Choosing eyepieces

Introduction

Basics

• For a "complete" set of formulas and definitions, check the ATM telescope formulas page on this site.
• Definitions
• Aperture: opening of the telescope (diameter of the objective). SYMBOL: D
• Focal length of the primary: SYMBOL F
• f-number: SYMBOL: f/ = F / D
• Focal length of the eyepiece: SYMBOL: f
• Apparent Field of View of the eyepiece: SYMBOL: AFoV
• Formulas
• Magnification: SYMBOL: M = F / f
• Field of View: SYMBOL: FoV = AFoV / M (this is an approximation)
• Minimal magnification: SYMBOL: M_min = D / maximal_eyepupil_opening.

Young people achieve a maximal eye pupil of about 7mm, older people will fall down to 6mm or even 5mm. Remember that the minimal magnification is that magnification at which there is still NO light that canNOT enter the eye pupil.
• Maximal useful magnification: SYMBOL: M_max = 2 * D[mm].
  This is not a strict value, but gives reasonably good results. With very good seeing, one can always try to go further!
• Dawes limit = 116 arcseconds / D[mm]
• Rayleigh limit = 138 arcseconds / D[mm].

Magnifications and Barlows

• When you purchase a Barlow interface, you virtually double the amount of eyepieces you have. A Barlow interface is an optical system which lenghtens the focal length (most of the times the focal length is multiplied by 2 or 3). When multiplying the focal length by an amount x, this also means that the combination Barlow + eyepiece gives x times the eyepiece's normal magnification. Remember that the magnification is dependent of both the focal length (F) of the telescope and of the focal length (f) of the eyepiece: M = F / f.
• The smallest magnification must be larger than the minimal magnification M_min = D / maximal_eyepupil_opening. This gives the longest focal length eyepiece (and... the most expensive too). For example, my (future) 14" (356mm) f/5 has a focal length of 70,2" (1783mm), hence the minimal magnification M_min = 356mm / 7mm = 51x. The focal length f of that eyepiece is then f = F / M_min = 1783mm / 51x = 35mm. I considered buying a 40mm Plössl, but my magnification power would be too small, resulting in light loss (not all the light can enter the eye), and therefore I bought a 32mm TeleVue Plössl.
• The largest magnification is difficult to choose: one has to take into consideration the maximal useful magnification (due to the limited aperture of your telescope, the angular resolution is limited, see Dawes and Rayleigh limits; therefore you will not see more detail when magnifying beyond a certain limit. You can compare this as if you were looking at your coputer or TV screen with a magnifying glass: at a certain point, the dots are that big, that you do not see any more detail...), the short eye relief (distance between the human eye and the front of the eyepiece) intrinsic to short length eyepieces, . . . the use of a Barlow interface can help a lot. Choose the "hi-power" eyepiece so that the eye-relief is still acceptable, and that the magnification is a bit below the maximal useful power; with the Barlow in place, the magnification may slightly exceed this limit (very interesting when the seeing is excellent).
  My maximal useful magnification is M_max = 2 * D[mm] = 2 * 356[mm] = 712x, which leads to an eyepiece with focal length f = F / M_max = 1783mm / 712 = 2.5mm. This is very small, and the eye relief would be too small too. Therefore I chose a 11mm TeleVue Plössl.
• Thus, one could make a table with the desired magnifications and barlow(s). Here's my example:

	32 mm Plössl		11 mm Plössl
	w/o 2x Barlow	with 2x Barlow	w/o 2x Barlow	with 2x Barlow
Magnification	56x	111x	162x	324x
Field of View	0.9°	0.45°	0.31°	0.154°

As you see, there is no overlap in magnifications when I choose a 2x Barlow. This would not be true with a 3x Barlow in my case.
• But then, you will want to know about the field of view of your eyepiece. . .

Field of View

• The Field of View of your scope is (almost) the apparent FoV of your eyepiece divided by the magnification. If you want to do rich field observations, then you will have to buy expensive wide-angle, low power (long focal length) eyepieces, such as Naglers (Tele Vue), or UWA (Meade). The better all-round eyepieces are Plössls or modified versions of this design (Televue, Vixen-LV, ...). A description of eyepieces follows. . .

Eyepieces

• Huygens: this were the first eyepieces ever designed. Consists of 2 planconvex lenses with the flat side pointing at the eye. Nowadays only used for solar and lunar observations by means of a solar or lunar filter, and even then only by means of projection on a screen (solar observations). Small AFoV (about 25-40°), no color correction at all). Small eyerelief.
• Huygens-Mittenzwey: a variant of the Huygens eyepiece. The lens which points to the object is replaced by a meniscus. Reasonable to good eyepiece for "slow" telescopes (f/12 or more). AFoV approx 45-50°. Small eyerelief.
• Ramsden: the first achromat, buit with two planconvex lenses, the convex sides point to each other. Still found nowadays, esp. in small version (.965"), suffers from color aberrations (but much less than the Huygens and Huygens-Mittenzwey eyepieces). Suffers from internal reflections. Useable for AFoV smaller than 35°. Small eyerelief (approx f / 5, thus often problematic if you wear glasses).
• Kellner:
• Orthoscopic:
• Plössl: Both eyelens and fieldlens are doublets. The modified Plössl's also incorporate a biconvex lens between the doublets (Tele Vue). Better all-round eyepieces, excellent images. Some (expensive) brands also correct for typical errors such as coma (often a major concern in "fast" scopes, like f/6 and faster). Very decent eye relief (40mm is possible with the large focal lengths). AFoV = 50°.
• LV-series (Vixen): a variant on the Plössl: a mini-Barlow is built into the eyepiece, allowing very small focal lenghts (up to 2.5mm!) and thus very high magnifications. AFoV is 50°.
• Ultra-wide angle (Erfle, König, Tele Vue Nagler, UWA, ...): Very expensive eyepieces with a large AFoV (82° for Tele Vue Nagler eyepieces). Excellent eyepieces, but also very bulky and heavy (tons of glass elements). You pay what you want. . .
• Erfle: AFoV up to 70°.
• König: Very-wide angle eyepiece, invented during WW II. Suffers often from internal reflections. (AFoV comparable to Erfle eyepieces).
• Nagler: Excellent, expensive, incredible AFoV: 82°.
• Monocentric: special eyepiece for demanding planetary observers. The monocentric eyepiece design povides only 2 air-to-glass surfaces, and consists of massive glass (triplet). Very sharp on-axis, very little to no internal reflections, but a very narrow apparent FoV (30°).
• Brandon coma corrector: this is not really an eyepiece, but an interface which (spectacularly) increases the "coma free" field. Also exists as combined Barlow.
• Barlow interface: also not an eyepiece, but an interface which allows higher magnification. . . while keeping the same eye relief.