## 3 Computer Optics for Controlling the Irradiance, and Wavefront Spatial Distributions
Investigations revealed characteristic features of the thermochemical and vibrational effects of laser irradiation when the process proceeded differently compared to conventional heating under isothermal conditions at an appropriate temperature [138]. The oxidation of metals is a process consisting of a series of sequential stages. These include the transportation of oxygen molecules from the gas volume to the boundary between the phases; the adsorption of oxygen on the surface; the transfer of reagents through the growing oxide layer; and the chemical oxidation reaction itself [139]. In this case, the total reaction rate is limited by the slowest stage. In the course of the chemical reaction under the influence of laser irradiation, the thermal and \"chemical\" degrees of freedom of the system become bound to each other. This connection is conditioned, on the one hand, by the so-called Arrhenius (exponential) dependence of the reaction rate constant on temperature, and, on the other hand, by the change in the absorption characteristics of the system during the chemical reaction [140]. The growth of the oxide film causes a change in the absorption capacity and hence a change in the rate of temperature increase [141; 142]. The main task is to prevent the thermochemical instability, i.e., the emergence of a positive feedback in the system and an avalanche-like acceleration of the oxidation reaction after a certain characteristic time after the beginning of the irradiation, meaning the reaction activation time, which is defined as the moment when the reaction rate is at its maximum. In a commonly applied problem statement for a laser based thermochemical reaction, the temperature change in the irradiated area is described by a heat balance equation [143]. In order to calculate the heating of a metal in an oxidising atmosphere, a system of equations consisting of a thermal conductivity equation with a laser heat source; a heat transfer equation with the medium; an oxidation kinetics equation, and an equation for the change in absorptivity during oxidation is solved [144]. The monochromaticity of the laser irradiation permits the introduction of thermal energy into the system for one reaction component only if the wavelength is chosen appropriately. This selectivity of the thermal feedback leads to entirely differing types of dynamic behaviour of the system when the wavelength of the beam is shifted from one reaction component to another. Thus, if the irradiation is absorbed by the end product of the reaction and the direct reaction is accelerated by the heat, a positive feedback is created in the system. As the concentration of the product grows, the absorption increases, the temperature of the system rises, and self-acceleration of the reaction, or thermochemical instability, takes place [145]. This is the case for the growth of oxide films on metallic materials during heating by laser irradiation. If in the opposite case, for example, the reaction product absorbs less irradiation than the initial matter, a negative feedback is created in the system; thus, the chemical process slows down and self-stabilises. Therefore, the absorbed energy has the meaning of the transmission coefficient through the feedback channel. This offers the possibility of controlling the system behaviour by changing the energy or power of laser beam, and its density distribution [146]. Using a frequency-modulated laser beam in the frequency range from 3 Hz to 5 kHz, in [147; 148] it has been demonstrated that the synergy of the thermal related (heat associated) effects of laser pulses and of laser-induced vibrations mainly in the sound frequency range allows for the significant increase in the diffusion coefficient in materials. The condition for intensifying mass transfer in the solid phase of the heated in an oxidation-free environment or selectively oxidable metallic materials was identified as a non-stationary stress-strain state caused by laser-induced vibrations [48].