# Defocus aberration

In optics, defocus is the one aberration familiar to nearly everyone who has ever needed eyeglasses or used a camera, videocamera, microscope, telescope, or binoculars, as it simply means out of focus. Optically, defocus refers to a translation along the optical axis away from the plane or surface of best focus. In general, defocus reduces the sharpness and contrast of the image. What should be sharp, high-contrast edges in a scene become gradual transitions. Fine detail in the scene is blurred or even becomes invisible. Nearly all image-forming optical devices incorporate some form of focus adjustment to minimize defocus and maximize image quality.

The degree of image blurring for a given amount of focus shift depends inversely on the lens f-number. Low f-numbers, such as f/1.4 to f/2.8, are very sensitive to defocus and have very shallow depths of focus. High f-numbers, in the f/16 to f/32 range, are highly tolerant of defocus, and consequently have large depths of focus. The limiting case in f-number is the pinhole camera, operating at perhaps f/100 to f/1000, in which case all objects are in focus almost regardless of their distance from the pinhole aperture. The penalty for achieving this extreme depth of focus is very dim illumination at the imaging film or sensor, limited resolution due to diffraction, and very long exposure time, which introduces the potential for image degradation due to motion blur.

The amount of allowable defocus may be tied to the resolution of the imaging media. High-resolution black-and-white (B&W) films can resolve image details down to 3 micrometers or smaller, with usable contrast at 150 cycles/millimeter or higher. Modern digital imaging chips and color print films are not as sharp as high-resolution B&W films, but have resolution comparable to each other, and are slightly more tolerant of defocus. If an imaging chip has 10 micrometer pixels, one cycle is therefore two pixels, equal to 20 micrometers or 0.020 millimeters, and the spatial cutoff frequency (limit of resolution) is thus 50 cycles/millimeter at focus.

Defocus is modeled in Zernike polynomial format as ${\displaystyle a(2\rho ^{2}-1)}$, where ${\displaystyle a}$ is the defocus coefficient in wavelengths of light. This corresponds to the parabola-shaped optical path difference between two spherical wavefronts that are tangent at their vertices and have different radii of curvature.