Fringe tracking in interferometers is typically analyzed with the implicit assumption that there is a single phase associated with each telescope in the array. If the telescopes have apertures significantly larger than r0 and only partial adaptive optics correction, then the phase measured by a fringe sensor may differ significantly from the “piston” component of the aperture phase. In some cas...

We study fringe subtrees of random m-ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that for the random m-ary search trees with m ≤ 26 and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree T converges to a normal distribution; more gene...

Dynamic full-field three-dimensional sensing of specular reflective surfaces can be conveniently implemented with fringe reflection technique. A monoscopic fringe reflectometric system can be adopted as a simple measuring setup. With the assistance of the windowed Fourier ridges method as an advanced fringe demodulation technique, only one cross grating is needed to reconstruct the three-dimens...

We have applied the technique of Fourier fringe analysis to microscopic interferograms of needle crystals that grow from a solution. We use a differential technique in which an empty field interferogram is compared with one that contains distortion and obscuration by the growing crystal, and we demonstrate both analytically and experimentally a phase shift sensitivity of 0.01 fringe with a spat...

Utilizing the asymptotic method of stationary phase, I derive expressions for the Fourier transform of a two-dimensional fringe pattern. The method assumes that both the amplitude and the phase of the fringe pattern are well-behaved differentiable functions. Applying the limits in two distinct ways, I show, first, that the spiral phase (or vortex) transform approaches the ideal quadrature trans...

The spectroscopic wavenumber is a proxy for the optical frequency, and avoids the necessity of writing factors of c everywhere. For optical and infrared radiation the wavenumber is conveniently expressed in units of inverse micrometers, thus a wavelength of 500 nm corresponds to 2.00 μm−1. The circular or angular wavenumber k = 2π/λ = 2πσ is often used, particularly in the context of the wave e...

The path length of a tree, that is the sum of the lengths of all root-leaf paths, is an important measure of eeciency of the tree. The fringe of a tree is the diierence between the lengths of the longest path and the shortest path in the tree. The minimal and the maximal path length of trees with N leaves and given fringe have been well studied. In this paper, we initiate the study of the expec...

Doignon and Falmagne have developed the concept of the fringe of a knowledge state based upon the neighborhood of knowledge states. This concept is useful for probabilistic assessment of knowledge and for the suggestion of training problems in an intelligent tutoring system. In this paper, a generalized definition of the fringe of knowledge states is introduced. An efficient procedure is presen...

5 In kinesiology research, fringe projection profilometry is used to measure 6 the surface shape and profile of ex-vivo beating animal heart. Deformation 7 of projected fringe pattern will be caused by non-flat shape of surface and 8 thus used to reconstruct the surface. In this course project, multiple-layer 9 neural network (MLNN) is used to recover the gradient information of the 10 surface ...