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How to select an eyepiece ?

The brightness and the limit magnitude (IV)

Using a same aperture and eyepiece, a f/10 scope will allow to get twice the magnification of a f/5 scope but with the great disadvantage to yield half the field of view and a dimmer image that the one of the faster scope. Comparing two optical systems, we can define the relative brigthness as the square of the exit pupil. In others words brightness is expressed by the exit pupil.

We easily understand that like aperture, as the exit pupil increases the relative brightness increases in a 2 power law making the image quickly brighter. The fact there is an obstruction in catadioptric and newtonian telescopes up to 40% by diameter will cause loss of light, resulting in lost of image brightness. The same problem occurs with binoculars using poor quality prisms and eyepieces.

Airy discs of a bright star as seen in a refractor and a 35% obstructed reflector. In the latter a noticeable fraction of the brightness is distributed in the rings. Created with Cor Berrevoets's Aberrator.

The brightness also depends on the diameter of the eye pupil. As we told before if you can benefit of an eyepiece which exit pupil diameter is nearly the same size as your own pupil, the light cone entering the eyepiece will reach the eye most efficiently. The pupil diameter varying with the age, at night children and aged people cannot take advantage of the largest exit pupils.

Like the contrast the brightness of an telescopic object depends on its nature and size, whether it is a point source or an extended object. Considering a point source like a star all the light collected will focused at the focal point and the exit pupil will never be larger than the eye pupil. Its brightness will thus increase with the square of the diameter (or linear with area).

For an extended object the rule is no more applicable as the light is spead out over a larger area, exceeding sometimes on tens of arc-minuts. In these conditions, when magnification increases, the brightness per surface unit decreases. Consequently there are both advantage and disavantage. On the plus side the sky background will become darker which will bring out more faint stars but on minus side any extended object will appear darker too.

Mathematically speaking there is a good reason to not use powerful eyepieces when looking at deep sky objects. We know that we can calculate the magnitude as being equals to 2.5*log10(brightness). Adding the eye pupil diameter E and the diameter of the primary objective D in our formula and neglecting losses, the brightness gain is given by the factor of (D2/E2) or, expressed in magnitudes, Δm = 2.5*log10(D2/E2) = 5*log10(D)-5*log10(E).

For a 5" NexStar (D = 127 mm) and an eye relief E = 7 mm the gain in magnitude reaches 6.3 which add to the visual limit magnitude of the sky. So with a sky limit magnitude of 6, the limit magnitude of this scope is 12.3. It goes up to 14 for a smaller exit pupil.

These formulae explain why whatever the f/ratio two scopes offering the same exit pupil will show the same object with the same brightness per surface unit, excepting the larger scope that will use a higher magnification. At last it stands out from the influence of the exit pupil on the brightness that a telescope could never show an extended object brighter than it would look with the naked eye, simply because magnifying an object with a telescope will decrease the exit pupil diameter and so the brightness and conversely the object will become brighter until the exit pupil will be limited by the eye pupil.

Optical system of the original Plössl (left) and the first wide field from Nagler (1984).

The brightness depends on the eyepiece design too. It is easily understandable that more your eyepiece includes lens-elements more the light encounters difficulties to reach your eye. If the dozen of more surfaces are not multicoated some percents of the incident light will be reflected on the lenses and lost in the system. For a 10 lens-elements eyepiece uncoated the loss can exceed 24% if you include a prism or a mirror diagonal in the ray path compared to a multicoated model. This is not the reason to reject all eyepieces using more than 4 lenses, including all super and ultra wide angulars as you cannot get the performances of a wide field eyepiece in a guenine Ortho or Plössl. It is also obvious that low to mid range eyepieces will display more residual aberrations than high-ends models.

The contrast

Photography teaches us that more the image is contrasty and bright, more the details vanishes. On the contrary, a low contrast means that the image will display an extended range of colors or grayscale but without really dark and white areas. So we have to find a compromise in which the highest and lower densities are preserved, what photogtraphers call the best gamma.

Applied to the sky observation, the problem is similar. Contrast and luminosity are obvious factors we have to consider as a dark image is always the negation of what we all expect from an eyepiece : see and not guess celestial bodies.

Due to the few lens-elements they use (4-5) Plössl's are the eyepieces providing the highest contrast, often the crispest and the clearest image. Disadvantage their field is often limited to ~50°. From left to right Paul Rini 12.5 mm Plössl, Skywatch 25 mm Plössl, Celestron Nexstar 13 mm Plössl, Meade 9.7 mm Super Plössl and Tele Vue 32 mm Plössl. Pictures are not to scale. Documents from manufacturers.

A high contrasted eyepiece is requested when you need to differentiate both dim and bright objects from each other and from the background. That helps in observing fainter objects like nebulosities and in discerning subtle visual details in planetaries observations. A high contrast is required when observing sunspots penumbra, divisions in Saturn ring, the Great red spot on Jupiter or Mars surface detail. The contrast depends on coatings which improve the image quality. It is also affected by factors like collimation, air turbulence, objective, prism and system luminosity which depends on the focal ratio.

Plössl's eyepieces are famous for the high contrast, which original design used 2 couples of symmetric lenses. But as we will explain further, all brands are not equivalent in that category, and even the most famous of them have competitors.

The coating

As I explain it in special report the coating is an antireflection material that prevents reflection and light scattering in eyepieces, minimizing light loss and thus increasing image contrast and sharpness.

A single layer of anti-reflection coating can reduce the loss to 1.5% and a multilayers composed of different coatings to as low as 0.25%. This explain why multicoatings provide the highest level of light transmission and yield images with the best contrast. A coated or fully coated eyepiece is insufficiently protected to provide sharp and contrasted images as respectively only one or all air-to-glass surfaces are coated with a single layer of antireflection material. Only the multiple layering, the "fully multicoated" offers the best transmission, which can reach 98.5% for a 6 lens-elements eyepiece.

This peculiar coating explain already why "multicoated" eyepieces like the Celestron Ultima's serie or Plössl's enhanced show a positive difference against a standard "full coated" Celestron Plössl.

At left, an uncoated glass. At right, a multicoated glass. Documents Dr Shene

The principle of coatings is to reduce the light reflecting on the glass surface. If the coating has a quarter wavelength thickness and the glass yields an index of refraction higher than the one of the coating the two reflections are in phase opposition and cancel. For one multicoated surface the transmission can increase up to 3.5%. Drawing by T.Lombry.

Looking inside an "fully multicoated" eyepiece without disassembled it, you must see one dark green or purple reflection for each air-to-glass surface. In a Tele Vue Plössl)s for example there are four such reflections (4 lenses) and twice more in 8-24 mm zoom's. But if you don't see them all this is because the cemented interface surface appears brighter than the air-to-glass multicoating.

The size and weight

In magazines or forums it is not always easy to appreciate visually an eyepiece. The critic can be in favour of a well-known model but the eyepiece can be so tall and so heavy that you cannot easily use it on your small scope fixed on its light aluminum tripod. In the past the discontinued 22mm Nagler II was 13 cm tall which gave its nickname "the grenade" as it was also nearly as heavy as this handy arm, 1 kg 42 gr ! Trying to place it on your small refractor mounted on a fragile tripod in a cold and dark night, and at the first gusty wind you will be in a cold sweat... Only advantage of such a monster, with its optical quality in that range of focals it has no other concurrent with an apparent field of view reaching 82°. We cannot really say it is on par with the 21mm Siebert which yields a similar field of view, even a bit larger in the field. Both are optically completely different (8 lenses vs 3, fully multicoated vs single coated, etc) and provide images which are not comparable.

So prior any investment, like any other collector item take a look at your potential eyepiece at a store and take it in your hand before to buy it. You could be surprised...

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