Laser beam scanning can be realized using two independently rotating, inline polarization gratings, termed Risley gratings, in a fashion similar to Risley prisms. The analytical formulas of pointing position as well as their inverse solutions are described. On this basis, the beam scanning is investigated and the performance of scanning imaging is evaluated. It is shown that the scanning function in 1D scanning evolves from a sinusoidal to triangular scan and the duty cycle increases rapidly as the ratio of grating period to wavelength is reduced toward 2. The scan pattern in 2D scanning is determined by the ratio k of the gratings' rotatory frequency. In imaging applications, when k tends toward 1 or -1, the scan pattern becomes dense and is inclined to be spiral or rose-like, respectively, which is desirable for the purpose of enhancing spatial resolution. There is a direct trade-off between spatial resolution and frame rate. The spiral and rose scanning enable multiresolution imaging, providing a preview of the scanned area in a fraction of the overall scan time, which is extremely useful for fast, real-time imaging applications.

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