We’re back! Last month we took a look at the characteristics and types of telescopes. This month we’re going to look at how we can manipulate tho characteristics and what we can accomplish by doing so.
Bear with me plea for a quick review of the three major characteris-tics of an optical system:
Aperture
The diameter of the objective lens or mirror. Aperture controls light gathering capacity and resolution.
愿意的英文
Focal Length
The distance the light travels from the objective element to prime focus. Focal length controls magnifi-cation or power. We learned that any change in the optical elements that changes magnification changes the focal length of the system.
Focal Ratio
The ratio of focal length versus aperture and designated by an f/stop number. Focal ratio is the speed of an optical system. Faster speeds mean lower power and higher resolu-tion. Slower speeds mean higher power and lower resolution.
Okay, let’s play! What we’re go-ing to do is e just how much per-formance we can squeeze out of our telescopes and what the road blocks are as we hit the limits. Let’s start with eyepieces.
Eyepieces and Magnification
Eyepieces, also known as ocu-lars, magnify the image produced by the OTA. The eyepiece power is constant but the resulting magnifica-tion depends on the focal length of the scope being ud.
Magnification is calculated as:
Mag = L OTA ÷ L EP
Where L OTA is the focal length of the tube and L EP is the focal length of the eyepiece. Yes, eyepieces have a focal length too. This is how they are classified. A 26mm eye-piece has a focal length of 26mm.
Okay, back to my 10”, 2,500mm
Schmidt. What is the magnification
of a 26mm eyepiece?
青蛙公主 日剧Mag = 2500 ÷ 26
Or 96X. Now compare that to
my 910mm focal length Newt.
Mag = 910 ÷ 26
Or 35X. About a third of my
longer focal length Schmidt.
So, to reach something ap-
proaching the same power with my
Newt will require something around a
infinitus9 to 10mm eyepiece.
Who es the relationship? The
focal length for an eyepiece that
gives reasonable performance for a
particular tube, is about 1% of the
focal length of the tube.
Keep in mind that aperture also
affects the utility of an eyepiece.
This is just a rule of thumb but is a
good starting point for eyepiece -
lection for a typical amateur scope.
The 26mm eyepiece is the one that
shipped with my SCT and is the one
I u most.
How about my highest power
eyepiece of 6.7mm?
Mag = 2500 ÷ 6.7
Or 373X. That’s getting up
there. In fact, it’s quite uncommon
for eing to be good enough to al-
low tho kinds of powers. Seeing is
one of tho limits we hit.
What about with my Newt?
Mag = 910 ÷ 6.7
Only 135X. That’s quite a bit
more reasonable. Nights with eing
good enough for this power are very
common indeed. However, this is
where aperture comes in to play.
Since my Newt has only a 4” aper-
ture, it will not gather nearly as much
light as my Schmidt. Aperture is also
a limit we hit when lecting an eye-
piece.
What should now be obvious is
that the best lection of eyepieces
for any particular scope is completely
dependent on the focal length and
speed of that scope and the average
eing we experience.
The lesson? Before we go shop-
ping for eyepieces, we need do a bit
of ciphering and determine what
range of powers is going to work
best for our tube. Buying that super-
duper high power eyepiece makes
since only if the scope has a fast fo-
cal ratio and we regularly experience
good eing.
Adding Barlows Lens
Who’s looking for a cheap way to
double the number of eyepieces they
own? Simple! Buy a Barlow. A Bar-
low is an element that increas
power. Barlows are classified by
their additional power. A 2X Barlow
magnifies two times when normally
placed just in front of the eyepiece.
linear
By using a Barlow, we change
the resulting power of the eyepiece
being ud by that same factor. So if
a 2X Barlow is ud on my SCT with
the 6.7mm eyepiece, the resulting
power is 373 x 2 or a whopping
746X.
Figure 1 shows the normal posi-
tion for a Barlow right before the eye-
piece.
Now here’s a trick. If we u a
1.25” diagonal and we place the Bar-
low in front of the diagonal, the re-
sulting magnification increa is not
2X power. It’s clor to 3X.
You don’t u a diagonal? You
can accomplish the same thing with
a simple tele-extender and a few
adapters. All we’re doing by posi-
tioning the Barlow in front of the di-
agonal is increasing the distance
between the eyepiece and the Bar-
low lens. So, by buying one Barlow
Optics 101 - How Our Telescopes Work
Part 2: Time to Play!
By Dan Lessmann
Figure 1: Configuration for f/20
from your eyepieces. Using a Bar-low and a diagonal makes each eye-piece like three. Double that again and each eyepiece is now like six!
A focal reducer’s benefit is an increa in the FOV and a faster speed. Its detriment is a reduction in magnification. We can easily e this in the Jupiter shots. The image in figure 4 is really too small to e much detail of the planet but notice the expan of black sky around the planet in this shot as compared to the 3X shot.
Now suppo that black sky is a nebula as in figure 5. For the types of objects we need less power and greater field of view. We also need better resolution since the objects are dimmer. So we need to speed up the optics.
Decreasing Focal Length Speeds Up The Focal Ratio
Focal reducers change focal lengths and ratios just like Barlows. Adding an f/6.3 focal reducer to my f/10 Schmidt means the focal ratio is:
10 x 0.63 = f/6.3
The effective focal length be-comes: 2500 x 0.63 = 1,575mm Now my long focal length, slow scope i
s a shorter focal length, me-
The were shot with the same camera and tube on the same night but including the Barlow in various positions is like having three pa-rate cameras. The same is true of eyepieces.
Increasing Focal Length Slows Down Focal Ratio
Adding a 2X Barlow doubles the power which means we double the focal length and the focal ratio. So, what was an f/10 optical system is now a much slower f/20 optical sys-tem. Slower ratios mean less light is reaching the eyepiece or camera.
At f/20 half of the light normally in the FOV now falls outside of the FOV. So the image of Jupiter at f/20 will be half as bright as at f/10, and one third as bright at f/30.
The exposures for the Jupiter images in figure 2 were indeed two and three times longer for the f/20 and f/30 shots. We can adjust the exposure time of a camera but not our eyes. So visually, the image is going to be dimmer at longer focal lengths and slower speeds.
We can also e the effect a slower speed has on resolution. Look at Europa just to the left of the planet in the top f/10 image. Europa is a nice, sharp pinpoint of light. At f/20 Europa is starting to fu
treaty
zz up a bit but this is a more aesthetically pleas-ing image becau the planet’s de-tails are more visible. At f/30 every-thing’s bigger still but the resolution is really beginning to suffer. Things just look out of focus and fuzzy.
Actually, all three images are in excellent focus and the eing that night was exceptional. What we’re eing is my scope’s limited ability to resolve detail with its fixed 10” aper-ture at long focal lengths and slower speeds. Barring eing, which is variable, this is the limit on the upper end of the power scale.
Adding Focal Reducers
As Barlows increa magnifica-tion reducers decrea it.
Figure 4 shows Jupiter again this time shot with an f/6.3 reducer. Note how much smaller Jupiter appears in
this image than in the other images.
Regardless, adding a reducer once
again doubles the available powers lens, we can triple the available pow-ers from our existing eyepieces. Fig-ure 2 shows this configuration.
Figure 3 shows the result of the different positions. Here’s our old friend Jupiter and a few of it’s companions.
From top to bottom the powers
are 1X (no Barlow), 2X and 3X.
Figure 2: Configuration for f/30
Figure 3: Effects of a Barlow Lens
Figure 4: Jupiter with an f/6.3 Reducer
Figure 5: A More Typical U For Re-
dium speed scope. How about with an f/3.3 reducer?
10 x 0.33 = f/3.3
The effective focal length be-comes:
2500 x 0.33 = 825mm
An f/3.3 scope is quite fast and the 825mm focal length is actually less than my 4” Newt at prime focus but with the much larger aperture of 10 inches. Time to retire the Newt!
With an f/3.3 reducer my SCT is now an excellent platform for quite wide field astrophotography or just viewing a big chunk of the sky. I can’t fit Andromeda but a lot of other “big” objects now fit just fine.
Also, consider the faster focal ratio. At f/3.3 I can theoretically view objects that are 66% dimmer than I can at f/10. This opens up obrving some of tho way out there, dim fuzzies in the deep sky catalogs.
Focal reducers introduce some new limits, this time on the low end of the power scale. If the focal length is reduced too much some new aberrations can popup. The are vingetting and coma.
Vingetting will show up as a dim-mer view around the periphery of the field of view that will fade to black if it’s extreme. This is caud by the focal reducer attempting to generate a field of view that is greater than the maximum field of view available from the aperture of the OTA. The black ring around the periphery of the FOV is actually an out of focus view of the front of the optical tube.
Coma will show up as an inability to focus the entire field of view espe-cially at the periphery. Coma makes stars look like little V’s with the V pointing towards the center of the field. This is caud by spherical aberration or a curvature of the focal plane. To minimize this, most focal reducers are also field flatteners.
Limits From Back and Front Focus
Back and front focus is the total travel available from the focur. For a rack and pinion focur, this is the distance from stop to stop on the rack.
The amount of focus travel limits the elements we can add. It’s quite easy to add elements where the fo-
cus travel is no longer adequate to
新achieve focus with tho elements.
The addition of a few adapters
can accommodate this if the problem
is not enough outward travel, back
focus. But if we can’t move the fo-
cur in far enough, front focus,
we’re probably stuck. Also keep in
mind that combinations of elements
can overrun our available focus
range. So it’s usually a ca of trial
and error with the elements to e if
we can achieve focus.
Figure 6 shows the condary
system required for my scope with
an f/3.3 focal reducer. Note the T-
adaptor and extenders that are re-
quired. The allow my focurs to
bring the image to focus.
Figure 7 shows the configuration
of the condary for an f/6.3 reducer.
Less back focus is required for this
reducer so the T-adaptor is shorter.
Note that the farther from native
focal ratio I go, the more adjustments
I’ve got to make to the condary
system’s optical train to achieve fo-
cus. We also lo some of the bene-
fit of the reducer as we move the
reducer farther away from the eye-
piece or camera. This is analogous
to the different positions of a Barlow.
There’s One Common Down-
side to Barlows and Focal Reduc-
ers
That’s more glass. Anytime light
pass through a layer of glass,
some of that light is absorbed or re-
flected instead of transmitted. So it’s
generally a good idea to keep the
layers of glass to a minimum.
You can minimize much of this
by buying high quality, fully-coated
components.
All of the Combinations
Let’s take a look at all of the pos-
二战老电影战争片sible focal ratios and focal lengths
with the equipment I’ve discusd.
No Barlows and no reducers:
f/10 and 2,500mm
2X Barlow in normal position:
f/20 and 5,000 mm
2X Barlow ahead of diagonal:
f/30 and 7,500 mm
f/6.3 focal reducer:
f/6.3 and 1,575 mm
f/6.3 reducer with 2X Barlow:
f/12.6 and 3,150mm
f/6.3 reducer, 2X Barlow ahead:
f/18.9 and 4,725mm
f/3.3 focal reducer:
f/3.3 and 825 mm
f/3.3 reducer with 2X Barlow:
f/6.6 and 1,650mm
f/3.3 reducer, 2X Barlow ahead:
f/9.9 and 2,475mm
All nine of the different optical
characteristics are possible with one
OTA just by the addition of one Bar-
low lens and a couple of focal reduc-
ers.
We can take tho nine configu-
rations and multiply them by the
number of eyepieces we have and
that’s the total number of combina-
tions we have available to us. For
me that’s eighty-one different combi-
nations and that’s way more than
enough!
A Bit More On Eyepieces
We haven’t discusd the vari-
ous types of eyepieces available. A
few comments on this would proba-
bly be appropriate.
The most commonly ud are
Plössl eyepieces and the are a
good start for our collections. There
are many other kinds that provide
Figure 6: Configuration for F/3.3
Figure 7: Configuration for f/6.3
wide or ultra wide fields of view or are specialized for guiding during photography. However, they all have one characteristics in common that we should know about.
Eye Relief
This is the distance our eye can be from the eyepiece while still being able to e the entire field of view. This is especially critical for tho of us that must wear eyeglass while obrving. This varies quite a bit bad on the power of the eyepiece, its type, its size and its brand. How-ever, shor
ter focal length (higher power) eyepieces have a shorter eye relief. We should take this into ac-count when lecting an eyepiece.
The size also affects eye relief. By size, I mean the size of the no-piece. Generally, the larger the size, the greater the eye relief. The most common size is 1 ¼”. 2” and 15/16” sizes are also available. Generally, 15/16” eyepieces come with less ex-pensive, low end scopes. 2” eye-pieces come with higher end scopes. Regardless, our focur’s diameter determines whether or not we can u larger eyepieces. Most quality scopes can accommodate both 1 ¼” and 2” eyepieces.
Eyepieces with greater eye relief are generally easier and more com-fortable to u so here’s another trick. Suppo I’m obrving some-thing and find that the optimal eye-piece for the object and the eing is a 14mm. My 14mm eyepiece has an okay eye relief but it’s not nearly as comfortable as some of my lower power ones.
So, instead of using the 14mm, I’ll install a 2X Barlow and my 26mm. It’s much more comfortable and I’m at virtually the same power as pro-vided by my 14mm. Or I may just go all out and install the Barlow in my f/30 (3X) position before the diagonal and u my 40mm. That big eye-piece is almost like watching TV and is VERY comfortable to u.
I do add some glass but, I’m us-ing a fully coated Barlow so the loss in light transmission is not terribly noticeable.
Eyepiece Field of View
We might also talk about the field of view available from a particular eyepiece and OTA.
In addition to focal length, eye-
pieces are rated by their inherent
field of view.
Most Plössl eyepieces have an
inherent field of view of around 40°.
The true field of view is found by di-
viding the inherent field of view by its
magnifying power on the OTA. Back
to my Schmidt and my 26mm eye-
piece with an inherent FOV of 40°.
The power is:
2500 ÷ 26 = 96X
So the true field of view is:
40 ÷ 96 = 0.4°
Or a little less than ½° of sky is
visible in the eyepiece at this focal
length. Of cour, if I throw a barlow
or focal reducer into the mix, I alter
makino
this FOV just as I alter the focal ratio
and focal length so I need to take
that into account as well.
Bringing It All Into Focus
Here’s what we’ve found out in
this part…
We found we don’t need a huge
collection of eyepieces.
Three or four will probably do
just fine. Adding Barlows and/or fo-
cal reducers, doubles, triples or more
the available powers of our eye-
pieces.
We found that Barlows and focal
coke怎么读reducers expand the scale of powers
available from our OTA and eye-
pieces.
However there are limits to this
expansion. On the upper end, e-
ing or poor resolution from a slow
focal ratio will limit us. On the low
end, vingetting or coma will limit us.
On either end the available focus
range can limit us but some T-
adaptors and tele-extenders can
handle some of this if the problem is
back focus.
We found before considering the
purcha of an eyepiece or Barlow,
we should do a bit of math to e just
what the resulting powers and focal
ratios will be.
We now know a good starting
point for eyepieces is to consider one
with a focal length somewhere
around 1% of the focal length of the
OTA for most amateur scopes.
We also know there’s not much
point in buying a 5X Power Mate if
our scope’s focal ratio or eing
won’t support that power.
What El?
other worldI think that’s about it. I hope this
ries of articles was helpful to you
and I will e you soon under some
nice, dark and clear skies!
