## 3 Computer Optics for Controlling the Irradiance, and Wavefront Spatial Distributions
The height of the micro-relief peaks varies from the root of the peak to its top, from 0 to \(\lambda/(2\mathrm{cos}\theta)\) for the reflective plate and from 0 to \(\lambda/(n-1)\) for the transmitting plate, where \(\theta\) is the angle of incidence of the beam on the optical element and \(n\) is the refractive index of the transmitting plate material [121]. The reflective plate is either an entirely metal plate or a metal plate with a reflective coating applied over the micro-relief. The transmission plate is made from a material that is nearly transparent to the laser beam. Diffractive optical elements synthesised by computer optics techniques allow us to perform the focusing of a laser beam into a predefined focal curve. Considering the complexity of solving the inverse focusing problem, the phase function of a diffractive optical element is more efficiently defined for focusing into simple focal curves, such as a straight-line segment, a ring, a half ring, etc. The most practical value lies in focusing the beam into a straight-line segment [122]. In most cases, a focal line of an arbitrary shape can be approximated by a set of linear segments with sufficient accuracy for practical purposes. Dividing the aperture of an optical element into several regions (by the number of line segments), each focussing the beam into a line segment of a desired length and direction, makes it possible to focus the beam into a complex focal curve. Thus, the problem of focusing into a linear segment can be regarded as a basic task for the formation of a focal line, which is a necessary step in the synthesis of diffractive optical elements for complex focal areas [123]. The maximum aperture size of a diffractive optical element is limited by three factors: physical, mathematical, and technological. The physical limitation is when the geometric optics and Kirchhoff approximations cannot be applied for large optical element apertures or large optical powers and the phase function calculation has to be carried out using the electromagnetic approach. A mathematical limitation is the lack or high complexity of methods for solving forward and backward wave diffraction problems in the general formulation [124]. By applying an iterative approach to the solution of the inverse diffraction problem under sharp focusing conditions, it is possible to obtain a complex distribution at the entry of the focusing system, creating the desired intensity distribution in the focal area. The complex distribution of the transverse components of the initial field, similar to the Laguerre-Gaussian mode with radial polarisation and focused into a light spot that is half the diffraction limit, was obtained in [125]. However, the most severe limiting factor of the maximum aperture size of diffractive optical elements is the technology of their production. The problems of developing technologies that allow for the transfer of the calculated relief function to the physical medium are also solved by a computer-controlled, software-driven technological automatic machines [126; 127]. The characteristic dimensions of diffractive optical elements correspond to the order of the irradiation wavelength. Distinct from refractive optics, such optical elements for a specified and complex beam focusing may well already be created [128; 129; 130]. With the flexibility of computer-aided design and the micro-relief capabilities of modern precision technology, a unique optical tool for the desired wavefront control or for the defined shaping of laser beams has been obtained [131]. Computer optics open up new possibilities for creating optical elements that allow one to adjust the amplitude and phase distribution of the field in light beams. Optical circuits using correctors allow for the formation of a wavefront of a predefined shape. The functional purpose of diffractive optical elements is either to create a reference aspherical wavefront of arbitrary order from a planar or spherical one, or to convert one wavefront into another, referred to as compensation [132].