For resolving biological samples in greater detail than naturally possible by the discrimination power of the human eye, scientists rst used technical aids like water drops or eye glasses. In the late sixteenth century, nally the rst compound microscopes with combinations of carefully cut lenses, resulting in an objective and ocular system, were built (Singer 1914). In 1873, when the physicists’ discussion on whether the nature of light is better described as a particle or by a wavelike behavior was at its climax, Ernst Abbe then introduced the term “numerical aperture” of a microscopic system, a dimensionless number that characterizes the range of angles over which the system can collect light

NA = n sin α

Here n is the index of refraction (air 1.00, water 1.33, typical immersion oil 1.52, or typical optical component glass 1.52 [Schott glass]), and α is the half-angle of

3.1 Short History of Microscopy

3.2 Choosing a Suitable Fluorophore

3.3 Mechanisms behind the Photoswitching of Fluorophores for

Super-Resolution Microscopy

3.4 Super-Resolution Microscopy without the Need of Photoswitching

3.5 Outlook References

the maximum light cone that can be collected by the lens system. Abbe further states that the nest detail that can be resolved is proportional to λ/2 NA, with λ being the wavelength of light (Abbe 1873).