Diffraction limit in the context of "Paraxial approximation"

When observing a star through a telescope, the atmosphere distorts the incoming light, making images blurry and causing stars to twinkle. The Fried parameter, or Fried's coherence length, is a quantity that measures the strength of this optical distortion. It is denoted by the symbol ${\displaystyle r_{0}}$ and has units of length, usually expressed in centimeters.

The Fried parameter can be thought of as the diameter of a "tube" of relatively calm air through the turbulent atmosphere. Within this area, the seeing is good. A telescope with an aperture diameter ${\displaystyle D}$ that is smaller than ${\displaystyle r_{0}}$ can achieve a resolution close to its theoretical best (the diffraction limit). However, for telescopes with apertures much larger than ${\displaystyle r_{0}}$—which includes all modern professional telescopes—the image resolution is limited by the atmosphere, not the telescope's size. The angular resolution of a large telescope without adaptive optics is limited to approximately ${\displaystyle \lambda /r_{0}}$, where ${\displaystyle \lambda }$ is the wavelength of the light observed. At good observatory sites, ${\displaystyle r_{0}}$ is typically 10–20 cm at visible wavelengths. Large ground-based telescopes use adaptive optics to compensate for atmospheric effects and reach the diffraction limit.