Digital holography for the reconstruction of particles suspended in diamagnetic drops levitated in a magneto-gravitational trap

The magneto‑gravitational trap developed in this work enables the stable levitation of millimetric diamagnetic microdroplets, allowing non‑invasive analysis of the particles suspended within them. Levitation is achieved by combining the gravitational potential with the magnetic contribution generated by an anti‑Helmholtz coil pair, which together create a local minimum of the total potential. The optical system is designed to provide uniform illumination of the levitated droplet: a beam modulated by an SLM passes through a half‑wave plate, is split by a polarizing beam splitter, recombined with a pump beam, and expanded to illuminate the entire trapping region. A dichroic mirror directs the wavelength of interest toward the sample while simultaneously transmitting the scattered light to the CCD, and a second laser supplies the reference beam for digital holography. An ultrasonic horn, coupled to metallic electrodes, introduces the droplet into the levitation region and can generate a controlled acoustic flow to gently redistribute the internal particles before acquisition. The overall architecture integrates magnetic, acoustic, and optical manipulation of the droplet into a single system, enabling precise control over both the sample position and the internal fluid conditions. This synergy makes it possible to explore experimental configurations that would be unattainable with conventional approaches. Three‑dimensional reconstruction of the complex optical field is performed through Fresnel propagation in the paraxial regime, producing amplitude and phase maps at multiple propagation distances. To identify the plane in which the suspended particles appear most sharply resolved, a focus metric based on the discrete wavelet transform is employed. This measurement exhibits a clear maximum at the focal plane, providing robust and computationally efficient axial localization. This conceptual framework lays the foundation for a new methodology dedicated to the three‑dimensional characterization of particles and microstructures within levitated water droplets.