A modification of the synthetic-cylindrical-wave-based holographic technique for determining radiation patterns and aperture fields of antennas is proposed. The modification is based on using both the sum and difference of the near field and reference signals to form the hologram via simple low-cost amplitude-only near field measurements. This approach when compared to the previous version, where only the sum signal is used, allows increased sample spacing, and also provides an improvement in quality of the final results. That is validated by several numerical simulations. Moreover, it allows cylindrical near-field antenna measurements and probe corrections.