Rotating vortex imaging implemented by a quantized spiral phase modulation

We demonstrate both theoretically and experimentally that a spiral mask with a finite number of discrete phase levels allows a defocusing induced rotation of the point spread function in the vortex imaging. Two experimental configurations based on a spiral phase modulation of light and a spiral filtering of the spatial spectrum are studied in a unified theoretical treatment. The rotating point spread functions are analyzed in detail for imaging realized by the vortex lens and the 4-f system used in the spiral phase contrast microscopy. The theoretical results are verified by experiments using a spatial light modulator. The method is applicable to a precise focusing and optical imaging allowing depth estimation from diffracted rotation. Apart from implementation simplicity, the main advantages of the method are high energy efficiency, a possibility to operate with either complex amplitude or spatial spectrum of light and variability allowing a simple control of number of lobes of the point spread function.