Single-image structured illumination using Hilbert transform demodulation

Structured illumination microscopy (SIM) achieves sectioning at depth by removing undesired light from out-of-focus planes within a specimen. However, it generally requires at least three modulated images with discrete phase shifts of 0, 120, and 240 deg to produce sectioning. Using a Hilbert transform demodulation, it is possible to produce both sectioning and depth information relative to a reference plane (i.e., a coverslip) using only a single image. The specimen is modulated at a known frequency, and the unmodulated portion of the image is estimated. These two components are used to provide a high-quality sectioned image containing both axial and lateral information of an object. The sectioning resolution with a single image is on par with that of a control three-image SIM. We are also able to show that when used with three images of discrete phase, this method produces better contrast within a turbid media than the traditional SIM technique. Because the traditional SIM requires alignment of three different phases, small differences in optical path length can introduce strong artifacts. Using the single-image technique removes this dependency, greatly improving sectioning in turbid media. Multiple targets with various depths and opaqueness are considered, including human skin in vivo, demonstrating a quick and useful way to provide noninvasive sectioning in real time.