Single-pixel imaging via orthogonal mechanical modulators and mixed derivatives of measured intensity

Single-pixel imaging (SPI) provides possibilities for image reconstruction in scenarios where array detectors are still unavailable. Although compressed sensing (CS) provided ways to recover images with subsampling, video imaging rates of dozens to a few hundred frames per second have become possible only with recent developments. Versatility is also a concern, as systems may rely on digital micromirror devices (DMDs) or other hardware that cannot operate in different wavelengths, such as terahertz (THz). Mechanical masks are an alternative in this context, but they lack reconfigurability and require delicate fabrication to achieve a high pixel count. In this work, we generalize the derivative optical imaging technique (DOIT), a recent technique that composes images from derivatives of a modulated one-dimensional illumination beam, to a two-dimensional encoding process by introducing an orthogonal modulator and imposing an integer multiplicity relation between their frequencies. The two-dimensional remapped signal presents DOIT-like profiles in both axes, and the image is revealed with a combination of derivatives. We demonstrate the ability of this double DOIT (2DOIT) to decode videos in real-time, at frame rates (12-240 frames per second). The pixel throughput depends only on the data acquisition rate, allowing the system to match or overcome state-of-the-art techniques. The system is simple to assemble in active and passive illumination schemes, and is a low-cost option that may be compatible with many applications outside the visible spectrum.