Microscopy is important for studying biological systems, natural materials, and human-made devices. Optical microscopes that use visible light are traditionally incapable of resolving objects smaller than one-half the wavelength of the light, which is a size scale generally smaller than bacteria, but larger than viruses. Research into superresolution microscopy enables visualization of even smaller objects, which can be used to identify viruses in medical testing, learn how the inner biological mechanisms of cells operate, quantify nanoscale pollutants in air and water, or characterize synthesized nanomaterials to ensure that they are being manufactured as desired. A specific type of optical microscopy, lensfree microscopy, relies on computational algorithms to reconstruct microscopic images from shadow patterns recorded on a camera sensor. It is more compact and cost-effective than traditional microscopes and offers a larger field of view. The objective of this project is to achieve superresolution with lensfree microscopes to visualize ultra-small objects while maintaining the aforementioned advantages of lensfree microscopy. In addition to graduate students, undergraduates and high schoolers are involved in the project, and a new teaching module is being created. The resolution limit in lensfree microscopy depends on a variety of factors, including signal-to-noise ratio, coherence, and diffraction. Coherent lensfree microscopy has previously achieved diffraction-limited resolution, while incoherent lensfree microscopy (e.g., fluorescence imaging) has previously demonstrated resolution that is several times worse than the diffraction limit. In this project, superresolution lensfree microscopy is being achieved by positioning a nanostructured mask within the evanescent field of an unknown object. This mask can encode high resolution information (in a way that is later decodable) about the object that would normally be lost due to diffraction. By systematically sweeping geometric parameters of the mask, the research team is generating knowledge of what range of resolution boost is possible. The impact of noise is being quantified. The speed and resolution performance of different reconstruction algorithms are being compared. Optical methods of superresolved mask geometry estimation are being tested. This knowledge can inform theoretical models that will then be used to guide parameter choices for future improvements that can enable better resolution with compact and portable equipment and fast computational reconstruction times. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.