Recording of a lensless quasi-Fourier hologram of an opaque screen is considered. The recordings are based on matching speckle fields of two exposures in the hologram plane. The operation of a shear interferometer in this case is analyzed with the use of coherent diffusely scattered fields for a higher than parabolic approximation. It is shown that the sensitivity range of the interferometer is limited because of aberrations of the reference wave, and aberrations in the object channel can lead to errors in control as well.