Ultrasound-modulated optical tomography (UOT) is an imaging technique that couples light and ultrasound in order to perform in-depth imaging of highly scattering media. In previous work, we introduced plane wave UOT, an imaging method analogous to x-ray tomography based on the filtered backprojection for image reconstruction. Angle-limited measurements, however, led to drastic loss of lateral spatial resolution. Here, we present a new structured ultrasonic plane wave UOT method that allows partial recovery of the resolution. For image reconstruction, we present a generalization of the Fourier slice theorem along with a generalized filtered backprojection formalism. The method is successfully tested on simulated and experimental data.