>I wonder if anyone can answer some questions for me about the lack of
>success I am having taking pictures with my scope (Leica 77APO) eyepiece 20X
>and my Olympus D600L digital camera?

Warning--I have no telescope, but I'm in the process of attaching my
digicam to my microscope, and the problems are basically the same.

The vignetting problem is typical. In 'real' through the 'scope (be it
tele or micro) photography, you remove the eyepiece and camera lens,
and use the 'scope as a lens. With a non-interchangeable lens, you get
stuck with kludges.

A few things that help:

Try bringing the camera a bit farther away from the eyepiece--as close
as posible is often too close, especially if there's a long eye relief.

Zoom in. This will decrease the vignetting, but also decrease the
field of view--the camera won't see as much as your eye will,
effectively increasing the magnification. Zooming in also decreases
the amount of light per area in the picture--you'll need even longer
exposures or wider aperture, or both, sometimes much longer exposure,
beyond what you can do by hand holding the camera.

Align as carefully as possible! Any small deviation will reduce the
camera's view of the image.

There's a company, scopetronix <http://www.scopetronix.com/>, that
caters to astronomy, and they have a wide range of interesting camera
adapters. Many work just fine for microscopes and presumably birding
scopes, as well as for astro telescopes. Some are inexpensive, some
aren't. Depending on what camera and scope you have, you may be able
to use one of the T-ring adapter systems, which is the cleanest way.
But even if your camera doesn't have filter threads and your eyepiece
is a non-standard diameter, there's a gadget that will let you mount
any camera that has a tripod mount to pretty much any eyepiece. It
takes practice to learn to use it, but it's better than most of the
alternatives I've seen, such as two tripods. To find them on the web
site, scroll down the index to Astrophotography and wander about
through the digicam and 35mm choices. It's all a tad confusing at
first exposure, but presumably they're willing to help via email.
--
Allyn Weaks allyn at tardigrade.net
Seattle, USDA zone 7-8
Pacific Northwest Native Wildlife Gardening: http://www.tardigrade.org/natives/