In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation.

The near field can be specified by the Fresnel number, F, of the optical arrangement. When ${\displaystyle F\ll 1}$ the diffracted wave is considered to be in the Fraunhofer field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written as

$${\displaystyle {\frac {F\theta ^{2}}{4}}\ll 1,}$$

where ${\displaystyle \theta }$ is the maximal angle described by ${\displaystyle \theta \approx a/L,}$ a and L the same as in the definition of the Fresnel number. Hence this condition can be approximated as ${\textstyle {\frac {a^{4}}{4L^{3}\lambda }}\ll 1}$.

The multiple Fresnel diffraction at closely spaced periodical ridges (ridged mirror) causes the specular reflection; this effect can be used for atomic mirrors.

Some of the earliest work on what would become known as Fresnel diffraction was carried out by Francesco Maria Grimaldi in Italy in the 17th century. In his monograph entitled "Light", Richard C. MacLaurin explains Fresnel diffraction by asking what happens when light propagates, and how that process is affected when a barrier with a slit or hole in it is interposed in the beam produced by a distant source of light. He uses the Principle of Huygens to investigate, in classical terms, what transpires. The wave front that proceeds from the slit and on to a detection screen some distance away very closely approximates a wave front originating across the area of the gap without regard to any minute interactions with the actual physical edge.

The result is that if the gap is very narrow only diffraction patterns with bright centers can occur. If the gap is made progressively wider, then diffraction patterns with dark centers will alternate with diffraction patterns with bright centers. As the gap becomes larger, the differentials between dark and light bands decrease until a diffraction effect can no longer be detected.

MacLaurin does not mention the possibility that the center of the series of diffraction rings produced when light is shone through a small hole may be black, but he does point to the inverse situation wherein the shadow produced by a small circular object can paradoxically have a bright center. (p. 219)