## 3 Computer Optics for Controlling the Irradiance, and Wavefront Spatial Distributions
In optical reference schemes the wavefront from the aspherical mirror or lens under study is analysed, while the compensator forms a reference wavefront for interferometric examination of the manufactured optical surface. This analysis is carried out by comparing the examined wavefront with the reference one according to the interferometric method. The shadowing method analyses the wavefront reflected or transmitted from the inspected element and transformed by the diffractive optical compensator. The Foucault knife-edge method is easier to implement but has a low signal-to-noise ratio as the zero spatial frequency, which is the most energetic frequency, is not being used for the analysis [133]. Ref. [134] aims to develop the methods of the laser-matter interaction with the application of freeform diffractive optics, capable of redistributing the laser beam intensity. Based on the use of methods for solving the inverse problem of heat conduction, an algorithm for the calculation of the power density distribution of the laser beam was developed in order to create a desired thermal effect on materials. An improvement in the parameters of the temperature field in the chrome-nickel-molybdenum steel during laser heat treatment was demonstrated. It was shown that the redistribution of the specific power in a moving heat source influences the temperature distribution in the processed area. Equality of maximum temperatures in the centre and at the periphery of the heat-affected zone is achieved [134]. In addition to achieving more uniform temperature conditions across the width of the heat-affected zone, the proposed approach allows us to increase the width of the targeted isotherms of the temperature field. Thus, with the same laser power, larger areas can be processed per unit of time, or the number of passes can be reduced. An example of the results of the calculation of the maximum temperature values before and after specific power adjustment is shown in Figure 7. A new approach for structures formation to improve the properties of materials by laser irradiation having a predetermined distribution of energy density has been applied. This is achieved by developing models of the process and modelling the effects of laser irradiation; designing special optical systems for appropriate beam shaping; investigating the structures and properties of materials subjected to laser irradiation [135; 136]. In addition to achieving a more uniform temperature regime across the width of the heat-affected zone, the introduced approach allows one to increase the width of the target temperature field isotherms. The energy parameters of the laser beam, including the spatial distribution of the energy density in the focusing area, are essential for creating a material heating zone with the required physical properties. An improvement of the beam shaping systems with freeform optics ensures flexible control and desired redistribution of the laser beam density. The important distinguishing aspect is the application of diffractive freeform optics for beam shaping to increase the precision of energy transfer to material surfaces, including those of a complex shape [137]. Laser Thermochemical Processes of the Formation of Quasi-One-Dimensional Nanostructured Metal Oxides  
Laser irradiation provides versatile opportunities for initiating chemical reactions through thermal exposure; through resonance excitation of energy levels of atoms and molecules;  
Figure 7: Maximum temperature values \(max[T(x,y,z)]_{y}\) across the width of the heat-affected zone of a rectangle-shaped heat source, obtained by calculation considering the power 950 W, a constant linear velocity \(v=1.1\times 10^{-2}\) m/s on the surface of chrome–nickel–molybdenum steel before (**a**) and after adjustment of power density (**b**). Temperature \(T\): (isothermal: 1–600 K; 2–750 K; 3–900 K; 4–1050 K; 5–1200 K) [134]. through excitation or breaking of molecular bonds attenuated by resonant electromagnetic excitation.