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.   Significance:  High-speed three-dimensional (3D) super-resolution microscopy is a unique tool to investigate various biological phenomena; yet the technology is not broadly adopted due to its high cost and complex system design.   Aim:  We present a compact, low-cost, and high-speed 3D structured illumination microscopy (SIM) based on a digital micromirror device and binary holography to visualize fast biological events with super-resolution.   Approach:  The 3D SIM uses a digital micromirror device to generate three laser foci with individually controllable positions, phases, and amplitudes via binary holography at the back aperture of objective lens to form optimal 3D structured patterns. Fifteen raw images are sequentially recorded and processed by the 3D SIM algorithm to reconstruct a super-resolved image.   Results:  Super-resolution 3D imaging at a speed of 26.7 frames per second is achieved with a lateral and axial resolution of 155 and 487 nm, which corresponds to a 1.65- and 1.63-times resolution enhancement, respectively, comparing with standard deconvolution microscopy.   Conclusions:  The 3D SIM realizes fast super-resolution imaging with optimal 3D structured illumination, which may find important applications in biophotonics.

Fast 3D super-resolution imaging using a digital micromirror device and binary holography