Inline mechano-vibration holography for simultaneous phase and elasticity mapping of soft samples

Off-axis holography enables single-shot phase retrieval but reduces spatial bandwidth, while in-line phase-shifting interferometry preserves bandwidth yet requires reference-path stepping and is sensitive to drift, limiting dynamic measurements. Moreover, viscoelastic mapping is rarely available from the same holographic measurement. We propose vibration-encoded in-line Mach-Zehnder holography for simultaneous thickness and viscoelasticity mapping of soft samples. Twelve holograms acquired over one vibration cycle are analyzed using Bessel-based harmonic inversion and robust regression to recover the static phase, modulation depth, and phase lag, yielding thickness and Kelvin-Voigt storage and loss modulus maps (E', E″). Simulations recover E' and E'' to within ∼2% across a wide E''/E' range and achieve sub-micron thickness error over 20-45 μm beads. Experiments on calibrated polyacrylamide beads show sub-micron thickness repeatability (median ∼0.57 μm over 40 repeats) and stiffness estimates typically within 10% of ground truth, and we further demonstrate the approach on adherent MCF-7 cells.