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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.
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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. |
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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.
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Optical
system of the original Plössl (left) and the first wide
field from Nagler (1984). |
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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.
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.
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At
left, an uncoated glass. At right, a multicoated glass.
Documents Dr Shene
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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.
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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...
Next chapter
The
sensitivity to moisture
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