The method of approximate calculation of the Kirchhoff’s integral

The article proposes a method of approximate calculation of the wave field gradient by its distribution on the only one closed surface. This allows calculating the Kirchhoff's integral without additional calculations or measurements of the electromagnetic field and opens up the opportunity to use it in practice along with the field equivalence principle. The comparison of the Kirchhoff's integral calculation accuracy with its vector forms showed that the proposed approximation for the wave field derivative leads to additional methodological errors, which are equivalent to the stray signal at the level less then −40 dB. At the same time, the use of Kirchhoff's integral instead of a widespread field equivalence principle in the electromagnetic field transformation algorithms reduces their computing complexity to 20 times.