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 ) 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 dualwavelength 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 ) 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.

Calcite dissolution rate spectra measured by in situ digital holographic microscopy

“…Water was delivered to the cell through chemically inert polymer tubing using a valveless piston metering pump. Additional details of the flow-through cell have been discussed elsewhere (Brand, 2017; Feng et al, 2017). …”

In situ nanoscale observations of gypsum dissolution by digital holographic microscopy

“…It is equipped with three different primary source wavelengths (λ 1 =665.5651 nm, λ 2 = 793.2365 nm, λ 3 = 681.0068 nm); λ 1 was used exclusively in this study. Additional details on the microscope configuration can be found elsewhere (Brand et al, 2017; Brand, 2017). …”

“…With a known pixel size, a full 3D reconstruction of the surface can be generated, and with measurements over small time intervals, the 4D space-time history of the surface can be recorded. Additional details about the data collection and processing, as well as measurement variability, are described in detail elsewhere (Brand, 2017; Brand et al, 2017). …”

“…Shot noise, a type of electronic noise that occurs in electronics and in photon counting devices, as well as noise from other sources, is inherent in interferometric measurement methods such as DHM (Charrière et al, 2006a,b, 2007; Pandey and Hennelly, 2011; Léon- Rodríguez et al, 2012; Pan et al, 2013; Brand, 2017) and can significantly compromise image quality. To reduce noise, temporal averaging of the phase maps (Kühn et al, 2008; Charrière et al, 2007) was used.…”

Dissolution Kinetics of Cubic Tricalcium Aluminate Measured by Digital Holographic Microscopy

“…The DHM utilized in this study was a Lyncée Tec model R-2203 (Lausanne, Switzerland) . Additional instrument details are reported elsewhere, , but briefly, a monochromatic coherent light source (665.5651 nm wavelength) is split into two beams known as the reference and object beams. The object beam is sent through an objective lens to the specimen surface, reflects into the instrument, and is recombined with the reference beam.…”