I use the microscope as an amateur biologist. I usually travel with KLM airlines, but I could travel with any company if needed. I did not find anything that could interdict one to carry a microscope on KLM's website. If there are special restrictions per country that you are aware of (related to this case), please specify.
There is nothing that prohibits you from carrying a microscope onboard an airplane.
One thing to mention is the tools that comes with it, if I am not mistaken microscopes comes with a set of tools (I have seen one made for amateurs), it comes with some sort of sharp tools and/or some kind of liquids in small bottles (I guess dye or something like that). These would be a problem and you need to check them in, but the microscope itself is fine.
For more details about items hand luggage items in EU, visit EASA's list of prohibited items in hand luggage.