Related papers: Optical systems with translational invariance
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We show that if a Lagrangian is invariant under a transformation (with the invariance defined in the standard manner), then the equations of motion obtained from it maintain their form under the transformation. We also show that the…
Many adaptive optics systems operate by measuring the distortion of the wavefront in one wavelength range and performing the scientific observations in a second, different wavelength range. One common technique is to measure wavefront…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
In this position paper, we consider the state of computer vision research with respect to invariance to the horizontal orientation of an image -- what we term reflection invariance. We describe why we consider reflection invariance to be an…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the…
It has been recently demonstrated that integrated optics could enhance accuracy, stability, and ease of use of stellar interferometry techniques. The subject of this thesis is the study of an optical component based on singlemode waveguides…
Q1: Why deploy N wavefront sensors on a three mirror anastigmat (TMA) and not N + 1? Q2: Why measure M Zernike coefficients and not M + 1? Q3: Why control L rigid body degrees of freedom (total) on the secondary and tertiary and not L + 1?…
Optically active spin defects in solids are promising platforms for quantum technologies. Here, we present a first-principles framework to investigate intersystem crossing processes, which represent crucial steps in the optical…
In recent years new types of coordinate transformations have appeared in cosmology on top of the standard gauge transformations, such as the dilatations and special conformal transformations, or the ones leading to (conformal) Fermi…
Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a…
Zernike polynomials are widely used mathematical models of experimentally observed optical aberrations. Their useful mathematical properties, in particular their orthogonality, make them a ubiquitous basis set for solving various problems…
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF)…
Optical resonators are one of the most promising optical devices for manufacturing high-performance pressure sensors for photoacoustic imaging. Among these, Fabry-P\'erot (FP) based pressure sensors have been successfully used for a…
Recent studies of the self-assembly of Langmuir monolayers have revealed novel forms of lateral molecular ordering. Such studies typically involve the use of grazing-incidence synchrotron radiation scattering, and the lateral order…
Imperfect photometric calibration of galaxy surveys due to either astrophysical or instrumental effects leads to biases in measuring galaxy clustering and in the resulting cosmological parameter measurements. More interestingly (and…