This work is devoted to the development of an algorithm for calculating the Fourier coefficients of functions of three variables using tomograms received from a computer tomograph. The problem is reduced to the calculation of triple integrals over the regions belonging to the unit cube and the form of which is determined by the presence of indices present in the Fourier coefficients. There are sets of indices for which these formulas are of the same type. In particular, we consider the case when all indices are positive and growing, or all indices are negative, etc. In this work, control calculations of Fourier coefficients are performed for some classes of indices and various test functions. A comparison of the obtained results with the exact results was carried out.