Determination of the Mössbauer absorption cross section,σ(E), and accurate reconstruction of the hyperfine field distributions of the invar alloy,Fe64Ni36, by the maximum entropy method (MEM) is presented. The procedure consists of threesteps: deconvolution of the Mössbauer spectra with the instrumental resolutionfunction using MEM, nonlinear transformation of the deconvoluted spectrum intoσ(E), and reconstruction of the hyperfine field distribution. In order to test the procedure of thedeconvolution and correction for thickness effect, several simulated spectra with thickness parameter1 < t < 50 and different values of Lorentzian FWHM of the source and absorber wereanalyzed. It is shown that the procedure of the deconvolution and extraction ofσ(E) works well for spectra whose lines contain at least five experimental points per FWHM.Reconstructed distributions of hyperfine field parameters, based on the extracted Mössbauercross section of the Fe–Ni invar alloy, measured with and without application of an externalmagnetic field, are discussed. The reconstruction has been made to test the earlierpostulated non-collinear ferromagnetic state of invar without referring to any specific modelin the analysis of the Mössbauer results. It is shown that marginal probability distribution ofhyperfine magnetic field consists of the main maximum at about 28 T and a broad tailextending down to 5 T. Observed isomer shift of the main maximum is small andpositive. The isomer shift decreases with magnetic field and attains negative valuesat the lowest fields. It is shown that the magnetic texture parameter does notdepend on the hyperfine magnetic field. One thus concludes that in the invar Ni–Fealloys, in contrast to some theoretical predictions, there is no evidence for differentarrangements of the iron magnetic moments as a function of the magnetic hyperfine field.