Subpixel-shift cyclic-Hadamard microscopic imaging using a pseudo-inverse-matrix procedure

We propose two subpixel-shift (SPS) imaging methods: a normal SPS (NSPS) and an interleaved SPS (ISPS) method. Both methods use a series of cyclic-Hadamard-mask illuminations and a single channel detector that enhances lateral spatial resolution in proportion to the number of shifts. A sample object (or the illumination mask) is moved in two dimensions in micro-step intervals within the range of an illumination mask unit pixel (or within a range that exceeds it). To reconstruct the original image, we use a pseudo-inverse-matrix procedure that ensures measurement precision in a least-squares sense. Numerical simulation and experimental results obtained using a transmission microscope are shown. Further preliminary results indicate that the SPS method has the potential to enable measurements exceeding the diffraction limit of optics.