We explore the convergence of the dual-space microscopy (DSM) phase-recovery algorithm. DSM is an optical microscopy technique based on simultaneous observation of an object in the position and momentum spaces. We present one-dimensional (1D) simulations of this technique, demonstrating that the DSM technique is capable to resolve periodic and nonperiodic structures with a resolution well below the Rayleigh resolution limit. Using a simple and faster 1D version of the full 2D DSM algorithm, we simulated the DSM technique for thousands of different samples. Our results demonstrate that the DSM algorithm always converges rapidly to the correct optical disturbance.