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Method proposed earlier for body reconstruction at its resonant frequencies is further developed. An attempt is made to establish the connection between the method applicability and existence of the Herglotz functions approximating the eigenoscillation field inside the body. Two propositions are given concerning convergence of the method for two cases when a Herglotz function coinciding with this field exists or not. Numerical results shoving the fast decreasing of the appropriate functional with increasing the number of measured patterns, are presented. Two ways of computer modeling of the input data are numerically compared.