is this the difraction limit of our microscope?

Yes, definitely this is due to diffraction. But I'm surprised by the contrast and number of fringes you have with white light. Is the focus optimized? The fringes can become larger if the image plane is not on the object plane. Is the light really white? The yellow fringe is suspicious. If you can change the illumination, you can try to find a white light with flat and large spectrum, it will help to reduce the fringes. A real white light will be better than a blue light. If you use a more monochromatic light (even if not coherent as a laser), eg a LED, diffraction will increase. The best is a real white light which "washes out" the fringes (adding all the fringes of different dimensions at the different wavelengths).