Sometimes it is extremely difficult to put two variably acquired images into
the same measurement space so that they can be differenced. Because of two
microscopes, it sounds here like you might need to have quite a bit of optical
knowledge and information.
You don't say what you are looking for among the microscope images or how
extensive this project will be, but it may be worthwhile to look deeper into
the Image Processing literature to learn something about stochastic processes.
There are a lot of techniques out there that will allow you to extract certain
pieces of information from the images without the need for pixel by pixel
comparisons ("overlaying" and subtracting normalized quantities). These
techniques typically rely on statistical representations of the image data and
less on spatial representations. Areas of interest (in medical imaging, a cell
or tumor or whatever), may be isolated and compared in this way.
