How will you track a moving image in the microscope?
Your question is hard to answer without more detail, including movement rate and required magnification. For relatively slow moving objects you can use a movable stage (X-Y stepper motors tied to a computer). Usually the direction of motion is erratic or unknown, and some digital tracking software will have to be written to drive the steppers so as to follow the designated object of interest. This may be something you have to develop yourself, although there may be some "tracking" software commercially available (or adaptable).
Note that you usually cannot take a video of the object as you track it, due to the quantum action of the stepper motors. However, this does not keep you from taking a series of stills (step - capture - step - capture - step ... etc.) and turning them back into a stop-action video. There are a lot of free or cheap programs out there to do that.
If the motion of the object is rapid, then you have a much bigger problem. One project I did some years back had this problem, and we could not actively track the sudden motion with a microscope. What we did instead was to reduce the microscope magnification, and significantly up the resolution of the high-speed camera (and yes, that was very expensive). At 1500 FPS, we could capture the object as it moved rapidly across the stage, then post-process the resulting frames to center on the object. The obvious limit here is that the object needs to cover a relatively small portion of the overall picture - which limits the magnification you can use. Of course, the offsetting advantage of this method is that you pay more for the camera, but don't have to have a movable stage on the scope.
on Dec 06, 2017