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The design of image reconstruction algorithms for near-range handheld synthetic aperture radar (SAR) systems has gained increasing popularity due to the promising performance of portable millimeter-wave (MMW) imaging devices in various…
Since its first demonstration in 1995, terahertz time-domain imaging has attracted an increasingly growing interest for its ability to reveal spectral fingerprints of materials, probe changes in refractive index and absorption, as well as…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…
A rigorous mathematical theory is developed to explain the super-resolution phenomenon observed in the experiment by F.Lemoult, M.Fink and G.Lerosey (Acoustic resonators for far-field control of sound on a subwavelength scale, Phys. Rev.…
We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our…
Plenty of quantum information protocols are enabled by manipulation and detection of photonic spectro-temporal degrees of freedom via light-matter interfaces. While present implementations are well suited for high-bandwidth photon sources…
The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…
We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate…
Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
We present a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static, spherically symmetric black hole spacetimes, developed entirely within Schwarzschild-like coordinates. Start ing from the…
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at…
This is the third article in a series of three dealing with the exploitation of speckle for imaging purposes. In complex media, a fundamental limit is the multiple scattering phenomenon that completely blurs the imaging process in depth.…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…