Methods for computing nanoparticle scattering for improved lens-free digital holographic imaging

The angular spectrum method (ASM) is commonly used for reconstructing images in digital holography for applications such as lens-free holography and metasurface design. The lack of Fraunhofer or Fresnel approximations and computational speed due to the fast Fourier transform makes ASM a competitive field propagation method. Using a thin-object approximation, ASM can also efficiently compute fields over large areas, enabling faster calculations than those using other methods such as finite difference time domain or Mie theory. However, thin-object approximations are not accurate for nanoscale objects and so ASM is currently unable to accurately recover nanoscale object information. Here we test three ASM transmission models that use a scalar description to model the interaction of a plane wave with a plane of randomly assembled nanoparticles and evaluate the accuracy of each against the discrete dipole method (DDA). Random distributions of nanoparticles are often used in super-resolution, sub-diffraction limit, or specialized sensing applications as they are easy to place. We study the performance of the three transmission models for gold and polystyrene nanospheres of 30 nm, 60 nm, and 100 nm in diameter for different particle densities. The performance of the models is evaluated against simulations using DDA, which is validated against Mie theory calculations, for the same configurations. We show transmission models in ASM that perform within 20% accuracy of the fields calculated using DDA.