The distribution of measurement points is important in reconstructing the vibro-acoustic source field using the near-field acoustical holography (NAH) based on the equivalent source method (ESM). Because too close measurement impose a limit in the implementation of ESM, an optimal arrangement of the hologram data is needed to enable a longer distance measurement although the points are still within the near field. In this work, the optimal measurement positions are determined by adopting the method that assures the independence among the measuring positions as far as possible. Singular value decomposition of the transfer matrix is employed in the loop-iteration calculation fashion, in which the candidate measuring point affecting the increase of singularity is eliminated at each iteration step. Comparison is made with the uniformly distributed hologram points, the monopole version of ESM model, and the patch holography method. The test results reveal that the acoustic field of sound sources can be reconstructed meaningfully from the optimized hologram points of underdetermined condition. Under the predetermined reconstruction accuracy, the test results varying the hologram distance show that it is possible to realize the underdetermined far-distance measurement than the usual NAH.