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When light is passed through aberrated optical systems, the resulting degradation in amplitude and phase has deleterious effects, for example, on resolution in imaging, spot sizes in focussing, and the beam quality factor of the output…
Two-wavelength adaptive optics (AO) systems sense turbulence-induced wavefront distortions using an artificial beacon or natural guidestar at one wavelength, while correcting and possibly transmitting at another. Although most existing AO…
Mirror Symmetry for a large class of three dimensional $\mathcal{N}=4$ supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of $\text{ALE}$ spaces. A pair of such mirror duals can be…
The averaging problem in general relativity concerns the difficulty of defining meaningful averages of tensor quantities and we consider various aspects of the problem. We first address cosmological backreaction which arises because the…
In magnetic resonance imaging (MRI), inhomogeneity in the main magnetic field used for imaging, referred to as off-resonance, can lead to image artifacts ranging from mild to severe depending on the application. Off-resonance artifacts,…
The recent history of optical design saw a progressive trend of also designing without rotational symmetry, especially spectrometers due to the use of reflective and diffractive elements in their designs. A freeform hyperspectral imager…
Off-axis parabolic mirrors (OAPMs) are widely used in the THz and mm-wave communities for spectroscopy and imaging applications, as a result of their broadband, low-loss operation and high numerical apertures. However, the aspherical shape…
Wavefront aberrations are identified as a major limitation in quantum sensors. They are today the main contribution in the uncertainty budget of best cold atom interferometers based on two-photon laser beam splitters, and constitute an…
Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…
Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with…
In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of…
Babinet complementary patterns of a spectrally tunable metamaterial incorporating a nematic liquid crystal are normally assumed to exhibit the same tuning range. Here we show that for a hybrid, terahertz liquid crystal-metamaterial, the…
The capability of the adaptive optics to correct for the segmentation error is analyzed in terms of the residual wavefront RMS and the power spectral density of the phase. The analytical model and the end-to-end simulation give…
Frustrated total internal reflection is analyzed from an unusual point of view Unlike most similar works, incident angles are used here as the scanning variable, instead of the tunneled film thickness. The theoretical framework is presented…
We consider compactification of M-theory on X7 with betti numbers (b_0, b_1, b_2, b_3, b_3, b_2, b_1, b_0) and define a generalized mirror symmetry (b_0, b_1, b_2, b_3) goes to (b_0, b_1, b_2 -rho/2, b_3+rho/2)$ under which rho =…
We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the…
The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete…
We present a brief review of our recent work [1] on asymmetrically warped brane models, where the background metric is characterized by different time and space warp factors. In particular we examine the case of bulk photons and we show…
Achromatic combinations of a diffractive Phase Fresnel Lens and a refractive correcting element have been proposed for X-ray and gamma-ray astronomy and for microlithography, but considerations of absorption often dictate that the…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…