In previous studies, a sound field separation technique based on the equivalent source method (ESM) was successfully applied to separate the incoming and outgoing fields composing a non-free field. However, if the incoming wave is scattered by the source surface, the outgoing field is not the field that would be generated by the source in a free field. The object of the present work was to provide an equivalent source technique that allows the recovery of that free field in a noisy environment. In this approach, the incoming and outgoing fields, including the scattered and directly radiated fields on the measurement surface, are separated to obtain the free-field pressure that would be radiated by the source in an anechoic environment. The recovered free-field pressure is then used to reconstruct the whole free field of the source by using near-field acoustical holography based on the ESM, which makes the results equivalent to those that could be obtained from a free-field measurement. A theoretical description of the technique is given first, and then three numerical cases are investigated to demonstrate the ability of the proposed method.