Phenomenological Description of the Electromagnetic Field and Coherent Images in Radio Engineering and Optical Systems

The basic principles of the scalar diffraction theory and the fundamental theorems of electromagnetic field calculation at any point in the volume from the field stated on the surface are analyzed. It follows from the analysis that the concretization of spatially-distributed boundary conditions for real earth surfaces considerably complicates the solution of diffraction problems. It is proposed to use the phenomenological description of electromagnetic fields in the domain of their registration. Examples of restoration of coherent images from the received fields in the Fresnel zone for remote sensing problems are give. The complex structure of the obtained coherent images requires their consideration not only in the form of Riemann integrals, but also as the Lebesgue, Stieltjes integrals, and the stochastic Ito integral.