Smoothing and differentiating experimentally measured magnetic field distribution in the gap of cyclotron electromagnet

We describe an algorithm for smoothing and differentiating an experimentally measured magnetic field distribution defined in a cylindrical coordinate system and set in the form of a table. Formulas for the local smoothing and differentiation of magnetic induction over arrays of various dimensions (3 × 3 × 3, 5 × 5 × 5, etc.) are presented. The obtained magnetic field components obey the Maxwell equations. Principles of the optimum choice of the smoothing step are considered and estimations of the accuracy and reliability of the computational process are given.