Holographic particle sizing techniques

Machine learning enables precise holographic characterization of colloidal materials in real time

Holographic particle characterization uses in-line holographic video microscopy to track and characterize individual colloidal particles dispersed in their native fluid media. Applications range from fundamental research in statistical physics to product development in biopharmaceuticals and medical diagnostic testing. The information encoded in a hologram can be extracted by fitting to a generative model based on the Lorenz-Mie theory of light scattering. Treating hologram analysis as a high-dimensional inverse problem has been exceptionally successful, with conventional optimization algorithms yielding nanometer precision for a typical particle's position and part-per-thousand precision for its size and index of refraction. Machine learning previously has been used to automate holographic particle characterization by detecting features of interest in multi-particle holograms and estimating the particles' positions and properties for subsequent refinement. This study presents an updated end-to-end neural-network solution called CATCH (Characterizing and Tracking Colloids Holographically) whose predictions are fast, precise, and accurate enough for many real-world high-throughput applications and can reliably bootstrap conventional optimization algorithms for the most demanding applications. The ability of CATCH to learn a representation of Lorenz-Mie theory that fits within a diminutive 200 kB hints at the possibility of developing a greatly simplified formulation of light scattering by small objects.

Photonic jet reconstruction for particle refractive index measurement by digital in-line holography

A new and computationally efficient approach is proposed for determining the refractive index of spherical and transparent particles, in addition to their size and 3D position, using digital in-line holography. The method is based on the localization of the maximum intensity position of the photonic jet with respect to the particle center retrieved from the back propagation of recorded holograms. Rigorous electromagnetic calculations and experimental results demonstrate that for liquid-liquid systems and droplets with a radius > 30µm, a refractive index measurement with a resolution inferior to 4 × 10^-3 is achievable, revealing a significant potential for the use of this method to investigate multiphase flows. The resolution for solid or liquid particles in gas is expected to be lower but sufficient for the recognition of particle material.

Mueller matrix holographic method for small particle characterization: theory and numerical studies

Holographic imaging has proved to be useful for spherical particle characterization, including the retrieval of particle size, refractive index, and 3D location. In this method, the interference pattern of the incident and scattered light fields is recorded by a camera and compared with the relevant Lorenz-Mie solutions. However, the method is limited to spherical particles, and the complete polarized scattering components have not been studied. This work extends the Mueller matrix formalism for the scattered light to describe the interference light field, and proposes a Mueller matrix holography method, through which complete polarization information can be obtained. The mathematical formalism of the holographic Mueller matrix is derived, and numerical examples of birefringent spheres are provided. The Mueller matrix holography method may provide a better opportunity than conventional methods to study anisotropic particles.

Robustness of Lorenz-Mie microscopy against defects in illumination

Lorenz-Mie analysis of colloidal spheres' holograms has been reported to achieve remarkable resolution not only for the spheres' three-dimensional positions, but also for their sizes and refractive indexes. Here we apply numerical modeling to establish limits on the instrumental resolution for tracking and characterizing individual colloidal spheres with Lorenz-Mie microscopy.

Ice crystal habits from cloud chamber studies obtained by in-line holographic microscopy related to depolarization measurements

We investigate hydrometeor habits at the AIDA chamber with a newly developed in-line holographic microscope HOLographic Imager for Microscopic Objects (HOLIMO). Sizes and habits of ice crystals and droplets in a mixed-phase cloud experiment are related to relative humidity with respect to ice (RH(ice)), temperature (T), and experiment time. This experiment is initiated with supercooled water drops. As a result, ice crystals within a maximum particle diameter size range of 2 to 118 microm (average size of 19 microm) are detected and 63% of them reveal regular habits. The observed particle habits match those predicted for a given RH(ice) and T. Two different growth modes emerge from this cloud. The first one appears during water injection and reveals mainly optical particle sizes in the range of 5 to 250 microm. The second mode grows to sizes of 5 to 63 microm, just after the particles of the first one fall out. It is found that an increasing aspect ratio chi of maximum length over thickness from 2 to 20 as obtained by HOLIMO corresponds to a decreasing linear depolarization ratio from 0.1 to 0.04, as independently obtained by depolarization measurements.

Characterizing and tracking single colloidal particles with video holographic microscopy

We use digital holographic microscopy and Mie scattering theory to simultaneously characterize and track individual colloidal particles. Each holographic snapshot provides enough information to measure a colloidal sphere's radius and refractive index to within 1%, and simultaneously to measure its three-dimensional position with nanometer in-plane precision and 10 nanometer axial resolution.

Four-dimensional dynamic flow measurement by holographic particle image velocimetry

The ultimate goal of holographic particle image velocimetry (HPIV) is to provide space- and time-resolved measurement of complex flows. Recent new understanding of holographic imaging of small particles, pertaining to intrinsic aberration and noise in particular, has enabled us to elucidate fundamental issues in HPIV and implement a new HPIV system. This system is based on our previously reported off-axis HPIV setup, but the design is optimized by incorporating our new insights of holographic particle imaging characteristics. Furthermore, the new system benefits from advanced data processing algorithms and distributed parallel computing technology. Because of its robustness and efficiency, for the first time to our knowledge, the goal of both temporally and spatially resolved flow measurements becomes tangible. We demonstrate its temporal measurement capability by a series of phase-locked dynamic measurements of instantaneous three-dimensional, three-component velocity fields in a highly three-dimensional vortical flow-the flow past a tab.

Airborne digital holographic system for cloud particle measurements

An in-line holographic system for in situ detection of atmospheric cloud particles [Holographic Detector for Clouds (HOLODEC)] has been developed and flown on the National Center for Atmospheric Research C-130 research aircraft. Clear holograms are obtained in daylight conditions at typical aircraft speeds of 100 m s(-1). The instrument is fully digital and is interfaced to a control and data-acquisition system in the aircraft via optical fiber. It is operable at temperatures of less than -30 degrees C and at typical cloud humidities. Preliminary data from the experiment show its utility for studies of the three-dimensional spatial distribution of cloud particles and ice crystal shapes.

Intrinsic speckle noise in off-axis particle holography

In holographic imaging of particle fields, the interference among coherent wave fronts associated with particle scattering gives rise to intrinsic speckle noise, which sets a fundamental limit on the amount of information that particle holography can deliver. It has been established that the intrinsic speckle noise is especially severe in in-line holography because of superposition of virtual image waves, the direct transmitted wave, and the real image. However, at sufficiently high particle number densities, such as those typical in holographic particle image velocimetry (HPIV) applications, intrinsic speckle noise also arises in off-axis particle holography from self-interference among wave fronts that form the real image of particles. To overcome the latter problem we have constructed a mathematical model that relates the first- and second-order statistical properties of the intrinsic speckle noise to relevant holographic system parameters. Consistent with our experimental data, the model provides a direct estimate of the information capacity of particle holography. We show that the noise-limited information capacity can be expressed as the product of particle number density and the extent of the particle field along the optical axis. A large angular aperture of the hologram contributes directly to achievement of high information capacity. We also show that filtering in either digital or optical form is generally ineffective in removing the intrinsic speckle noise from the particle image as a result of the similar spectral properties of the two. These findings emphasize the importance of angular aperture in designing holographic particle imaging systems.

Intrinsic aberrations due to Mie scattering in particle holography

Holography of small particles is a newly revived topic because of its importance in holographic particle image velocimetry (HPIV). However, the property of particle images formed through holography remains largely unexplored. This fact undermines the measurement reliability of HPIV techniques and has become one of the obstacles in the full deployment of HPIV. We study the intrinsic aberrations in the holographic particle image introduced by particle light scattering and investigate how accurately holography can deliver information about the particles that are being imaged. Consistent with our experimental observations, simulations based on Mie scattering theory show that even with a perfect hologram the reconstructed particle images demonstrate complex three-dimensional morphologies and bodily shifts. These characteristics, manifested as image aberrations, result from uneven scattering amplitude and phase distributions across the finite aperture of the hologram. Such aberrations degrade the signal-to-noise ratio in the reconstructed image as well as introducing systematic errors in detected particle image positions. We examine the effect of these aberrations on HPIV measurements.

Holographic imaging of semitransparent droplets or particles

The formation of images of semitransparent spherical particles illuminated with coherent light is described from a diffraction theory viewpoint. Such images are distinctly different from those of opaque particles. The primary optical phenomena involved are illustrated by experimental results, and practical implications for holographic imaging of sprays are noted.

Determination of size and position of fast moving gas bubbles in liquids by digital 3-D image processing of hologram reconstructions

An experimental setup for digital 3-D image processing from hologram reconstructions is described. The real image as obtained upon reconstruction of the hologram with its conjugated reference wave is scanned by a movable image dissector camera without imaging optics and serves as analog 3-D picture input storage to the computer. This scheme has been developed to analyze automatically fast moving bubble fields in liquids recorded by high speed holographic techniques. A computer code has been written combining standard methods like gradient filtering from the field of image processing with specially developed algorithms for speckle noise suppression to locate and count the bubbles in the image volume and to determine their morphological data.

Absorption and phase in-line holograms: a comparison

Improved methods of processing in-line holograms are presented for both phase and absorption modes, and the physical characteristics of the subsequent reconstructed images are compared. This comparison leads to the conclusion that the phase hologram may have advantages which have been hitherto unrecognized.

Holographic particle velocity measurement in the Fraunhofer plane

Double exposure holograms of a moving particle field having a 1-D velocity distribution are produced. The Fraunhofer plane is observed on reconstruction, and it is shown that for a Gaussian velocity distribution, the fringes which modulate the diffraction pattern have spacings characteristic of the peak velocity. Known and measured peak velocities are compared, and the effect of the velocity distribution width on the fringe contrast is demonstrated.