Phase Uncertainty in Digital Holographic Microscopy Measurements in the Presence of Solution Flow Conditions

Abstract

Digital holographic microscopy (DHM) is a surface topography measurement technique with reported sub-nanometer vertical resolution. Although it has been made commercially available recently, few studies have evaluated the uncertainty or noise in the phase measurement by the DHM. As current research is using the DHM to monitor surface topography changes of dissolving materials under flowing water conditions, it is necessary to evaluate the effect of water and flow rate on the uncertainty in the measurement. Uncertainty in this study was concerned with the temporal standard deviation per pixel of the reconstructed phase. Considering the effects of solution flow rate, magnification, objective lens type (air or immersion), and experimental configuration, measurements under static conditions in air and in water with an immersion lens yielded the smallest amount of uncertainty (mean of ≤ 0.5 nm up to 40× magnification). Increasing the water flow rate resulted in an increase in mean uncertainty to ≤ 0.6 nm up to 40× with an immersion lens. Observations of a sample through a glass window at 20× magnification in flowing water also yielded increasing uncertainty, with mean values of ≤ 0.5 nm, ≤ 0.8 nm, and ≤ 1.1 nm for flow rates of 0 mL min−1, 15 mL min−1, and 33 mL min−1. Different hologram acquisition rates (12.5 s−1 and 25 s−1) did not significantly impact the uncertainty in the phase. Collecting holograms in single-wavelength versus dual-wavelength modes did impact the uncertainty, with the mean uncertainty at 10× magnification for the same wavelength being ≤ 0.5 nm from the single-wavelength mode compared to ≤ 1.5 nm from the dual-wavelength mode. When the quantified uncertainty was applied to simulated dissolution data, lower limits of measured dissolution rates were found below which the measured data may not be distinguishable from the uncertainty in the measurement. The limiting surface-normal dissolution velocity is −10−11.7 m s−1 for experiments with an immersion lens in flowing water conditions and −10−11.7 m s−1, −10−11.4 m s−1, and −10−11.0 m s−1 for static (0 mL min−1), slow (≤ 15 mL min−1), and fast (≤ 109 mL min−1) flowing water conditions in experiments with a glass window, respectively. The data presented by this study will allow for better experimental design and methodology for future dissolution or precipitation studies using DHM and will provide confidence in the data produced in postprocessing.