some rambling questions on projection (positive and negative)

Let's start with positive projection, i.e. eyepiece projection. Ray
tracing puts the exit pupil where the light beams (rays) converge. You
can get a bit more magnification by putting the focal plan further back
from this spot, say with an extension tube. Now with the extension
tube, is the focal plane sitting past the point where the rays
converge, i.e. have you gone to a negative (diverging) projection? Or
when you refocus the scope to compensate for the extension tube, does
the exit pupil spot now again correspond to the location of the focal
plane?

With negative projection (i.e. a barlow), the rays are diverging, so it
isn't hard to visualize the magnification getting greater the further
back the focal plane sits. However, haven't you created a situation
where you are just asking for light to be reflecting off the extension
tube due to the diverging rays? This could effect contrast. I noticed
on my Nikon tc201 (2x teleconverter) that there does appear to be a bit
of baffling at the back (lens mount).

Miso at Sushi wrote:
Let's start with positive projection, i.e. eyepiece projection. Ray
tracing puts the exit pupil where the light beams (rays) converge.

Which light beams? The exit pupil is where the different light pencils
have the smallest hull. It is not where the focal plane is.

You can get a bit more magnification by putting the focal plan further
back from this spot, say with an extension tube. Now with the extension
tube, is the focal plane sitting past the point where the rays
converge, i.e. have you gone to a negative (diverging) projection? Or
when you refocus the scope to compensate for the extension tube, does
the exit pupil spot now again correspond to the location of the focal
plane?

In order to use negative projection, you must put your projecting lens
before prime focus. The projected focus is then a greater distance
back, yielding power amplification. But the projecting lens has to be
a negative lens, such as a Barlow or similar (e.g., Powermate).

In positive projection, the projecting lens is placed after prime focus,
so that it catches the diverging light rays and focuses them to converge
back at a secondary, projected focal plane. Extending the distance
between the projecting lens and the focal plane with an extension tube
will not change this into negative projection--it will only increase the
power amplification.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Brian Tung wrote:
Miso at Sushi wrote:
Let's start with positive projection, i.e. eyepiece projection. Ray
tracing puts the exit pupil where the light beams (rays) converge.

Which light beams? The exit pupil is where the different light
pencils
have the smallest hull. It is not where the focal plane is.

So where does the eye "sit"? Before or after the smallest hull?


You can get a bit more magnification by putting the focal plan
further
back from this spot, say with an extension tube. Now with the
extension
tube, is the focal plane sitting past the point where the rays
converge, i.e. have you gone to a negative (diverging) projection?
Or
when you refocus the scope to compensate for the extension tube,
does
the exit pupil spot now again correspond to the location of the
focal
plane?

In order to use negative projection, you must put your projecting
lens
before prime focus. The projected focus is then a greater distance
back, yielding power amplification. But the projecting lens has to
be
a negative lens, such as a Barlow or similar (e.g., Powermate).

In positive projection, the projecting lens is placed after prime
focus,
so that it catches the diverging light rays and focuses them to
converge
back at a secondary, projected focal plane. Extending the distance
between the projecting lens and the focal plane with an extension
tube
will not change this into negative projection--it will only increase
the
power amplification.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Miso at Sushi wrote:
So where does the eye "sit"? Before or after the smallest hull?

Well, if you're doing eyepiece projection or Barlow projection, the
eye does not sit anywhere. It's a photographic technique, not a visual
one.

When you observe directly through the telescope (that is, with your eye),
the eye is right at the exit pupil. That way, the eye gets the full
benefit of light rays from both the center of the field of view and the
edge of the field.

For example, let's suppose you're observing the Moon through a 4-inch
(100 mm) refractor at 100x, and it just barely does fill the field of
view. Light emanates from the eye lens of the eyepiece, entering your
eye and forming an image on your retina.

Let's take a look at how it does so. Suppose that the telescope has a
focal length of 1000 mm, and the eyepiece a focal length of 10 mm; this
yields the magnification of 100x I mentioned above. Light from the
center of the Moon is collected across the entire 4-inch diameter of
the objective and is focused down to a point 1000 mm behind that
objective, along the axis of the telescope. This point is called the
focal point.

Of course, the light does not stop at that point. It continues passing
through that point and begins diverging immediately. After a distance
of 10 mm it encounters the eyepiece and is focused to a cylinder of
light rays--that is, neither converging nor diverging. (That's why I
said that the light rays do not converge at the exit pupil.)

How big is this cylinder? Well, it came from a cone whose tip is at the
focal point. Since light converged from the 100 mm objective over a
distance of 1000 mm (the objective's focal length), it must then diverge
to a base of 1 mm over a distance of 10 mm (the eyepiece's focal length).
That is the diameter of the exit pupil: 1 mm. If you follow the math,
you can see how the formula for exit pupil diameter must be the diameter
of the objective divided by the magnification (which is itself the ratio
of the focal length of the objective to the focal length of the eyepiece).

That is not the only bundle of light, of course. There is the bundle
yielded by (say) the top of the Moon. Light from the top of the Moon
passes through the objective and is focused to a point that is also
1000 mm behind the objective. However, light from the top of the Moon
has had to travel downwards (with respect to the axis of the telescope)
to reach the objective, meaning that the focus point of the light from
the top of the Moon is *below* the telescope's axis, by about 4 mm.

Just as before, this new light cone immediately begins diverging and
encounters the *bottom* of the eyepiece. The eyepiece focuses the cone
down to a cylinder; furthermore, the cylinder is aimed back up, so that
it intersects the cylinder from the center of the Moon maybe 8 mm in
back of the eyepiece. If you place your eye right at that intersection,
you can see not only the center of the Moon, but also the top (and every
other part of the Moon, too). Of course, since the latter cylinder is
coming from the bottom of the eyepiece, it looks like the top of the
Moon is there. We say that the telescopic view of the Moon is inverted.

That distance at which the *cylinders* intersect is called the eye
relief; here, it is 8 mm. It differs a lot from eyepiece to eyepiece.
So, light does intersect at the exit pupil in a sense, but it is not in
any way a focal plane. You can not take an image at the exit pupil, but
you *can* put your eye there and see the image perfectly clearly. This
is because your eye has a lens to focus the cylinders back to cones
whose tips rest in an image on your retina.

Hope that helps.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

You apparently have some basic misconceptions about telescope systems.
The whole telescope system (telescope plus the eyepiece) is an afocal
system - the light is a parallel beam of light - at the output of the system
so your eye can see the image of the sky. As such, there is no focal point
of the light coming out of the telescope system.
A barlow changes the angle at which the light is coming to a focus and as
such, changes the angular relationship of the lightbeam to the focus plane,
the place at which the light from the sky comes to a focus with the angles
of the various paoints of the sky. The eyepiece looks at this virtual image
(virtual because it isn't the end of the system) and turns focuses on that
plane and turns the lightpath back to a parallel beam of light. Please note
that if you put your eye at the focal plane, you'd see the light allright
but that would be just an area of light rather than seeing the stars that
you want to look at.
Adjusting the eyepiece away from that focal plane then makes the light come
to a focus (if the EP is fruther away from the telescope's focal plane)
somewhere past the EP and thus you get a second focal plane for the camera's
detector.

--
Why isn't there an Ozone Hole at the NORTH Pole?

wrote:
Let's start with positive projection, i.e. eyepiece projection. Ray
tracing puts the exit pupil where the light beams (rays) converge. You
can get a bit more magnification by putting the focal plan further back
from this spot, say with an extension tube. Now with the extension
tube, is the focal plane sitting past the point where the rays
converge, i.e. have you gone to a negative (diverging) projection? Or
when you refocus the scope to compensate for the extension tube, does
the exit pupil spot now again correspond to the location of the focal
plane?

With negative projection (i.e. a barlow), the rays are diverging, so it
isn't hard to visualize the magnification getting greater the further
back the focal plane sits. However, haven't you created a situation
where you are just asking for light to be reflecting off the extension
tube due to the diverging rays? This could effect contrast. I noticed
on my Nikon tc201 (2x teleconverter) that there does appear to be a bit
of baffling at the back (lens mount).

In addition to what the other guys said, maybe you can play a bit
with this simple ray-tracer:

http://astro.avtanski.com/cgi-bin/optic.cgi

Click on the "view diagram" button and you will see the ray traces.
You can experiment with moving the barlow and the eyepiece to
focus at different distances, to get idea how it all works.

Regards,

- Alex

Actually, I meant where does the eye sit when using an eyepiece?

I know the math behind what you wrote, but never had a good feeling for
what was happening physically. I understood all your explanations
except how eye relief works. Again, I know what eye relief is, but I'm
going to have to digest this a bit to understand the physics.

Anyway, thank all for your help. Also thanks to Alexander for the
diagram builder.

Brian Tung wrote:
Miso at Sushi wrote:
So where does the eye "sit"? Before or after the smallest hull?

Well, if you're doing eyepiece projection or Barlow projection, the
eye does not sit anywhere. It's a photographic technique, not a
visual
one.

When you observe directly through the telescope (that is, with your
eye),
the eye is right at the exit pupil. That way, the eye gets the full
benefit of light rays from both the center of the field of view and
the
edge of the field.

For example, let's suppose you're observing the Moon through a 4-inch
(100 mm) refractor at 100x, and it just barely does fill the field of
view. Light emanates from the eye lens of the eyepiece, entering
your
eye and forming an image on your retina.

Let's take a look at how it does so. Suppose that the telescope has
a
focal length of 1000 mm, and the eyepiece a focal length of 10 mm;
this
yields the magnification of 100x I mentioned above. Light from the
center of the Moon is collected across the entire 4-inch diameter of
the objective and is focused down to a point 1000 mm behind that
objective, along the axis of the telescope. This point is called the
focal point.

Of course, the light does not stop at that point. It continues
passing
through that point and begins diverging immediately. After a
distance
of 10 mm it encounters the eyepiece and is focused to a cylinder of
light rays--that is, neither converging nor diverging. (That's why I
said that the light rays do not converge at the exit pupil.)

How big is this cylinder? Well, it came from a cone whose tip is at
the
focal point. Since light converged from the 100 mm objective over a
distance of 1000 mm (the objective's focal length), it must then
diverge
to a base of 1 mm over a distance of 10 mm (the eyepiece's focal
length).
That is the diameter of the exit pupil: 1 mm. If you follow the
math,
you can see how the formula for exit pupil diameter must be the
diameter
of the objective divided by the magnification (which is itself the
ratio
of the focal length of the objective to the focal length of the
eyepiece).

That is not the only bundle of light, of course. There is the bundle
yielded by (say) the top of the Moon. Light from the top of the Moon
passes through the objective and is focused to a point that is also
1000 mm behind the objective. However, light from the top of the
Moon
has had to travel downwards (with respect to the axis of the
telescope)
to reach the objective, meaning that the focus point of the light
from
the top of the Moon is *below* the telescope's axis, by about 4 mm.

Just as before, this new light cone immediately begins diverging and
encounters the *bottom* of the eyepiece. The eyepiece focuses the
cone
down to a cylinder; furthermore, the cylinder is aimed back up, so
that
it intersects the cylinder from the center of the Moon maybe 8 mm in
back of the eyepiece. If you place your eye right at that
intersection,
you can see not only the center of the Moon, but also the top (and
every
other part of the Moon, too). Of course, since the latter cylinder
is
coming from the bottom of the eyepiece, it looks like the top of the
Moon is there. We say that the telescopic view of the Moon is
inverted.

That distance at which the *cylinders* intersect is called the eye
relief; here, it is 8 mm. It differs a lot from eyepiece to
eyepiece.
So, light does intersect at the exit pupil in a sense, but it is not
in
any way a focal plane. You can not take an image at the exit pupil,
but
you *can* put your eye there and see the image perfectly clearly.
This
is because your eye has a lens to focus the cylinders back to cones
whose tips rest in an image on your retina.

Hope that helps.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

You want to put the entrance pupil of your eye (the pupil) at the exit
pupil of the eyepiece so that all of the rays eminating from the
eyepiece enter your eye.

Similarly for afocal projection in a camera, however, you can't get the
exit pupil of the eyepiece lens positioned at the entrance pupil of the
camera lens. So, you just get it close enough so that the angular rays
from the eyepiece are within the capture range of the camera lens.

Brian Tung wrote:

Well, [...]

That distance at which the *cylinders* intersect is called the eye
relief; here, it is 8 mm. It differs a lot from eyepiece to eyepiece.
So, light does intersect at the exit pupil in a sense, but it is not in
any way a focal plane. You can not take an image at the exit pupil, but
you *can* put your eye there and see the image perfectly clearly. This
is because your eye has a lens to focus the cylinders back to cones
whose tips rest in an image on your retina.

Hope that helps.

Delurking to thank you for posting this, Brian. It clarified several
things for me, and it was written with your usual lucidity.

- Ernie http://home.comcast.net/~erniew

Ernie Wright wrote:
Delurking to thank you for posting this, Brian. It clarified several
things for me, and it was written with your usual lucidity.

Hi, Ernie! You're very welcome.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt