Diffraction-limited system

Other factors may affect an optical system's performance, such as lens imperfections or aberrations, but these are caused by errors in the manufacture or calculation of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.

At small apertures, such as f/22, most modern lenses are limited only by diffraction and not by aberrations or other imperfections in the construction.

In astronomy, a diffraction-limited observation is one that achieves the resolution of a theoretically ideal objective in the size of instrument used.

Optical telescopes on the Earth work at a much lower resolution than the diffraction limit because of the distortion introduced by the passage of light through several kilometres of turbulent atmosphere.

Radio telescopes are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible.

is called the numerical aperture (NA) and can reach about 1.4–1.6 in modern optics, hence the Abbe limit is

The combined effect of the different parts of an optical system is determined by the convolution of the point spread functions (PSF).

The point spread function of a diffraction limited circular-aperture lens is simply the Airy disk.

There are techniques for producing images that appear to have higher resolution than allowed by simple use of diffraction-limited optics.

[8] Although these techniques improve some aspect of resolution, they generally come at an enormous increase in cost and complexity.

Simultaneously illuminating from all angles (fully open condenser) drives down interferometric contrast.

Unlike methods relying on localization, such systems are still limited by the diffraction limit of the illumination (condenser) and collection optics (objective), although in practice they can provide substantial resolution improvements compared to conventional methods.

Various near-field techniques that operate less than ≈1 wavelength of light away from the image plane can obtain substantially higher resolution.

These techniques exploit the fact that the evanescent field contains information beyond the diffraction limit which can be used to construct very high resolution images, in principle beating the diffraction limit by a factor proportional to how well a specific imaging system can detect the near-field signal.

The data recorded by such instruments often requires substantial processing, essentially solving an optical inverse problem for each image.

In total internal reflection fluorescence microscopy a thin portion of the sample located immediately on the cover glass is excited with an evanescent field, and recorded with a conventional diffraction-limited objective, improving the axial resolution.

This includes nearly all biological applications in which cells span multiple wavelengths but contain structure down to molecular scales.

In recent years several techniques have shown that sub-diffraction limited imaging is possible over macroscopic distances.

These techniques usually exploit optical nonlinearity in a material's reflected light to generate resolution beyond the diffraction limit.

The nonlinear response to illumination caused by the quenching process in which adding more light causes the image to become less bright generates sub-diffraction limited information about the location of dye molecules, allowing resolution far beyond the diffraction limit provided high illumination intensities are used.

This non-uniformity in light distribution leads to a coefficient slightly different from the 1.22 value familiar in imaging.

As opposed to light waves (i.e., photons), massive particles have a different relationship between their quantum mechanical wavelength and their energy.

This relationship indicates that the effective "de Broglie" wavelength is inversely proportional to the momentum of the particle.

Other massive particles such as helium, neon, and gallium ions have been used to produce images at resolutions beyond what can be attained with visible light.

Such instruments provide nanometer scale imaging, analysis and fabrication capabilities at the expense of system complexity.

Memorial in Jena, Germany to Ernst Karl Abbe , who approximated the diffraction limit of a microscope as , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture ).
Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.