= Diffraction-limited 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 $T(u,v)e^{i\phi(u,v)}$, after removing the ideal focusing phase. The <amplitude spread function> is proportional to its scaled <Fourier transform>:
$$
h(x,y)\propto\iint T(u,v)e^{i\phi(u,v)}\exp\left[-\frac{2\pi i}{\lambda f}(ux+vy)\right]\,du\,dv.
$$
Here $(u,v)$ are pupil coordinates, $(x,y)$ are image coordinates, $f$ is <focal length>, and $\lambda$ 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.<MIT 2.71 and 2.710 Optics, Spring 2014 by Nicholas X. Fang/Review for Optics>[pp. 6–8, §§D(c), E: lens Fourier transform and pupil transfer function]{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.
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