A diffraction-limited system refers to an optical system that is limited in resolution by the diffraction of light rather than by other factors such as optical aberrations or imperfections in the optical components. In such systems, the smallest details that can be resolved are determined by the wavelength of light being used and the numerical aperture of the optical system.
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A diffraction-limited system has an optical response close to the ideal diffraction response for its specified optical pupil, wavelength and optical focus. Improving the optical aberrations further makes little difference to that response. This describes the optics: a poorly sampled or noisy detector can still deliver an image with much worse usable diffraction-limited resolution.
The optical pupil determines which wave amplitudes and wave phases contribute to an image point. In a scalar, paraxial approximation at the focal plane of an optical lens in air, write the pupil transmission as , after removing the ideal focusing phase. The amplitude spread function is proportional to its scaled Fourier transform:Here are pupil coordinates, are image coordinates, is focal length, and is the wavelength in air. For a uniformly transmitting, unobscured circular optical pupil at ideal optical focus, the result is an Airy disk with surrounding rings. A blocked centre, support structures, or nonuniform transmission changes the ideal point spread function; “diffraction limited” does not specify one universal spot shape. The existing Fourier model of a Lyot coronagraph illustrates how pupil and focal masks deliberately alter this response.[ref]
Optical aberrations add pupil wave phase errors. Defocus contributes a quadratic pupil wave phase in the paraxial approximation, redistributing light intensity from the best-focused spot. The Strehl ratio compares the peak with the ideal response for the same pupil and total radiant flux. A broad optical spectrum produces a weighted sum of wavelength-dependent point spread functions; chromatic aberration can additionally change optical focus with wavelength. Thus the operating conditions belong with any claim that a system is diffraction limited.