We present a computational method to increase the effective NA of a holographic microscopy system operating in air. Our optical system employs a reflection Mach-Zender architecture and computational reconstruction of the full complex (phase and amplitude) wavefront. Based on fundamental diffraction principles, different angles of incident illumination result in different diffracted orders of the object wave being imaged. We record, store, and computationally recombine these object waves to expand the spatial frequency response. Experimental results demonstrate an improvement in the effective NA of our system from 0.59 to 0.78.