Modulation Transfer Function for Development to Complete Field Neutralization

Despite advances in miniaturization of CMOS sensors, current submillimeter diameter microendoscopic systems rely on coherent fiber bundles to transfer the image from its collection point to the detector. Determining the resolution of an endoscopic optical system that employs a fiber bundle is nontrivial, and there is limited published information about how to calculate the theoretical modulation transfer function (MTF) of a system that may include a distal lens, fiber bundle, relay optics, and a camera sensor. While the fiber bundle is frequently considered the resolution-limiting element, greater information may be gained from computing the full system MTF. In this paper, we describe a resolution cascade method that calculates theoretical MTFs for common components, as well as for the entire microendoscopic system. These theoretical calculations compare favorably to experimentally gathered data for four different optical configurations. The software developed for these calculations is freely available to predict the MTF of other coherent fiber bundle-based systems. Brief instructions and necessary assumptions/conditions are described.

The edge method for measuring the modulation transfer function (MTF) has recently gained popularity due to its simplicity and appropriateness particularly for digital imaging systems. Often edge test devices made of rather thin metal sheets are used, which are semitransparent to x rays and may generate scattered radiation. The effect of this scattered radiation on the determined MTF was investigated both theoretically (assuming an ideal detector) and experimentally using a CsI-based digital detector. It was found that the MTF increases due to the scattered radiation for all spatial frequencies larger than 0 mm(-1). The theoretical model developed in this study predicts that the maximum error compared to the true detector MTF is given by S/A, where A is the attenuated fraction and S is the scattered fraction reaching the detector, relative to the incident radiation. Theoretical and experimental results are in good agreement for radiation qualities corresponding to general radiography (RQA3, RQA5, and RQA7), whereas for chest beam quality (RQA9) the experimentally observed MTF error is larger than predicted by the simple model, possibly because the energy response of the CsI-based detector differs from that of an ideal one. The theoretical MTF error reaches a value of 18% for a 0.25 mm thick lead edge of RQA9. Since the MTF enters squared into the determination of the detective quantum efficiency (DQE), an error of at least 36% in DQE may result when using this edge test device. In conclusion, the use of fully absorbing edge material is advised for MTF determination with the edge method.

The Modulation Transfer Function (MTF) is a fundamental imaging system design specification and system quality metric often used in remote sensing. The MTF describes the attenuation of sinusoidal waveforms as a function of spatial frequency. Practically, MTF is a metric quantifying the sharpness of the reconstructed image. The Knife-Edge method is becoming widely applied for its advantage of simplified target and accurate computer calculation. Noise in CCD image system is inevitable, thus the SNR becomes a factor influencing the MTF measurement. In this paper, we build relationships between SNR, luminance and MTF. In conclusion, SNR is related with luminance levels linearly. SNR rises with increasing luminance. The higher SNR, the more curves conform to the theoretical MTF.

The turbulence of the atmosphere puts an upper limit on the quality of the image of a ground object obtained by long-exposure photography from low or high altitudes in the atmosphere or in the space. By using good optics and high resolution film or CCD and a stable platform, this limit could be approached but not exceeded. A useful quantity for indicating the magnitude of this limit is the integral of the modulation transfer function (MTF) associated with the turbulence. In this work, we introduce a new method for measuring the MTF of the atmosphere in the surface layer, based on moire technique. In this technique, from a low frequency Ronchi grating, installed at a certain distance from a digital camera equipped with a tele lens, successive images are recorded and then transferred to a PC. By rotating each image by θ/2 and -θ/2, say ±3°, and superimposing them, a large number moire patterns are produced. The average transmittance function of the superimposed image gratings is measured in a moire fringe interval. The latter function is measured by scanning the moire pattern by a slit parallel to moire fringes. It is shown theoretically that from the Fourier transform of the latter function the MTF of the atmosphere can be deduced, if the MTFs of the imaging system and the grating are given or their effects are negligible. The atmospheric MTFs have been measured at different turbulence conditions. Also, we have studied the behavior of the atmospheric MTF respect to exposure time.

A unified modeling approach for rotating flexible shaft-disk systems with general boundary and coupling conditions

The presampling modulation transfer function (MTF) of a digital imaging system is commonly determined by measuring the system’s line spread function (LSF) using a narrow slit or differentiating the detector’s edge spread function (ESF) with an edge device. The slit method requires precise fabrication and alignment of a slit as well as a high radiation exposure. The edge method [3] is a complicated image processing procedure, requiring determination of the edge angle, reprojection, sub-binning, smoothing and differentiating the ESF, and spectral estimation. In this paper, a simple method is employed to evaluate the MTF using an edge device. The image processing procedures required by this method involve simply the determination of the over-sampling rate and the Fourier transform of the modified ESF. Differentiation and signal to noise ratio (SNR) improvement are jointly applied in the Fourier domain. The MTFs obtained by this simple method are compared to the theoretical MTF and the previously proposed more complicated edge method. The experimental results show that the proposed method provides a simple, accurate and convenient measurement of the presampling MTF for digital imaging systems.

Modulation transfer function (MTF) is an important parameter for image quality evaluation of on-orbit optical image systems. Various methods have been proposed to determine the MTF of an imaging system which are based on images containing point, pulse and edge features. In this paper, the edge of the moon can be used as a high contrast target to measure on-orbit MTF of image systems based on knife-edge methods. The proposed method is an extension of the ISO 12233 Slanted-edge Spatial Frequency Response test, except that the shape of the edge is a circular arc instead of a straight line. In order to get more accurate edge locations and then obtain a more authentic edge spread function (ESF), we choose circular fitting method based on least square to fit lunar edge in sub-pixel edge detection process. At last, simulation results show that the MTF value at Nyquist frequency calculated using our lunar edge method is reliable and accurate with error less than 2% comparing with theoretical MTF value. © 2017 SPIE.

The most general admissible boundary conditions are derived for an idealized Aharonov–Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the Aharonov–Bohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the Aharonov–Bohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

Nonlinear dynamics of straight fluid-conveying pipes with general boundary conditions and additional springs and masses

The ability to improve visualization of structural information in digital radiography without increasing radiation exposures requires improved image quality across all spatial frequencies, especially at high frequencies. The detective quantum efficiency (DQE) as a function of spatial frequency quantifies image quality given by an x-ray detector. We present a method of increasing DQE at high spatial frequencies by improving the modulation transfer function (MTF) and reducing noise aliasing. The Apodized Aperature Pixel (AAP) design uses a detector with micro-elements to synthesize desired pixels and provide higher DQE than conventional detector designs. A cascaded system analysis (CSA) that incorporates x-ray interactions is used for comparison of the theoretical MTF, noise power spectrum (NPS), and DQE. Signal and noise transfer through the converter material is shown to consist of correlated an uncorrelated terms. The AAP design was shown to improve the DQE of both material types that have predominantly correlated transfer (such as CsI) and predominantly uncorrelated transfer (such as Se). Improvement in the MTF by 50% and the DQE by 100% at the sampling cut-off frequency is obtained when uncorrelated transfer is prevalent through the converter material. Optimizing high-frequency DQE results in improved image contrast and visualization of small structures and fine-detail.

Although there are various methods to measure the modulation transfer function (MTF) of charge-coupled devices (CCD), the interferometric fringe pattern method has advantages over others, such as canted slit sources, bar targets, knife-edge, laser-speckle patterns, random noise pattern, etc. Our interferometric method is relatively simple and versatile: It requires no critical optics and no focusing or precision alignment, the entry array is tested, the contrast ratio of the test pattern is high enough, the spatial frequency of the fringe pattern can vary continuously. Our method generates the formation of a sinusoidal intensity fringe pattern by the interference of two monochromatic plane waves, and straightforward projects it onto the CCD array under test. The construction of the experimental device is based on the Fresnel Double-Mirror structure. A 2.5 mw He-Ne laser with the wavelength of 632.8 nm is used as the light source, the laser beam is spatially filtered by a 10 μm pinhole and expanded to a diameter of 30 mm, and the resulting wave front is divided by two mirrors, which incline to each other at a small angle, and interfered. One of the mirrors is rotatable to vary the frequency of the pattern. The CCD array is mounted on a stage, which is also rotatable to make that the CCD array takes different angle with the fringe pattern direction, to receive the patterns. With the method we provided, the spatial frequency can be extended to some 2 times the Nyquist frequency of the CCD array to study the aliasing effect. In the Cartesian coordinates, the x- and y- axis MTFs (at angle 0° and 90°) of the CCD array were measured, the other three MTFs (at angle 26.56°, 45° and 63.44°), which nobody has done before, were also tested offering a more comprehensive characterization of the CCD array.

The three most commonly used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant-charge or constant-potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary condition depends on the details of the dissociation/association process.

Static and dynamic analysis of two-phase peridynamic one-dimensional systems is thoroughly investigated in this paper for various boundary conditions by exact and numerical approaches. Such a nonlocal study concerns the axial or torsional responses of two-phase peridynamic rods or the behavior of a two-phase peridynamic string. For a normalized exponential kernel, the integro-differential equation of the two-phase peridynamic problem can be converted as a linear higher-order differential equation with constant coefficients. Exact static solutions of fixed–fixed and fixed–free two-phase peridynamic axial rod (TPPAR) under uniform distributed loading and concentrated force are analytically derived. It is shown that the pure peridynamic rod problem can be ill-posed due to a conflict between the natural boundary condition and the peridynamic constitutive boundary condition. The two-phase peridynamic problem may be justified from physical arguments, and is also seen as a regularized peridynamic problem. The exact eigen-frequencies of the two-phase peridynamic rods are also analytically obtained for various boundary conditions, including fixed–free, fixed–fixed or free–free boundary conditions. These theoretical approaches are corroborated by numerical investigations based on Finite Difference Method (FDM), Finite Element Method (FEM), exact FEM and variational iterative methods. Two FDM schemes are presented for the statics and the vibration of two-phase peridynamic rods, with convergence orders of 1 and 2, respectively. Moreover, three different FE procedures are proposed as: (1) FEM for direct solving the integro-differential equations of two-phase peridynamic one-dimensional system, (2) FEM for discretizing the pure differential equations, and (3) Exact FEM to obtain both the exact stiffness matrix and exact dynamic stiffness matrix of two-phase peridynamic one-dimensional system, based on Eisenberger’s methodology. The order of convergence for the first and the second proposed FEM is equal to 2 and 4, according to the type of selected finite elements. Moreover, the third proposed FEM based on the exact shape function of the peridynamic problem gives the exact solution from one single FEM element. In addition, the variational iterative method of Stodola–Vianello is successfully applied to the two-phase peridynamic eigenvalue problems.

Efficient spectral-Galerkin methods for polar and cylindrical geometries