Abstract
Abstract Physical and mathematical model of the control system parameters of the optical signal using the sensor of the external action on the basis of a diffraction grating with variable characteristics (the lattice period; the width of the transparent strip (zone); width of the absorbing strip (zone)) are developing. A mathematical model of the diffraction grating is constructed on the basis of equations to calculate the resulting intensity and amplitude of the interference light passing through the grating. For the model of a lattice with a round hole, equations containing special functions of the Bessel function type, calculated numerically by calculating convergent infinite power series and integrals which are not calculated analytically, are proposed. The degree of accuracy of the developed model is determined by the severity of the underlying fundamental equations of theoretical and mathematical physics.