Sub-micron weak phase particle characterization using the reconstructed volume intensities from in-line digital holography microscopy

Abstract

Digital holography microscopy is a powerful technique for retrieving particle properties that are often challenging to obtain with other methods. However, analyzing holographic data using non-linear fitting algorithms and machine learning is difficult without prior information. In this paper, we present a novel technique for sizing and determining the refractive index of sub-micron, weak phase, spherical particles using the Rayleigh-Sommerfeld diffraction theory. Our method involves reconstructing the volume of synthetic holograms using the HoloPy software for particles of different sizes and material properties. We then fit a Gaussian function at the point of numerical re-focus, as given by the first local minima after the Gouy-phase shift, for size and sub-pixel position estimates. By retrieving the magnitude and location of the maximum scattered intensity, we build a scattered interpolant that relates all the parameters of interest. We demonstrate that our technique had a mean error in particle refractive index of 1.24 ± 1.74% with synthetic data and accurately estimates the size and refractive index of similar-sized nanoparticles in experiments. Compared to least-squares fitting, our method performs similarly with synthetic data but outperformed it with experimental data, showcasing its superior accuracy and reliability. Furthermore, we use our technique combined with function-fitting approaches. This hybrid method uses our proposed technique to approximate the initial conditions of non-linear fitting algorithms, leading to improved accuracy. Finally, we explore the potential of using the intensity cubes as well-defined thresholds to differentiate particles from interference caustics in a reconstructed volume. Overall, our results demonstrate the efficacy and accuracy of our technique for retrieving particle properties from holographic data, even when prior information was not available. This technique could have broad applications in the field of nanoparticle characterization.