Diffraction-limited System - The Abbe Diffraction Limit For A Microscope

The Abbe Diffraction Limit For A Microscope

The observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit. Ernst Abbe found in 1873 that light with wavelength λ, traveling in a medium with refractive index n and converging to a spot with angle will make a spot with radius

The denominator is called the numerical aperture (NA) and can reach about 1.4 in modern optics, hence the Abbe limit is roughly d=λ/2. With green light around 500 nm the Abbe limit is 250 nm which is large compared to most nanostructures or biological cells which have sizes on the order of 1μm and internal organelles which are much smaller. To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample.