Abbe’s equation

The principle of an electron microscope is based on the light microscope except that electrons are used instead of light. The resolving power of any microscope is given by Abbe s equation... 

Dispersion is the variation of the index of refraction with the wavelength of the incident light. Its variation as a function of wavelength is a reciprocal function also called Abbe s equation ... 

The ability to discern fine details within a magnified image is referred to as the resolution of a microscope. Since light is used as the illumination source in optical microscopy, the resolution is expressed in the same units as the wavelength of light (nm). The theoretical resolution, R, of any optical system may be calculated using Abbe s equation (Eq. 1) ... 

Refractive Index. The refractive indices of the bulk polymers were measured by using an Abbe s refractometer at room temperature. In order to measure the refractive indices at several wavelengths, an interference filter was inserted in the refractometer. Two or three measurements were made at each wavelength and averaged. Usually, the refractive-index data were fit to a three-term Sellmeier dispersion equation of the form (P) ... 

R /f is the numerical aperture (N.A.) and is marked on all objective lenses, together with the magnification. For example, a x25 objective with N.A. = 0.5 is expected to resolve detail of the order of 2X 1 m, ideally. Equation (2.1) has been derived by considering diffraction by a coherently illuminated periodic object. Rayleigh s well-known criterion of resolution, derived for a nonperiodic object incoherently illuminated, gives nearly the same limit of resolution as that determined from the Abbe approach and need not be considered here (see, e.g., Giancoli 1984). 

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