So far it all seems easy - we just make a lens which is very wide compared to its working distance. Unfortunately lenses are not perfect, and two imperfections are particularly problematic. Spherical aberration is an inherent property of a simple lens - the lens is more powerful at the edge that in the centre, so the image will not be sharp.

Chromatic aberration is an inherent property of glass - it has different refractive indices at different wavelengths. That is why a prism splits white light into a spectrum. This means that we cannot get all colours in focus at the same time. We can overcome this by using just one colour, and this works well, for example, when looking at living cells under phase contrast. But in the wider picture, we would be throwing out one of the great advantages of light microscopy - the ability to show different structures or substances in different colours.

Unfortunately, both these aberrations get worse with increasing NA, and they do so very much more rapidly than the resolution increases. Without correcting these aberrations we cannot hope to make a usable high-NA lens. Fortunately we can correct them, but it requires multiple optical elements, which is why high-NA objectives are expensive. However, spherical aberration can only be corrected for one precise set of optical conditions and, for example, using the wrong thickness of coverslip, or using an oil-immersion lens on a sample in water, will spoil the correction. It becomes so tricky that very high NA objectives often have a correction collar to adjust for different coverslip thicknesses (in a dry lens) or temperature and salinity (in a water lens).

Chromatic correction come in various grades, from achromat (basic correction) through fluorite (better) to apochromat (best). Best correction is not always best for your experiment, though, since apochromats contain a lot of glass and will therefore absorb more light than fluorites. Some apochromats also do not transmit UV very well, which can be a problem in fluorescence. Also, lenses are only corrected for a particular range of wavelengths - usually blue to red. Their performance can be very bad outside this range, and with the increasing use in microscopy of violet and UV at the short end and far-red and near IR at the long end, this can be a problem. Apochromats with different correction ranges have become available to meet this need.

Finally, the objective is only one of several optical elements in a microscope, and manufacturers design all of these to work together. Swapping objectives between different brands of microscope is therefore not a good idea.