This article represents what I have learned by practical experience, discussing this issue online and from books and other online resources. Some of the online information on this subject is flat wrong and a lot of it is half-right and incomplete. I invite serious critique and corrections - especially from anyone with formal optical training.
This article only adresses vignetting. I suggest visiting www.digibird.com for a general primer on digiscoping and afocal imaging.
The factors that lead to vignetting are actually pretty simple to understand. There are four primary factors to consider: eyepiece AFOV, camera lens FOV, eyepiece eye relief, and camera lens entrance pupil location. These four factors relate to each other in correlated pairs.
1) The AFOV (apparent field of view) of the telescope's eyepiece must be the same as or larger than the camera's FOV (field of view). A camera and lens with a FOV of 45 degrees will always vignette if the AFOV (apparent field of view) of the attached eyepiece and scope is less than 45 degrees.
2) The eye relief an eyepiece must extend to the entrance pupil of the camera lens in order for the camera lens to "see" the entire FOV of the eyepiece. If the eye relief falls significantly short or extends significantly past the entrance pupil, there will be smaller AFOV available to the camera lens. In this case, vignetting might (but won't necessarily) occur.
It sounds simple and it is. And it makes sense when you consider why manufacturers specify the eye relief and AFOV numbers for their eyepieces. They want you to know how close your eye should be to the eyepiece in order to see the full view (especially important for eyeglass wearers). And they want to give you some idea of how wide or narrow that view will be.
Afocally coupling a camera to a telescope, is simply replacing our eye with a camera. The width of the view matters to the camera just as it matters to our eye. And it should be no surprise that the camera will also need to be placed at the appropriate "eye relief" distance from the eyepiece. These ideas are straighforward and are essentially the same rules that apply to normal visual telescope use. Unfortunately, determining the entrance pupil for a camera lens isn't nearly as easy as determining it four the much simpler lens systems in our eyes. Almost all eyepieces are designed for the human eye, not the camera. The main difference between the camera and the eye (at least for these purposes) is that the location of the camera's entrance pupil is usually fairly deep withing the camera lens. You might think of the camera as an "eye" with unusually thick glasses (sometimes extremely thick glasses) in front of it. It is the depth of the entrance pupil for the range of camera focal lengths that is the primary determinant of how easy it will be to get a good unvignetted zoom range in an afocal system.
The basics are simple in concept but can get a bit more complicated when we have to calculate their values.
• The published AFOV values for eyepieces may not be precisely accurate, but they are usually close. You can measure it more precisely while the eyepiece is mounted to a telescope if a very accurate number is important to you. Some spotting scope manufacturers post just this type of data for their various spotting scope and eyepiece combinations. The information is usually expressed in feet or meters of view at a specified distance. For our purposes, we need to convert this to an angular value in degrees. Use the same procedure I outlined for calculating the camera FOV. Just replace the camera's focal length with the distance to the target and then replace the the one-half value of the film or sensor diagonal with one-half of the field of view distance. This is also a good way to calculate the FOV of any scope. Simply set up the scope at a known distance and aim it at a yardstick or similar object with known dimensions and do the calculations as outlined for the manufacturer's specifications. Once you know the scope's FOV, simply multiply that number by the scope's magnification and you have the AFOV as seen at the eyepiece.
• Eye relief numbers are usually about right, but can vary depending on the scope that the eyepiece is attached to. These numbers but may also fail to accourt for the recess of the the eyelens in the eyepiece housing. An eyepiece with 30mm of eye relief having an eyelens that is recessed 10mm only has 20mm of effective eye relief for afocal coupling. Of course if you can remove some of the material that creates the recess, then the effective eye relief will be increased. But many people don't really want to grind away metal from their nice eyepieces.
• Camera FOV can be determined by a pretty straightforward calculation. Though I betting most people won't want to do the math. I've provided a list of precalculated 35mm equivalents toward the bottom of the Camera FOV page to make it even easier.
• The camera's entrance pupil is the one number that will be difficult to obtain. And to make matters even more poorly defined, the entrance pupil usually moves as the camera lens is zoomed. So it is no surprise that the location of the entrance pupil is seldom accurately known and is typically deduced by noting the eye relief needed to give the camera the full AFOV of the eyepiece. From a practical standpoint, most people rely on trial and error and the experience of others. Cameras that are known to have favorable characteristic are the Nikon Coolpix 99x/4500 series, CP5000, CP8400, and CP5200. Canon's A95 gets does well. The compact swivel body Kyocera/Contax cameras are getting very favorable comments recently(SL400R, SL300R t* etc.) This list is not exhaustive. I currently use a Coolpix 5000.
The following examples illustrate how these principles are applied in practice . The first example is entirely hypothetical and will step you through the process.
Lets assume you know that:
Your eyepiece has a 20mm eye relief and an AFOV of 50 degrees while mounted on your telescope.
Your camera lens needs 20mm or more of eye relief (this is the approximate average eye relief needed for a Coolpix 990,995,4500,5000, 8400).
You could then predict with some confidence that vignetting with this combination will begin to occur when the camera's FOV is 50 degrees or greater. This would be at a 12mm focal length on a Coolpix 5000 and at about a 10mm focal length on a Coolpix 990, 995 or 4500.
This gives us a very good prediction of the widest angle that will give an unvignetted view. But what about the other focal lengths? The entrance pupil probably changes location as the lens is "zoomed". Ideally, the distance between the eyepiece and camera lens would adjust dynamically to match the moving entrance pupil. But for practical reasons, the eyepiece mounting is almost always fixed. Typically, the eyepiece to camera lens spacing is optimized for the widest angle of view possible (as we have done). When the camera lens is then zoomed to a narrower view (more "telephoto") the entrance pupil might very well shift away from optimal placement. But this may not present a problem since the camera's FOV is reduced as the camera is zoomed. As long as the camera's FOV narrows more quickly or at the same rate as the narrowing AFOV from the eyepiece, no vignetting will be seen. Many cameras achieve a fairly wide zoom range this way even though the camera's entrance pupil is seldom optimally placed. When the camera's FOV is less than the AFOV of the eyepiece, you have more flexibility with the placement of the entrance pupil. This tradeoff between AFOV and eye relief seems to work quite well with most of the Coolpix cameras and may very well work similarly with other brands - especially if they exhibit the same back and forth motion of their shutter/iris groups.
If vignetting does occur at an intermediate zoom point, then it might be better to try an eyepiece to camera spacing that works better at the intermediate focal length. It would be time consuming, but determining the entrance pupil location for a continuous range of focal lengths would help to determine the best compromise. Most people do not do this though. They usually rely on trial and error.
The principles involved are simple. But implementing them with a continuously changing zoom lens does complicate things a bit.
This is an example from an actual setup with a number of unknowns. The "telescope" is a Rubinar 1000mm f/10 camera lens that is often sold with additional attachments as a small astronomical telescope. At the time of this test, I did not have a finder for this scope so I could not use my 1.25" eyepieces directly. I decided to make my own eyepiece in a direct mounting assembly. So I had to determine all of the pertinent information about the eyepiece. I did this by viewing a ruler from a short distance. The calculations follow:
Distance to ruler = 2750mm
Width of view = 73mm
Diameter of exit pupil = 3.5mm
Eye relief =  30mm
Magnification = 28.57
EP focal length = 35mm
FOV = 1.52 degrees
AFOV = 43.45 degrees
The AFOV number was a bit disappointing for me since I was hoping for a wider view from my homemade eyepiece. I was hoping for something a bit over 50 degrees since the CP5000 camera I intend to use on this combination has a lens that tends toward wider angles. I mounted the camera to the "scope" and eypiece combination and zoomed the lens until vignetting was gone. I then took a picture and checked the picture data. The focal length was 13.6mm. 13.6mm equates to a 44mm camera FOV. The actual results were very close to what was predicted. This tells me that the eyepiece to camera distance is very near optimal and that no amount of adjustment to it will widen the view. If I want to use the camera at a wider zoom setting, then I need a wider view from the eyepiece.
There are a few of these out there on the internet and I'll quickly address two of them here. Originally, I intended to provide a detailed debunking of them, but decided against it. If people will apply the four criteria I have outlined, they should quickly see for themselves that these "myths" are simply partial truths probably derived from partial understanding. I will add only a short commentary to these two myths.
I hope this clears some of the confusion that surrounds the issue of vignetting and afocal coupling of cameras to telescopes and provides assistance to others in resolving real-world afocally coupling issues. It really is pretty darned simple in concept and not that difficult to calculate in practice. Once you know what your camera's eye relief requirements are, it is pretty simple to match up the eyepiece's AFOV with the camera's FOV.
I think anybody selling digiscoping or afocal eyepieces definitely should publish eye relief and AFOV data. It is at least as important as knowing that an eyepiece's eye lens is flush mounted and it is more important than knowing the eyepiece's eye lens diameter. It would also be great if information about the entrance pupil location/eye relief requirements of a variety of cameras could be collected and compiled to aid others in combining scopes to cameras. Very little of this kind of information is readily available.
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