Photographing what human eyes can see through optical instruments
If the lens dimensions and entrance pupil of a digital camera is similar to that of the human eye, the camera can be put in place of an eye and take photos looking into optical instruments such as microscopes, telescopes, binoculars, and hand lenses (loupes). That's called 'afocal coupling'. If the camera lens diameter is too large, as if often the case, or if the entrance pupil is too deep within the lens, there will be vignetting (figure 1). Vignetting isn't fatal -- the central area is still useful -- but the camera's pixels aren't being put to maximum advantage.
Fig 1. Severe vignetting
The Canon A75 and Canon A570 IS both work well. Vignetting disappears with zooming beyond about 2x. To check a particular camera, simply hold it up to any optical eyepiece and see how it looks (zooming will probably help). Obviously there's going to be vignetting if the camera lens is much larger diameter than a human eye (eg., DSLR lenses) and thus likely larger diameter than eyepieces designed for the human eye.
This page describes some adapters I've built to match Canon A75 and A570 cameras to a variety of optics. The emphasis is on portability and ruggedness. Holding a camera to binoculars works, but not as well as a purpose-built telephoto lens.
Simply put the camera up to the eyepiece
The simplest way to take a photo looking through an optical instrument is to zoom in and position the lens of the camera so that it looks into the instrument, as close as possible and aligned to the optical axis. But there are hazards and difficulties: The camera lens could be damaged by contact; it's hard to keep the camera steady (especially for long exposures); it's hard to align the axes; often stray light leaks in. But it works surprisingly well.
Use an adapter to align camera with optical axis
Many point & shoot cameras, including the Canon A75 and A570, can be fitted with filter adapter that mounts on the camera around the lens and presents a threaded end for 52 mm filters (see figure 2); the camera's lens extends as usual inside the enclosure. A nearly-clear (eg., skylight) or clear-glass plano filter attached to a filter adapter can serve as protection for placing the camera against eyepieces, and a brace to help steady the camera. Added a paper 'donut', as pictured in figure 2, helps block stray light and provides a cushion between the glass of the filter and eyepieces. This also provides a flat surface that helps align the optical axes.
The last degree of freedom, lateral alignment of the optical axes, can be handled by building an adapter to fit over an instrument's eyepiece, as shown in figure 2 (bottom-left). It's made of ABS plastic cut from from a plumbing coupler, with holes drilled and threaded for nylon screws. Fortuitously, the diameter of the ABS part fits nicely within the interior of the 52 mm filter (otherwise, some padding or shimming would be needed). The ring also provides a larger area that can help steady the camera while the photograph is taken, and in cases where the eyepiece is vertical, the ring can even balance the camera, free-standing, allowing the self-timer to be used.
Fig 2. Stabilizing and alignment ring, and plane glass filter with light mask.
There are more complicated designs available commercially -- do an internet search, for example on 'digital camera adapter telescope'.
Hand lens (loupe) mounted in a filter
I had good results doing ad hoc macrophotography by just shooting through a hand lens (eg., see sand micrograph gallery), and to make that much easier and portable, I disassembled a hand lens to obtain the lens and then mounted it in a filter ring, as illustrated in figure 3 below.
Filter rings were obtained from a used camera store, taking care to get ones that have an interior ring that screws into the outer ring to hold the glass (as opposed to plastic ones into which the glass filter was pressed). Note the two slots visible in the inner ring in the filter leaning against the camera in figure 3; look for filters with those slots. Often camera shops will have a tool that makes it easy to unscrew that ring. The inner and outer ring are sometimes made of hard plastic instead of metal; that works.
A shortcoming of the filter mount is that it is wider than required and thus shades the subject much more than necessary. But it is easy to carry the filter-mounted lens in a ziplock bag, and the filter can be used on any camera that takes that filter size (both the Canon A75 and A570 use 52 mm filters, for example).
Fig 3. Hand lens (loupe lens) mounted in re-purposed filter ring
One of the filter mounts in figure 3 was made rugged with hardboard and plywood, using a 10x doublet, and the other with two maple veneer 'business cards' from Lee Valley that I cross-laminated, using a 20x triplet (lighting is harder with the limited working distance).
Binoculars as a digiscope
It works to just put the lens up to binoculars, but having a platform to align and hold steady their optical axes makes it much more convenient. The platform in figure 4 can be hand-held or mounted on a tripod. Nuts and bolts that match the camera and tripod threads are readily available from hardware stores; just pick a material thin enough for the tripod screw to reach through with enough threads to attach a nut or wingnut. Here's a video of ravens in aerobatic flight captured via this set-up.
Fig 4. Binoculars as a digiscope
Making Digital Camera Microscope Adapters (search in that page for the section "Understanding and Avoiding Vignetting")