2D Transfer Functions Research Articles

Topological evolution of acousto-optic transfer functions in biaxial crystals

Modern applications of acousto-optic tunable filters (AOTFs) range from hyperspectral imaging in space research and biomedical optics to optical manipulation and ultrafast laser pulse shaping. The design of all AOTFs is based on optical anisotropy of crystals; until now, however, only uniaxial crystals have been used. Lower symmetry and outstanding acousto-optic (AO) properties of some new biaxial crystals make them promising candidates for qualitative improvements in this field. Anisotropic AO interaction in crystals allows angular noncritical phase-matching (NPM) configurations that are commonly used in different AOTF types. In this work, we perform a comprehensive geometrical and topological analysis of 2D transfer functions of AO interaction under NPM condition in biaxial crystals. The topological classification of the 2D transfer functions under an angular NPM condition is proposed. In principle, in the planes of a biaxial, the same types of transfer function exist as in uniaxial crystals, including cross-like topology of collinear diffraction, circular topology, and ultrawide angle topology. In addition, new topological types of the AO 2D transfer function are reported, which exist only in biaxial crystals.

Morse–Smale decomposition of multivariate transfer function space for separably-sampled volume rendering

We present a topology-guided technique for improving performance of multifield volume rendering with peak finding and preintegration with 2D transfer functions. We apply Morse–Smale decomposition to segment the multidimensional transfer function domain. This segmentation helps to reduce the number of cases where sampling in transfer function space should be performed, effectively reducing the rendering cost for equivalent sampling quality. We show that the overall performance is increased depending on the topology of a transfer function.

Transfer function combinations

Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions.

Automatic Transfer Functions Based on Informational Divergence

In this paper we present a framework to define transfer functions from a target distribution provided by the user. A target distribution can reflect the data importance, or highly relevant data value interval, or spatial segmentation. Our approach is based on a communication channel between a set of viewpoints and a set of bins of a volume data set, and it supports 1D as well as 2D transfer functions including the gradient information. The transfer functions are obtained by minimizing the informational divergence or Kullback-Leibler distance between the visibility distribution captured by the viewpoints and a target distribution selected by the user. The use of the derivative of the informational divergence allows for a fast optimization process. Different target distributions for 1D and 2D transfer functions are analyzed together with importance-driven and view-based techniques.

Fast computation of 2D transfer functions from adaptive optics data

AbstractThe use of atmospheric transfer functions is common in image reconstruction techniques such as speckle interferometry to calibrate the Fourier amplitudes of the reconstructed images. Thus, an accurate model is needed to ensure proper photometry in the reconstruction. The situation complicates when adaptive optics (AO) are used during data acquisition. I propose a novel technique to derive two‐dimensional transfer functions from data collected using AO simultaneously with the observations. The technique is capable to compute the relevant transfer functions within a short time for the prevailing atmospheric conditions and AO performance during data acquisition (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

2D Histogram based volume visualization: combining intensity and size of anatomical structures

Surgical planning requires 3D volume visualizations based on transfer functions (TF) that assign optical properties to volumetric image data. Two-dimensional TFs and 2D histograms may be employed to improve overall performance. Anatomical structures were used for 2D TF definition in an algorithm that computes a new structure-size image from the original data set. The original image and structure-size data sets were used to generate a structure-size enhanced (SSE) histogram. Alternatively, the gradient magnitude could be used as second property for 2D TF definition. Both types of 2D TFs were generated and compared using subjective evaluation of anatomic feature conspicuity. Experiments with several medical image data sets provided SSE histograms that were judged subjectively to be more intuitive and better discriminated different anatomical structures than gradient magnitude-based 2D histograms. In clinical applications, where the size of anatomical structures is more meaningful than gradient magnitude, the 2D TF can be effective for highlighting anatomical structures in 3D visualizations.

Direct Measurement of Transfer Functions in Kelvin Probe Force Microscopy Using Artificially Patterned Surface Potentials

We report a direct measurement of two-dimensional (2D) transfer functions of conductive probes used in Kelvin probe force microscopy (KFM). The 2D transfer functions are obtained by measuring a well-defined step pattern of surface potentials, prepared on thin films of tris(8-hydroxyquinolinato)aluminum(III) (Alq3) by contact-mask exposure. The experimentally obtained 2D transfer functions are highly asymmetric and are spread over 50 µm. A new finding is the observation of negative values in the KFM transfer function, which cannot be explained by conventional KFM formula. The reconstruction of true surface-potential profiles by model-fitting calculation is demonstrated. The technique presented in this study, i.e., the preparation of surface-potential patterns on Alq3 thin films, is ideal for determining the KFM transfer functions experimentally.

Microtremor Measurements in the City of Palermo, Italy: Analysis of the Correlation between Local Geology and Damage

Abstract This study presents the results of 90 seismic ambient noise measurements in Palermo, the main city of Sicily (Italy). The dataset has been processed using the horizontal-to-vertical spectral ratio (HVNSR) technique and interpreted in terms of local geology, which is characterized by the presence of alluvial sediments of two riverbeds masked by urbanization since the seventeenth century. HVNSRs show significant variations in the study area: when the transition stiff to soft is crossed, a typical spectral peak appears in the HVNSRs, mostly in the frequency band 1–2 Hz, and exceeding a factor of 3 in amplitude. Using available information on subsurface geological structure, we compute theoretical 1D and 2D transfer functions. The resonance frequencies of soft soils obtained by HVNSR are well reproduced by the fundamental frequencies from numerical modeling. The distribution of frequency peaks of HVNSR and their amplitudes are also compared with the local damage caused by historical earthquakes. Previous studies demonstrated that damage variations in Palermo were controlled more by near-surface geology than building vulnerability. A uniform vulnerability is an ideal condition to test statistical methods and their capability in seeking correlation between HVNSR and potential damage due to local geological conditions. We apply two well-established multivariate statistical methodologies (factor analysis and canonical correlation) to the HVNSR dataset and macroseismic data (damage grades of the European macroseismic scale). Through these analyses we quantify the significance of the correlation between the HVNSR peak in the low-medium frequency range (0.5–3 Hz) and the occurrence of the highest damage grades. This approach allows us (1) to estimate the threshold value in the resulting linear combination of the HVNSR amplitudes, which separates zones of light damage from zones of significant damage, and therefore (2) to improve the spatial definition of potentially high hazard zones through a denser grid of microtremor measurements.

Measurement of photo‐patterned surface potential of Alq3 thin films by Kelvin‐force microscope together with near‐field optical stimulation

AbstractUniform and extremely high surface potentials of tris(8‐hydroxyquinolinato) aluminum(III) (Alq3) thin films, formed spontaneously by vacuum evaporation of Alq3 in the dark, are patterned by contact‐mask photo‐exposure. The resulting surface‐potential patterns are observed by scanning‐probe Kelvin‐force microscope (KFM). Surface‐potential patterns on Alq3 thin films can be preserved in the dark for more than a year at − 20 °C. The dependence of photo‐induced reduction of surface potentials on photo‐exposure intensity is reproduced well by fitting calculation based on the assumption that the drift of photo‐excited electrons/holes decreases the surface potential. Two‐dimensional (2D) transfer functions of KFM probes are discussed from KFM potential profiles obtained for a step pattern of surface potential. Near‐field optical stimulation through an aperture of an optical fiber probe is demonstrated as scanning near‐field optical microscope (SNOM) combined with KFM (SNOM‐KFM). A photoemission pattern from an aperture of SNOM probes can be visualized as a surface‐potential pattern on Alq3 thin films by means of SNOM‐KFM measurements. Copyright © 2008 John Wiley & Sons, Ltd.

Controllable and Observable Polynomial Description for 2D Noncausal Systems

Two-dimensional state-space systems arise in applications such as image processing, iterative circuits, seismic data processing, or more generally systems described by partial differential equations. In this paper, a new direct method is presented for the polynomial realization of a class of noncausal 2D transfer functions. It is shown that the resulting realization is both controllable and observable.

Dynamics of Broad Emission‐Line Region in NGC 5548: Hydromagnetic Wind Model versus Observations

We analyze the results of long-term observations of broad-line region (BLR) in the Sy1 galaxy NGC 5548 and provide a critical comparison with the predictions of a hydromagnetically-driven outflow model of Emmering, Blandford and Shlosman. This model was used to generate a time series of CIV line profiles that have responded to a time varying continuum. The model includes cloud emission anisotropy, cloud obscuration, a CLOUDY-generated emissivity function and a narrow-line component used to generate the line profiles, and is driven with continuum input based on the monitoring campaigns of NGC 5548. The line strengths, profiles and lags are compared with the observations. It reproduces the basic features of CIV line variability in this AGN without varying the model parameters. The best fit model provides the effective size, the dominant geometry, the emissivity distribution and the 3D velocity field of the CIV BLR and constrains the mass of the central BH. The inner part of the wind appears to be responsible for the anisotropically emitted CIV line, while its outer part remains dusty and molecular, thus having similar spectral characteristics to a molecular torus, although its dynamics is fundamentally different. In addition, our model predicts a differential response across the CIV line profile, producing a red-side-first response in the mid-wings followed by the blue mid-wing and by the line core. Based on the comparison of data and model cross-correlation functions and 1D and 2D transfer functions, we find that the rotating outflow model is compatible with observations of the BLR in NGC 5548.

097 2D transfer-functions based controller design for differential linear repetitive processes

097 2D transfer-functions based controller design for differential linear repetitive processes

2D Transfer-Functions Based Controller Design for Differential Linear Repetitive Processes

Abstract This paper develops the basis of a 2D transfer-function approach to the control of differential repetitive processes.

2D-transfer functions and stability tests for differential non-unit memory linear multipass processes

A transfer-function description for differential non-unit memory linear multipass processes is developed as the basis for further control theoretical and design developments. This description is the natural generalization, in a well-defined sense, of its well-known counterpart from standard linear systems theory. Furthermore, as a first application to control related problems, the use of this description in the development of stability tests is considered. The end product of this analysis is computationally feasible tests which can be implemented using well-established tests from standard linear systems theory.