Abbe’s Theory of Image Formation in the Microscope

Abstract

Abbe’s seminal theory of image formation in the microscope “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung” was published in Archiv für mikroskopische Anatomie (Abbe, 1873a). Abbe developed a theory of image formation in the optical microscope that was based on the diffraction of light by the specimen and the subsequent formation of an image. Abbe’s theory introduced the concept of numerical aperture (NA) and the main factors that affect two-point resolution in the optical microscope (Abbe, 1882a, b). Earlier, in 1870 Abbe began his investigations into numerical aperture in the light microscope (Auerbach, 1918, 1922). These main factors are (1) the wavelength of illumination and (2) the numerical aperture of the microscope objective. If both these factors are known through measurements, then the two-point resolution of the optical microscope can be calculated (Abbe, 1873a).