Developing a Reliable Holographic Flow Cyto-Tomography Apparatus by Optimizing the Experimental Layout and Computational Processing.

Digital Holographic Tomography (DHT) has recently been established as a means of retrieving the 3D refractive index mapping of single cells. To make DHT a viable system, it is necessary to develop a reliable and robust holographic apparatus in order that such technology can be utilized outside of specialized optics laboratories and operated in the in-flow modality. In this paper, we propose a quasi-common-path lateral-shearing holographic optical set-up to be used, for the first time, for DHT in a flow-cytometer modality. The proposed solution is able to withstand environmental vibrations that can severely affect the interference process. Furthermore, we have scaled down the system while ensuring that a full 360° rotation of the cells occurs in the field-of-view, in order to retrieve 3D phase-contrast tomograms of single cells flowing along a microfluidic channel. This was achieved by setting the camera sensor at 45° with respect to the microfluidic direction. Additional optimizations were made to the computational elements to ensure the reliable retrieval of 3D refractive index distributions by demonstrating an effective method of tomographic reconstruction, based on high-order total variation. The results were first demonstrated using realistic 3D numerical phantom cells to assess the performance of the proposed high-order total variation method in comparison with the gold-standard algorithm for tomographic reconstructions: namely, filtered back projection. Then, the proposed DHT system and the processing pipeline were experimentally validated for monocytes and mouse embryonic fibroblast NIH-3T3 cells lines. Moreover, the repeatability of these tomographic measurements was also investigated by recording the same cell multiple times and quantifying the ability to provide reliable and comparable tomographic reconstructions, as confirmed by a correlation coefficient greater than 95%. The reported results represent various steps forward in several key aspects of in-flow DHT, thus paving the way for its use in real-world applications.

On the Optimal Field Sensing in Near-Field Characterization.

We deal with the problem of characterizing a source or scatterer from electromagnetic radiated or scattered field measurements. The problem refers to the amplitude and phase measurements which has applications also to interferometric approaches at optical frequencies. From low frequencies (microwaves) to high frequencies or optics, application examples are near-field/far-field transformations, object restoration from measurements within a pupil, near-field THz imaging, optical coherence tomography and ptychography. When analyzing the transmitting-sensing system, we can define "optimal virtual" sensors by using the Singular Value Decomposition (SVD) approach which has been, since long time, recognized as the "optimal" tool to manage linear algebraic problems. The problem however emerges of discretizing the relevant singular functions, thus defining the field sampling. To this end, we have recently developed an approach based on the Singular Value Optimization (SVO) technique. To make the "virtual" sensors physically realizable, in this paper, two approaches are considered: casting the "virtual" field sensors into arrays reaching the same performance of the "virtual" ones; operating a segmentation of the receiver. Concerning the array case, two ways are followed: synthesize the array by a generalized Gaussian quadrature discretizing the linear reception functionals and use elementary sensors according to SVO. We show that SVO is "optimal" in the sense that it leads to the use of elementary, non-uniformly located field sensors having the same performance of the "virtual" sensors and that generalized Gaussian quadrature has essentially the same performance.

Different Metrics for Singular Value Optimization in Near-Field Antenna Characterization.

We deal with the use of different metrics in the framework of the Singular Value Optimization (SVO) technique for near-field antenna characterization. SVO extracts the maximum amount of information on an electromagnetic field over a certain domain from field samples on an acquisition domain, with a priori information on the source, e.g., support information. It determines the field sample positions by optimizing a functional featuring the singular value dynamics of the radiation operator and representing a measure of the information collected by the field samples. Here, we discuss in detail and compare the use, in the framework of SVO, of different objective functionals and so of different information measures: Shannon number, mutual information, and Fisher information. The numerical results show that they yield a similar performance.

Rolling angle recovery of flowing cells in holographic tomography exploiting the phase similarity.

Holographic tomography allows the 3D mapping of the refractive index of biological samples thanks to reconstruction methods based on the knowledge of illumination directions or rotation angles of the imaged sample. Recently, phase contrast tomographic flow cytometry by digital holography has been demonstrated to reconstruct the three-dimensional refractive index distribution of single cells while they are flowing along microfluidic channels. In this system, the illumination direction is fixed while the sample's rotation is not deterministically known a priori but induced by hydrodynamic forces. We propose here a technique to retrieve the rolling angles, based on a new phase images similarity metric that is capable of identifying a cell's orientations from its 3D positioning while it is flowing along the microfluidic channel. The method is experimentally tested and also validated through appropriate numerical simulations. We provide demonstration of concept by achieving reconstruction of breast cancer cells tomography.

Two-dimensional fast marching for geometrical optics.

We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.

Multi-resolution imaging with an optimized number and distribution of sampling points.

We propose an approach of interest in Imaging and Synthetic Aperture Radar (SAR) tomography, for the optimal determination of the scanning region dimension, of the number of sampling points therein, and their spatial distribution, in the case of single frequency monostatic multi-view and multi-static single-view target reflectivity reconstruction. The method recasts the reconstruction of the target reflectivity from the field data collected on the scanning region in terms of a finite dimensional algebraic linear inverse problem. The dimension of the scanning region, the number and the positions of the sampling points are optimally determined by optimizing the singular value behavior of the matrix defining the linear operator. Single resolution, multi-resolution and dynamic multi-resolution can be afforded by the method, allowing a flexibility not available in previous approaches. The performance has been evaluated via a numerical and experimental analysis.

Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm.

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

Shape identification by physical optics: the two-dimensional TE case.

A method is provided for reconstruction of the shape of perfectly conducting objects in a homogeneous space starting from knowledge of the scattered far field under the incidence of TE-polarized plane waves. The Kirchhoff model of scattering permits linearization of the inverse problem, which is further simplified by adopting an asymptotic approximation. Thus the problem is tackled with an approach based on singular-value decomposition already developed for the TM case.

Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity.

The problem of determining the shape of perfectly conducting objects from knowledge of the scattered electric field is considered. The formulation of the problem accommodates the nature of the distribution of the induced surface current density. Thus, as the unknown representing the object's contour, a single layer distribution is chosen so that the contour of the scatterer is described by its support. The nonlinear unknown-data mapping is then linearized by means of the Kirchhoff approximation, and the problem is recast as the inversion of a linear operator acting on a distribution space. An extension of the singular value decomposition approach to solve the linearized problem is provided and numerical results are presented.

In-depth resolution from multifrequency Born fields scattered by a dielectric strip in the Fresnel zone.

The achievable depth resolution in reconstructing the permittivity profile of a dielectric strip under the Born approximation when data are collected in the Fresnel zone is studied. We consider a rectilinear measurement aperture and an orthogonal and centered rectilinear investigation domain. The roles of the aperture extent and frequency diversity are highlighted.