Lens-free microscopes can utilize holographic reconstruction techniques to recover the image of an object from the digitally recorded superposition of an unperturbed plane wave and a wave scattered by the object. Image reconstruction most commonly relies on the scalar angular spectrum method (ASM). While fast, the scalar ASM can be inaccurate for nanoscale objects, either because of the scalar approximation, or more generally, because it only models field propagation and not light-matter interaction, including inter-particle coupling. Here we evaluate the accuracy of the scalar ASM when combined with three different light-matter interaction models for computing the far-field light scattered by random arrays of gold and polystyrene nanoparticles. Among the three models—a dipole-matched transmission model, an optical path length model, and a binary amplitude model—we find that which model is most accurate depends on the nanoparticle material and packing density. For polystyrene particles at any packing density, there is always at least one model with error below 20%, while for gold nanoparticles with 40% or 50% surface coverage, there are no models that can provide errors better than 30%. The ASM error is determined in comparison to a discrete dipole approximation model, which is more computationally efficient than other full-wave modeling techniques. The knowledge of when and how the ASM fails can serve as a first step toward improved resolution in lens-free reconstruction and can also be applied to other random nanoparticle array applications such as lens-based super-resolution imaging, sub-diffraction beam focusing, and biomolecular sensing.

Current commercial air-quality monitoring devices lack a large dynamic range, especially at the small, ultrafine size scale. Furthermore, there is a low density of air-quality monitoring stations, reducing the precision with which local particulate matter hazards can be tracked. Here, we show a low-cost, lensfree, and portable air-quality monitoring device (LPAQD) that can detect and measure micron-sized particles down to 100 nm-sized particles, with the capability to track and measure particles in real time throughout a day and the ability to accurately measure particulate matter densities as low as 3 μg m −3 . A vapor-condensed film is deposited onto the coverslip used to collect particles before the LPAQD is deployed at outdoor monitoring sites. The vaporcondensed film increases the scattering cross section of particles smaller than the pixel size, enabling the sub-pixel and sub-diffraction-limit-sized particles to be detected. The high dynamic range, low cost, and portability of this device can enable citizens to monitor their own air quality to hopefully impact user decisions that reduce the risk for particulate matter-related diseases.

The angular spectrum method is commonly used to reconstruct images in lens-free digital holography and to design metasurfaces. For nanostructured objects, we show the range of cases for which this approach provides accurate results.