Not to be confused with flat-field correction

Flat-field correction

thumb|210px|The brightness variation due to [[vignetting]], as shown here, can be corrected by selectively brightening the perimeter of the image.Flat-field correction is a technique used to improve quality in digital imaging...

, which refers to brightness uniformity.

Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis (or a non-flat object past the hyperfocal distance

Hyperfocal distance

In optics and photography, hyperfocal distance is a distance beyond which all objects can be brought into an "acceptable" focus. There are two commonly used definitions of hyperfocal distance, leading to values that differ only slightly:...

) cannot be brought into focus on a flat image plane.

Consider an "ideal" single-element lens system for which all planar wave fronts are focused to a point a distance f from the lens. Placing this lens the distance f from a flat image sensor, image points near the optical axis will be in perfect focus, but rays off axis will come into focus before the image sensor, dropping off by the cosine of the angle they make with the optical axis. This is less of a problem when the imaging surface is spherical, as in the human eye

Human eye

The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

.

Most current photographic lens

Photographic lens

A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.While in principle a simple convex lens will suffice, in...

es are designed to minimize field curvature, and so effectively have a focal length that increases with ray angle. However, film cameras could bend their image planes

Film plane

A film plane is the area inside any image taking device with a lens and a digital sensor or film; such as a camera. The film plane varies in distance from the lens focal point in each manufacturer...

 to compensate, particularly when the lens was fixed and known. This also included plate film

Photographic plate

Photographic plates preceded photographic film as a means of photography. A light-sensitive emulsion of silver salts was applied to a glass plate. This form of photographic material largely faded from the consumer market in the early years of the 20th century, as more convenient and less fragile...

, which could still be bent slightly. Digital sensors

Silicon photonics

Silicon photonics is the study and application of photonic systems which use silicon as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the infrared, most commonly at the 1.55 micrometre wavelength used by most...

generally cannot be bent, though large mosaics of sensors (necessary anyway due to limited chip sizes) can be shaped to simulate a bend over larger scales.
The Petzval field curvature is equal to the Petzval sum over an optical system,
where is the radius of the ith surface and the ns are the indices of refraction on the first and second side of the surface.