Knowing the limit

Abstract

x y d = 2n sin a λ aperture appears as an ' Airy disc' , as described by George Airy in 1835. Later, the mathematical foundations for quantifying diffraction-limited microscopy were noticed by Emile Verdet but fully described and formalized by Ernst Abbe. In his landmark paper of 1873, Abbe reported that the smallest resolvable distance between two points using a conventional micro-scope may never be smaller than half the wavelength of the imaging light. Although no mathematical equations actually appear in the paper, Abbe stated in this and fol-lowing papers that the resolution was limited by diffraction to half the wavelength modified by the refrac-tive index of the medium and the angle of the cone of focused light. Based on the resulting equation, one can improve spatial resolution by using light with a shorter wave-length (for example, ultraviolet), but in biological samples, this is undesirable because of the greater potential for sample damage and increased light scattering within a tissue. Reciprocally, longer wave-lengths improve tissue penetration at the expense of point separation. Abbe's mathematical foundations of image formation and lens aberra-tions provided for the proper design of microscope lenses, accomplished in collaboration with Carl Zeiss and Otto Schott. Abbe's quantitative insights greatly enhanced the quality of microscope optics, contribut-ing enormously to improved data collection and an enhanced user experience for the microscopist. Of course, the success of Abbe, Zeiss and Schott in designing lenses also had an enormous impact on the … Abbe's study influenced the field so greatly that very few attempts were made to overcome the diffraction limit… Without light microscopy, our knowledge of 'little biology' would be severely impaired. The ability to observe migrating cells, examine the distribution of organelle populations or predict putative protein interac-tions (based on proximity) drive modern cell-biological research. However, these observations have physical limits, governed by the properties of light, which conse-quently restrict our view of this cellular world. In light microscopy, when light passes through an opening it is dif-fracted, affecting the spatial resolu-tion or, in other words, the smallest separation that two objects can have and still be discerned. When this opening is a lens, the diffraction pattern created by light passage through the illuminated circular eventual success of the microscopy manufacturer Carl Zeiss itself. But besides these tangible legacies, another long-lasting legacy brought about by Abbe's work included the establishment of physical boundaries in imaging for quite some time. In fact, Abbe's study influenced the field so greatly that very few attempts were made to overcome the diffraction limit, despite the increasing neces-sity to enhance resolution and to improve the visualization of cellular structure. Rather, other techniques were developed to provide these data, such as replacing photons with elec-trons in the development of electron microscopy. Only more recently have scientists revisited Abbe's limit and successfully increased the resolu-tion of light microscopy through a variety of innovative strategies (see