Fourier Wavefront Reconstruction Over a Rectangular Pupil The iterative and boundary methods developed here for circular and elliptical pupils are based on a method to reconstruct the wavefront over the rectangular pupil. To fully understand this development, it is necessary to first summarize the approach used by Freischlad and Koliopoulos to derive an inverse spatial filter to reconstruct a w...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

— We show that the Fourier-Laplace transform of a regular holonomic module over the Weyl algebra of one variable, which generically underlies a variation of polarized Hodge structure, underlies itself an integrable variation of polarized twistor structure. Résumé (Transformation de Fourier-Laplace d’une variation de structure de Hodge complexe polarisée) Nous montrons que le transformé de Fouri...

We have developed a new algorithm and configuration for self-eliminating the autocorrelation of the object wave in Fourier-domain optical coherence tomography. A self-interferogram of the object wave is acquired synchronously with the standard interferogram of the recombined object and reference waves. The former is then subtracted from the latter after Fourier transformation. The algorithm is ...

Mirror symmetry conjecture identi…es the complex geometry of a CalabiYau manifold with the symplectic geometry of its mirror Calabi-Yau manifold. Using the SYZ mirror transform, we argue that (i) the mirror of an elliptic Calabi-Yau manifold admits a twin Lagrangian …bration structure and (ii) the mirror of the Fourier-Mukai transform for dual elliptic …brations is a symplectic Fourier-Mukai tr...

The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...

Camera stabilization is an important task for video analysis. In this report, we describe a method for estimating and stabilizing camera motion between two images via 2D image registration. Our approach is based on a pair-wise registration of images parameterized by 2D affine or projective transformation. Pair-wise image registration estimates transformation parameters for each pair of consecut...