparent Field of View: The width of view your eye has when looking through just the eyepiece. Its angular value, measured in degrees is a function of the size of the Field Stop.
  • Written on the eyepiece in millimeters (mm), leaving you to calculate the True Field of View of the eyepiece with the telescope.
True Field of View: The actual width of view your eye has through the eyepiece-telescope optical system, an angular measurement in degrees.
True field of view = Eyepiece Field Stop Diameter / Telescope Focal Length x 57.3
True field of view = Apparent Field of View / Magnification
  • The second equation is a formula that can be used when the Eyepiece Field Stop Diameter is not given. It is a an approximation.
Exit Pupil: It is the diameter of the beam of light, coming from the lens of the eyepiece, measured in millimeters (mm),  before it enters the eye. It is the size of the image formed from the eyepiece.
Exit Pupil = Eyepiece Focal Length / Telescope Focal Ratio
Exit Pupil = Telescope Aperture / Telescope magnification
  • Exit Pupil is a important factor in choosing eyepieces because of the limitations of the human eye. At best the eye dilates to about 7 mm in the dark. This measurement decreases with age, from 7mm as a teenager, down to about 4 or 5mm at age 65. If the Exit Pupil of the eyepiece is larger than the maximum dark dilation of the eye, not all the light from the eyepiece will enter into the eye, hence detail will be lost in the image. At the other end of the scale, an eyepiece of Exit Pupil less than 0.5mm will reveal defects in the eye such as ‘floaters’. It may be a good idea to have your specific maximum pupil dilation measured in the dark before purchasing an eyepiece.
  • The longest focal length of eyepiece to use with your telescope and specific pupil measurement: Telescope Focal Ratio x Maximum Dark Dilation of Pupil 
Eye Relief: It is the distance, measured in millimeters (mm), from the outside of the eyepiece lens where you place your eye to see the full field of view.
  • The appropriate eye relief is important for the observers comfort. Too little eye relief can cause vignetting or field reduction, the “keyhole effect”. Too much eye relief makes it difficult to place the eye in the ideal location in the field, unless an eyecup is used.
  • Non eye glass wearers can comfortably use an eyepiece with eye relief down to about 8 mm.
  • If eyeglasses are used but not to correct astigmatism, they are not needed when observing.
  • If eyeglasses are used to correct astigmatism then they must be worn for observing. In this case, eyepieces of no smaller than 15 mm but preferably between 18 to 20 mm should be chosen.
  • Many eyepieces can accept Dioptrix. The Dioptrx is an accessory not necessarily brand specific, made to fit over compatible eyepieces to accommodate the users astigmatism.
  • Traditionally, eye relief was strictly related to the focal length of an eyepiece (the shorter the focal length, the shorter the eye relief). Thankfully today, many modern eyepiece designs now provide wonderfully long eye relief regardless of focal length… a significant benefit for eyeglass wearers.

     


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