A method is presented for obtaining optical reconstructions from holograms recorded at wavelengths that are substantially longer than optical ones. The method makes use of a reference wave that is added digitally to the recorded wave front. The reference wave is constructed so that there is a minimum mean square deviation between the reconstructed wave from a given object point and an ideal wave from the same point at the reconstruction wavelength. The hologram scaling factor, the size of the reconstructed object and the position of the reconstructed object relative to the reconstructing hologram can be chosen in the optimization procedure. Thus it is possible to make several scaled down holograms from one recording to improve the depth resolution of the reconstruction. The main function of the optimized reference wave is to compensate for aberrations due to the discrepancy between the size of the original hologram measured in recording wavelengths and the size of the scaled down hologram measured in reconstruction wavelengths.