Filtering In Fourier Space Research Articles

Fourier space control in an LCLV feedback system

We show that a control technique, based on feedback filtered at a Fourier plane, can stabilize the spatio-temporally disordered output of a nonlinear optical system. We demonstrate this in an experiment with a LCLV feedback system and in a theoretical model. We stabilize the system and select square and roll patterns. The technique is non-invasive in that the control signal becomes small when control is achieved. A combination of real- and Fourier-space filtering can stabilize patterns in any chosen region of the transverse space.

Manipulation, Stabilization, and Control of Pattern Formation Using Fourier Space Filtering

We present an experimental realization of an almost noninvasive stabilization and manipulation method of coexisting and underlying states of pattern forming systems. In a photorefractive single feedback system, a ring control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few percent of the system's intensity. We were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as underlying solutions. By positive (in-phase) and negative (out-of-phase) control, rolls could be excited in parameter regions where hexagonal structures are preferably stable.

Controlling pattern formation and spatio-temporal disorder in nonlinear optics

We present a feedback control method for the stabiliza- tion of unstable patterns and for the control of spatio-temporal disor- der. The control takes the form of a spatial modulation to the input pump, which is obtained via filtering in Fourier space of the output electric field. The control is powerful, exible and non-invasive: the feedback vanishes once control is achieved. We demonstrate by means of computer simulation, the effect of the control in two different optical systems.

Linear feature enhancing by Hyperbolic-Gaussian filtering

Abstract Abstract. A new methodology for the linear feature enhancing of an image by filtering in Fourier space is presented. As a first step, the Fourier spectrum of the image is used to construct its rose diagram. A new filter is then applied in enhancement directions which are chosen directly from the rose diagram. In Fourier space, the proposed filter's transfer function is a surface whose section perpendicular to the enhanced direction is a Gaussian curve. The construction of this surface is made in such a way that filtering in any direction is allowed. A sequence of analysis for the construction of an enhanced image using this filter is proposed. As an optional step, after constructing the enhanced image a binariza-tion can be made to facilitate the linear feature map extraction. The proposed binarization corresponds to the application of a local threshold technique. A pseudocode summary of each of the steps is included. A comparison with a simple directional filter is made.

Optical diffraction of stretched lacunary spring networks

A network of randomly occupied sites connected by springs is submitted to an external stretch; the optical diffraction pattern of the distorted network is experimentally and analytically studied. Some regions are just shifted as a whole and related shifts are measured by means of diffraction, some regions are uniformly distorted and this distortion is optically detected. The techniques of pattern reconstruction in real space by filtering in Fourier space enable typical defects to be localized. Fractal random media are also considered

Actin Structure and Function Studied by Electron Microscopy and Image Processing

During the past few years analog and digital image processing techniques have become indispensable tools for the study of protein structure by electron microscopy [for reviews see e.g. 1,2,3]. The two most frequently used among these techniques are ‘image enhancement’ and ‘structure reconstruction'. Image enhancement techniques are used to objectively extract the reproducible structural features contained in noisy images recorded from the specimen under investigation, by combining their redundant information by means of ‘real space averaging’ or ‘Fourier space filtering'. The prerequisite for the ultimate success of these techniques is the ability to properly align the images relative to each other. The purpose of structure reconstruction techniques is to determine the three-dimensional structure of proteins by combining a set of sufficiently independent two-dimensional projection images recorded from the object under study - hence three-dimensional reconstruction techniques. This step becomes necessary, because biological specimens are generally translucent to the electron illumination, and therefore micrographs recorded from them in transmission mode represent projection images of the inherently threedimensional specimen that superimpose structural features from different depth within it.