# Diffractive Optical Element

Diffractive Optical Elements are a special type of optical element that is used to obtain complex radiance patterns from a simple laser beam. These elements started to emerge at approximately the same time that digital computers started to become widespread. The main cause behind it is that the relation between the output and input plane, that is, the plane of the diffractive optical element and the replay field, is the diffraction integral which for a piecewise, or pixelated element can be solved numerically with great accuracy. A diffractive optical element is said to be piecewise because it consists of many modulating sub-areas, also called pixels, that impart a local phase delay to the wavefront of the input beam. After some propagation, interference occurs among the disturbances caused by this local phase delay, resulting in a modified intensity distribution.

This type of group interference phenomena is called diffraction. It is only in some special and simple cases that the diffraction integral can be solved analytically. For an array of elements, as in the case at hand with the diffractive optical element, it can only be solved numerically. For that reason it was the advent of digital computers that paved the way for the design of these structures.

Thus, by using algorithms that rely on the solution of the diffraction integral, diffractive optical elements can then be designed to perform any desired complex transformation on an input beam. The algorithms themselves are indeed more complicated than just solving the diffraction integral as there are many constraints that need to be considered, such as pixel size, accuracy of phase delay and the number of phase levels.

There are many applications for diffractive optical elements. They can be used to obtain Top Hat or Flat Top beams from Gaussian single mode lasers. They can also be used to alter the focal spot irradiance distribution not only laterally but also longitudinally. This means that the diffractive optical element can be used to increase the depth of field of an optical system. A diffractive optical element can also be used also to generate arrays of dots that later can be used in structured illumination. This type of illumination is critical for LIDARs and three- dimensional reconstructions.

Diffractive optical elements are thin and lightweight. Many types are also completely insensitive to lateral misalignments so they can be inserted in any optical system with minimum impact on the overall volume of the system.