Derek Overdahl wrote:
I came across a table that shows the relationship between aperture, f ratio
and the resulting diffraction limited field diameter. Expert:

8" f4 ~100 arcsecs
8" f6 ~250 arcsecs

In looking at the full chart it appears that the longer focal length the
larger the diffraction limited field of view - really quite dramatic when
comparing an 8'' f4 to say an f8 - a factor of near 4 times.

Some questions....

So? What exactly is the difference any way? Sure an f4 is harder to
collimate but beyond that does this really change the performance of a scope
once it is done well?

How can I translate this into something that means something to me...
What is an Arcsecond and where exactly is it measured? Take for example a
8'' f4 Newt - does this mean my collmination of the light path from the
primary to the secondary needs to be within a 100 arcseconds of where it is
supposed to be? And how does that translate to something I can relate to?

Any input would be appreciated thanks?

The problem is that even assuming that a primary mirror in a Newtonian
telescope is perfectly figured, the image it produces is only free of
aberrations at the very center of the field of view. As you move away
from the center of the field of view, coma becomes increasingly apparent.

Coma is an aberration that makes point sources (like stars) take on a
comet-like appearance, with the tails pointing away from the field of
view. There is no coma at the center of the field of view, but coma
increases linearly with "off-axis angle"--a measure of how far the object
is away from the center of the field of view. The off-axis angle can be
thought of as the angle between where the object is as seen from the
telescope, and where the telescope is actually pointed. Therefore, it
the telescope is pointed directly at the object, the off-axis angle is
zero, and the object appears at the center of the field of view.

So when we say that coma increases linearly with off-axis angle, we mean
that if you double the off-axis angle, the coma too is doubled, and so on.
If the object is far enough away from the center of the field of view,
the coma effect is stronger than the diffraction effect that is inherent
in the formation of the image. The area of the field of view within which
coma is *less* than diffraction, so to speak, is the diffraction-limited
field.

Because the (true) field of view of a telescope plus eyepiece is generally
fairly small (typically a degree or less), the off-axis angle for any
object that you can see in the eyepiece is reasonably small. But in
fast telescopes (those with low focal ratios), coma increases so rapidly
that it becomes a major factor well within the field of view.

To give you an idea of how small an angle is required to make coma readily
apparent, a degree is 1/90 of a right angle--the angle between the zenith
and the horizon. An arcminute is 1/60 of a degree, and an arcsecond is
1/60 of an arcminute (and therefore 1/3,600 of a degree). It is a very
small angle. The fact that an 8-inch f/4 mirror has a diffraction-limited
field of only 100 arcseconds across means that you have to be pointed
within 50 arcseconds (1/72 of a degree) of an object for that object's
image to be diffraction-limited.

Fortunately, there are a number of solutions. One is to get a coma
corrector, like Tele Vue's Paracorr. This is an accessory that you fit
into the eyepiece holder like a Barlow, and you put eyepieces into it.
It largely eliminates the coma.

Another solution, if you are designing a telescope, is to use a slower
(that is, larger) focal ratio. For a given aperture, coma decreases as
the inverse square of the focal ratio, so that an 8-inch f/6 has only
16/36 = 4/9 of the coma that the 8-inch f/4 does. That is why the f/6
has a diffraction-limited field over twice as wide as the f/4 does.

To first order, collimation merely centers the diffraction-limited field
in the field of view. If the telescope is poorly collimated enough, the
entire diffraction-limited field will be *outside* the field of view,
resulting in poorer views.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
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