Introduction
As was mentioned in the introduction, the first role of a microscope is to improve the visualization of very small objects by a human observer. Two essential characteristics of a microscope are therefore its magnification and resolution limit. For a 'diffraction-limited' objective (meaning an objective limited by diffraction and not by its defects or aberrations), the resolution limit \(r\) is proportional to the (mean) wavelength \(\lambda\) and inversely proportional to the object-side numerical aperture \(NA_{obj}\), i.e. \(r= Cte \cdot \lambda /NA_{obj}\). The precise value of this constant \(Cte\) is somewhat arbitrary; when using the Rayleigh criteria with incoherent illumination, \(Cte \sim 0.61\) (see basic optics course or [ [1]]). The object-side numerical aperture of the objective is defined by \(NA_{obj} = n\cdot |sin(\alpha_{obj,max} ) |\) where \(n\) is the index of refraction of the material located between the object and the objective, and \(\alpha_{obj,max}\) is the angle formed by the optical axis and the most marginal ray penetrating through the microscope objective. Therefore, microscope objectives must have a very large numerical aperture and be well corrected for optical aberrations. Those objectives are made of numerous lenses that are very precisely positioned with respect to one another, and therefore are rather fragile and expensive. On another note, to obtain a better spatial resolution, it is interesting to work in a medium of refractive index larger than \(1\), such as water (\(n \simeq 1.33\)) or an immersion oil (cedar or synthetic oil, \(n \simeq 1.52\)), to obtain numerical apertures larger than \(1\). Thus, the objectives of largest magnification (\(\times 100\)) are usually (oil) immersion objectives with numerical apertures often larger than \(1.25\).
However, using those objectives of very high numerical aperture and corrected for most optical aberrations is not without certain problems, that are described in this section.