Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads.

We present a new method to achieve autofocus in digital holographic microscopy. The method is based on inserting calibrated objects into a sample placed on a slide. Reconstructing a hologram using the inverse problems approach makes it possible to precisely locate and measure the inserted objects and thereby derive the slide plane location. Numerical focusing can then be performed in a plane at any chosen distance from the slide plane of the sample in a reproducible manner and independently of the diversity of the objects in the sample.

Reconstruction of in-line holograms: combining model-based and regularized inversion.

In-line digital holography is a simple yet powerful tool to image absorbing and/or phase objects. Nevertheless, the loss of the phase of the complex wavefront on the sensor can be critical in the reconstruction process. The simplicity of the setup must thus be counterbalanced by dedicated reconstruction algorithms, such as inverse approaches, in order to retrieve the object from its hologram. In the case of simple objects for which the diffraction pattern produced in the hologram plane can be modeled using few parameters, a model fitting algorithm is very effective. However, such an approach fails to reconstruct objects with more complex shapes, and an image reconstruction technique is then needed. The improved flexibility of these methods comes at the cost of a possible loss of reconstruction accuracy. In this work, we combine the two approaches (model fitting and regularized reconstruction) to benefit from their respective advantages. The sample to be reconstructed is modeled as the sum of simple parameterized objects and a complex-valued pixelated transmittance plane. These two components jointly scatter the incident illumination, and the resulting interferences contribute to the intensity on the sensor. The proposed hologram reconstruction algorithm is based on alternating a model fitting step and a regularized inversion step. We apply this algorithm in the context of fluid mechanics, where holograms of evaporating droplets are analyzed. In these holograms, the high contrast fringes produced by each droplet tend to mask the diffraction pattern produced by the surrounding vapor wake. With our method, the droplet and the vapor wake can be jointly reconstructed.

Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology.

Reconstruction of phase objects is a central problem in digital holography, whose various applications include microscopy, biomedical imaging, and fluid mechanics. Starting from a single in-line hologram, there is no direct way to recover the phase of the diffracted wave in the hologram plane. The reconstruction of absorbing and phase objects therefore requires the inversion of the non-linear hologram formation model. We propose a regularized reconstruction method that includes several physically-grounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation on reconstructions of accurate simulations of in-line holograms based on the Mie theory. As our approach is adaptable to several in-line digital holography configurations, we present and discuss the promising results of reconstructions from experimental in-line holograms obtained in two different applications: the tracking of an evaporating droplet (size ∼ 100µm) and the microscopic imaging of bacteria (size ∼ 1µm).

In-line particle holography with an astigmatic beam: setup self-calibration using an "inverse problems" approach.

The use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g., cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography setup, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices, is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental setup adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies.

Accurate 3D tracking and size measurement of evaporating droplets using in-line digital holography and "inverse problems" reconstruction approach.

Digital in-line holography was used to study a fast dynamic 3D phenomenon: the evaporation of free-falling diethyl ether droplets. We describe an unsupervised reconstruction algorithm based on an "inverse problems" approach previously developed by our team to accurately reconstruct 3D trajectories and to estimate the droplets' size in a field of view of 7 × 11 × 20 mm 3. A first experiment with non-evaporating droplets established that the radius estimates were accurate to better than 0.1 µm . With evaporating droplets, the vapor around the droplet distorts the diffraction patterns in the holograms. We showed that areas with the strongest distortions can be discarded using an exclusion mask. We achieved radius estimates better than 0.5 µm accuracy for evaporating droplets. Our estimates of the evaporation rate fell within the range predicted by theoretical models.

Evaporating droplet hologram simulation for digital in-line holography setup with divergent beam.

Generalized Lorenz-Mie theory (GLMT) for a multilayered sphere is used to simulate holograms produced by evaporating spherical droplets with refractive index gradient in the surrounding air/vapor mixture. Simulated holograms provide a physical interpretation of experimental holograms produced by evaporating Diethyl Ether droplets with diameter in the order of 50 µm and recorded in a digital in-line holography configuration with a divergent beam. Refractive index gradients in the surrounding medium lead to a modification of the center part of the droplet holograms, where the first fringe is unusually bright. GLMT simulations reproduce this modification well, assuming an exponential decay of the refractive index from the droplet surface to infinity. The diverging beam effect is also considered. In both evaporating and nonevaporating cases, an equivalence is found between Gaussian beam and plane wave illuminations, simply based on a magnification ratio to be applied to the droplets' parameters.

Interferometric laser imaging for respiratory droplets sizing.

Due to its importance in airborne disease transmission, especially because of the COVID-19 pandemic, much attention has recently been devoted by the scientific community to the analysis of dispersion of particle-laden air clouds ejected by humans during different respiratory activities. In spite of that, a lack of knowledge is still present particularly with regard to the velocity of the emitted particles, which could differ considerably from that of the air phase. The velocity of the particles is also expected to vary with their size. In this work, simultaneous measurements of size and velocity of particles emitted by humans while speaking have been performed by means of Interferometric Laser Imaging Droplet Sizing (ILIDS). This technique allowed us to detect emitted particles with size down to 2 µm as well as to quantify all three components of the velocity vector and the particle concentration. The outcomes of this work may be used as boundary conditions for numerical simulations of infected respiratory cloud transmission.

Size measurement of bubbles in a cavitation tunnel by digital in-line holography.

Digital in-line holography (DIH) with a divergent beam is used to measure size and concentration of cavitation bubbles (6-100 µm) in hydrodynamic facilities. A sampling probe is directly inserted in the cavitation tunnel, and the holograms of the bubbles are recorded through a transparent test section specially designed for DIH measurements. The recording beam coming from a fiber-coupled laser diode illuminates the sample volume, and holograms are recorded by a CMOS camera. From each hologram, the sampling volume can be reconstructed slice by slice by applying a wavelet-based reconstruction method. Because of the geometry of the recording beam, a magnification ratio must be introduced for recovering the 3D location and size of each bubble. The method used for processing holograms recorded in such a configuration is presented. Then, statistical results obtained from 5000 holograms recorded under different pressures in the cavitation tunnel are compared and discussed.

Time gate, optical layout, and wavelength effects on ballistic imaging.

A method to distinguish a hidden object from a perturbing environment is to use an ultrashort femtosecond pulse of light and a time-resolved detection. To separate ballistic light containing information on a hidden object from multiscattered light coming from the surrounding environment that scrambles the signal, an optical Kerr gate can be used. It consists of a carbon disulfide (CS(2)) cell in which birefringence is optically induced. An imaging beam passes through the studied medium while a pump pulse is used to open the gate. The time-delayed scattered light is excluded from measurements by the gate, and the multiple-scattering scrambling effect is reduced. In previous works, the two beams had the same wavelength. We propose a new two-color experimental setup for ballistic imaging in which a second harmonic is generated and used for the image, while the fundamental is used for gate switching. This setup allows one to obtain better resolution by using a spectral filtering to eliminate noise from the pump pulse, instead of a spatial filtering. This new setup is suitable for use in ballistic imaging of dense sprays, multidiffusive, and large enough to show scattered light time delays greater than the gate duration (tau=1.3 ps).

Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments.

Forward light scattering of femtosecond pulses through strongly scattering media is investigated experimentally and numerically. Computations are based on a semi-Monte Carlo method including polarization effects when experiments depend on a Ti:sapphire regenerative amplifier (100 fs, 1 kHz, 1 mJ@ 800 nm). The temporal separation between ballistic light and scattered light is exhibited and used to perform optical depth measurements up to 22 (transmission factor of approximately 10(-10)). Quantitative comparisons between experiments and Monte Carlo simulations show a good agreement. Temporal forward scattered light evolutions with concentration and particle size are presented. Numerical results show that the early scattered light contains information on particle size, opening the way to particle sizing in strongly scattering media.