Image-free active autofocusing with dual modulation and its application to Fourier single-pixel imaging

Autofocusing is widely used in applications where sharp image acquisition or projection is needed. Here we report an active autofocusing method for sharp image projection. The method works with wide-field structured illumination and single-pixel detection. To find the focus position, the method illuminates the target object with a set of 3-step phase-shifting Fourier basis patterns repeatedly and collects the backscattered light by using a single-pixel detector through a grating. Dual modulation-dynamic modulation by the time-varying structured illumination and static modulation by the grating-embeds the depth information for the target object in the resulting single-pixel measurements. As such, the focus position can be determined by recovering the Fourier coefficients from the single-pixel measurements and searching for the coefficient with the maximum magnitude. High-speed spatial light modulation not only enables rapid autofocusing but also makes the method work even when the lens system is in continuous motion or the focal length of the lens is continuously adjusted. We experimentally validate the reported method in a self-built digital projector and demonstrate the application of the method in Fourier single-pixel imaging.