In order to produce high quality objectives, Abbe made significant contributions to the diagnosis and correction of optical aberrations, both spherical aberration and coma aberration, which is required for an objective to reach the resolution limit of . In addition to spherical aberration, Abbe discovered that the rays in optical systems must have constant angular magnification over their angular distribution to produce a diffraction limited spot, a principle known as the Abbe sine condition. So monumental and advanced were Abbe's calculations and achievements that Frits Zernike based his phase contrast work on them, for which he was awarded the Nobel Prize in 1953, and Hans Busch used them to work on the development of the electron microscope.