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 that works with wide-field structured illumination and single-pixel detection. To identify the best 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 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 of the target object in the resulting single-pixel measurements. As such, the best focus position can be determined by surveying the maximum Fourier coefficient magnitude recovered from the single-pixel measurements. High-speed spatial light modulation enables the reported method to achieve rapid autofocusing even if the lens system is in continuous motion or the focal length of the lens is adjusted continuously. We experimentally validate the reported method in a self-built digital projector and demonstrate the application of the method in autofocusing Fourier single-pixel imaging. The method may find applications in various fields where sharp image projection is needed.