Abbe diffraction limit

The minimum spacing at which a conventional optical microscope can distinguish two points, set by illumination wavelength and the objective’s numerical aperture.

Diffraction: The spreading and interference of waves when they encounter an aperture or obstacle. Diffraction spreads light from each point, limiting how finely an optical system can separate nearby details.
Spatial frequency: The number of repeating spatial cycles per unit distance. Abbe’s account treats fine specimen detail as high spatial-frequency structure.
Rayleigh criterion: A rule that defines two point sources as just resolved when one image maximum coincides with the other’s first minimum. It assesses point-source separation rather than the spatial-frequency cutoff central to Abbe’s criterion.
Optical microscopy: Microscopy that forms images using visible or ultraviolet light and optical components. The Abbe limit sets a central constraint on the detail conventional optical microscopes can resolve.
Wavelength: The distance between successive points of equal phase in a wave. Shorter illumination wavelengths reduce the minimum resolvable spacing.
Coherent illumination: Illumination in which waves maintain a stable phase relationship. The classical Abbe formula assumes coherent illumination, unlike common incoherent imaging conditions.
Sparrow criterion: A resolution rule marking the separation at which the intensity profile between two point images loses its central dip. It sets a distinct threshold for judging when adjacent images merge.
Fluorescence microscopy: Imaging that detects light emitted by fluorescent molecules excited by illumination. Its resolution depends on wavelength and objective aperture, while fluorescence enables specialized super-resolution methods.
Optical transfer function: A system’s frequency-domain description of how it transfers contrast from an object to an image. Its cutoff spatial frequency expresses the image-detail limit imposed by diffraction.
Fourier optics: The analysis of optical propagation and imaging using spatial Fourier transforms. It explains how apertures select the spatial frequencies that form an image.

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