Aperture Function Research Articles

Evolution of Coal Permeability during Gas Injection—From Initial to Ultimate Equilibrium

The evolution of coal permeability is vitally important for the effective extraction of coal seam gas. A broad variety of permeability models have been developed under the assumption of local equilibrium, i.e., that the fracture pressure is in equilibrium with the matrix pressure. These models have so far failed to explain observations of coal permeability evolution that are available. This study explores the evolution of coal permeability as a non-equilibrium process. A displacement-based model is developed to define the evolution of permeability as a function of fracture aperture. Permeability evolution is tracked for the full spectrum of response from an initial apparent-equilibrium to an ultimate and final equilibrium. This approach is applied to explain why coal permeability changes even under a constant global effective stress, as reported in the literature. Model results clearly demonstrate that coal permeability changes even if conditions of constant effective stress are maintained for the fracture system during the non-equilibrium period, and that the duration of the transient period, from initial apparent-equilibrium to final equilibrium is primarily determined by both the fracture pressure and gas transport in the coal matrix. Based on these findings, it is concluded that the current assumption of local equilibrium in measurements of coal permeability may not be valid.

Accumulation of ammonium and reactive oxygen mediated drought-induced rice growth inhibition by disturbed nitrogen metabolism and photosynthesis

Nitrogen (N) deficiency and drought are two key limiting factors for rice production worldwide, but the relationship of drought stress with N homeostasis in rice is rarely advanced. The aim of this study was to dissect the physiological effects of drought stress on rice growth that coupled unbalanced N metabolism. Water-deficient stress (WD) limited stomatal aperture function and activity of Rubisco carboxylase to photosynthesis. The rate of total electron transport (Jt) and the electron to carboxylation (Jc) were considerably decreased, whereas the proportion of e− flow to photorespiration was stimulated by WD, especially at 1600 μmol m−2 s−1 PPFD. Concurrently, the expressions of glycolate oxidase genes (GOX1, GOX5) and glycine decarboxylase complex (GDCH, GDCP and GDCT) were significantly induced in leaves of WD treatment, which led to the accumulation of reactive oxygen species in leaves. With the photosynthetic change, nitrate uptake and reduction were suppressed. Moreover, the enhanced photorespiration generated excess NH3 accumulation in leaves and stimulated the expressions of GS1;1, GS1;2 and GS2, which were tightly coupled with the expressions of PEPC1 and PEPC2 under WD stress. Our results suggest that the inhibited nitrate reduction associated with diminished electron transport rate, and the photorespiration-associated accumulation of hydrogen peroxide and NH3 were critical in the drought-induced rice growth inhibition.

Crosstalk Modeling in Lens Based Free Space Optical Interconnects Systems with Circular Symmetry

We introduce convenient model and an optimization scheme to optimize the signal-to-crosstalk ratio (SCR) in a free space optical interconnects (FSOIs) system that uses microlenses with finite circular apertures. In this model, we consider both the stray light crosstalk and the crosstalk due to the diffraction at the microlens apertures to evaluate the SCR. Using cylindrical form of Collins diffraction integral and the Laguerre–Gaussian (LG) beam model, we derive an approximate closed form formula for the optical field of a multimode LG beam propagating through circular apertured FSOIs by expanding the hard edge circular aperture function of the microlens in terms of complex Gaussian functions. The analyses indicate that the size of the detector is an important factor to optimize the SCR for both the apertured and the unapertured misaligned FSOIs system. The effect of higher order mode of the laser source on the SCR is also considered.

Power Profiles and In Vitro Optical Quality of Scleral Contact Lenses: Effect of the Aperture and Power.

To assess the power profile and in vitro optical quality of scleral contact lenses with different powers as a function of the optical aperture. The mini and semiscleral contact lenses (Procornea) were measured for five powers per design. The NIMO TR-1504 (Lambda-X) was used to assess the power profile and Zernike coefficients of each contact lens. Ten measurements per lens were taken at 3- and 6-mm apertures. Furthermore, the optical quality of each lens was described in Zernike coefficients, modulation transfer function, and point spread function (PSF). A convolution of each lens PSF with an eye-chart image was also computed. The optical power fluctuated less than 0.5 diopters (D) along the optical zone of each lens. However, the optical power obtained for some lenses did not match with its corresponding nominal one, the maximum difference being 0.5 D. In optical quality, small differences were obtained among all lenses within the same design. Although significant differences were obtained among lenses (P<0.05), these showed small impact in the image quality of each convolution. Insignificant power fluctuations were obtained along the optical zone measured for each scleral lens. Additionally, the optical quality of both lenses has showed to be independent of the lens power within the same aperture.

The Propagation Properties of a Longitudinal Orbital Angular Momentum Multiplexing System in Atmospheric Turbulence

A novel multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM) carried by frozen waves with different longitudinal patterns is studied in this paper. The longitudinal OAM multiplexing (LOAMM) system is simulated under atmospheric turbulence, which is based on the split-step Fourier transform method and includes multiple random phase screens. The influences of system parameters on the average OAM mode probability densities are analyzed and discussed, such as propagation distance, strength of turbulence, sizes of finite aperture function, OAM mode numbers, and source parameters. It is found that in the limited apertures, the detection probability spectrum of the LOAMM system is inversely proportional to OAM mode numbers, strength of turbulence, and propagation distance. The bit-error rate and aggregate capacities are compared between the traditional OAM-based space-division-multiplexing (OAM-SDM) system with Bessel beams and our proposed LOAMM system. Our work should contribute to proving that the LOAMM system has a number of advantages over the OAM-SDM system in FSO communication.

Fractional Fourier transform of double-half inverse Gaussian hollow beams

In this paper, we study an appropriate mathematical model of dark-hollow beam by concerning double-half inverse Gaussian hollow (DHIGH) beams passing through fractional Fourier transform (FRFT) optical systems. Based on Collins integral formula and using the expression of the hard-edged aperture function into a finite sum of complex Gaussian functions, analytical expressions for the propagation properties of DHIGH beams through the FRFT optical systems without and with apertures have been derived in detail. Some numerical simulations are given to illustrate the normalized intensity distribution of DHIGH beams in a FRFT system by studying the important factors of both incident beams order and the FRFT order. Our results obtained by using an approximate analytical formula, are in a good agreement with those obtained by using numerical integral method. The results show that the FRFT optical system is a convenient way for DHIGH beams shaping.

A General Precipitation-limited LX–T–R Relation among Early-type Galaxies

Abstract The relation between X-ray luminosity (L X) and ambient gas temperature (T) among massive galactic systems is an important cornerstone of both observational cosmology and galaxy-evolution modeling. In the most massive galaxy clusters, the relation is determined primarily by cosmological structure formation. In less massive systems, it primarily reflects the feedback response to radiative cooling of circumgalactic gas. Here we present a simple but powerful model for the L X–T relation as a function of physical aperture R within which those measurements are made. The model is based on the precipitation framework for AGN feedback and assumes that the circumgalactic medium is precipitation-regulated at small radii and limited by cosmological structure formation at large radii. We compare this model with many different data sets and show that it successfully reproduces the slope and upper envelope of the L X–T–R relation over the temperature range from ∼0.2 keV through . Our findings strongly suggest that the feedback mechanisms responsible for regulating star formation in individual massive galaxies have much in common with the precipitation-triggered feedback that appears to regulate galaxy-cluster cores.

Comparing the effect of aperture extension on the peak sidelobe level of sparse arrays.

The reduced number of sensors in sparse arrays create high peak sidelobe levels (PSLs). This letter compares the PSLs of minimum redundancy arrays (MRAs), minimum hole arrays (MHAs), and co-prime sensor arrays (CSAs) (conventionally beamformed and product processed) with fully populated uniform linear arrays (ULAs) as a function of aperture using both numerical simulations and experimental data. This letter finds that PSLs of MRAs, MHAs, and conventionally processed CSAs are much higher than the ULA PSL and are largely insensitive to aperture extension. In contrast, CSA product processing decreases the PSL with increasing aperture, eventually matching the ULA PSL.

Articulatory correlates of phonemic and coarticulatory nasalization

Phonological theory distinguishes nasal and oral vowel counterparts by velopharyngeal port opening, neglecting other phonetic differences between phonemic and coarticulatory nasalization. Recent articulatory work provides evidence of oropharyngeal distinctions, in addition to velic lowering. This study (12 Brazilian Portuguese speakers) uses real-time MRI to investigate oropharyngeal differences between oral, phonemically nasal, and phonetically nasalized vowels /a, i, u/. Tissue boundaries in midsagittal vocal tract images were automatically detected to reveal each vowel repetition’s aperture function. Principal Components Analysis determined vocal tract regions responsible for the greatest variance in the data. Time-dynamic analyses of vocal tract area in these regions used smoothing spline ANOVA. Results show the tongue body and/or hyperpharynx as the most important articulators. For /a/, nasal vowels demonstrate wider hyperpharyngeal and narrower tongue body regions compared to oral vowels. For /u/, o...

Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit**Project supported by the National Natural Science Foundation of China (Grant No. 11574272) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LY16A040014).

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.

Simulation of the effect of incline incident angle in DMD Maskless Lithography

The aim of this study is to provide a simulation method for investigation of the intensity fluctuation caused by the inclined incident angle in DMD (digital micromirror device) maskless lithography. The simulation consists of eight main processes involving the simplification of the DMD aperture function and light propagation utilizing the non-parallel angular spectrum method. These processes provide a possibility of co-simulation in the spatial frequency domain, which combines the microlens array and DMD in the maskless lithography system. The simulation provided the spot shape and illumination distribution. These two parameters are crucial in determining the exposure dose in the existing maskless lithography system.

Orbital angular momentum density and spiral spectrum of Lorentz–Gauss vortex beams diffracted by a rectangular aperture

Based on the expansions of the Lorentz distribution and the aperture function, an analytical expression of Lorentz–Gauss vortex beams with a topological charge of ±1 diffracted by a rectangular aperture is derived. One can judge the sign of the topological charge from the normalized intensity and the phase distributions. The effects of the rectangular aperture on the orbital angular momentum density and the spiral spectrum are investigated, respectively. When the length and the width of the rectangular aperture are not equal, the orbital angular momentum density distribution becomes twisted and tilted. When the size of the rectangular aperture increases, the magnitude of the orbital angular momentum density and the weight coefficient of the dominant spectrum both increase, while the weight coefficients of other minor spectra decrease. In addition, the expansion of the spiral spectrum in the case of rectangular aperture is smaller than that in the case of the single slit. The difference between the adjacent spectra in the case of the rectangular aperture is four, which is twice the difference in the case of the single slit. Moreover, the weight coefficient of the dominant spectrum in the case of the rectangular aperture is relatively larger. To measure the topological charge of the diffracted Lorentz–Gauss vortex beam, this research denotes that the rectangular aperture is superior to the single slit.

Effective aperture of X-ray compound refractive lenses.

A new definition of the effective aperture of the X-ray compound refractive lens (CRL) is proposed. Both linear (one-dimensional) and circular (two-dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76, 600-603; (2003). J. Exp. Theor. Phys. 97, 204-215; (2009). J. Surface Investig. 3, 358-364; (2012). J. Synchrotron Rad. 19, 84-92; Kohn et al. (2003). Opt. Commun. 216, 247-260; (2003). J. Phys. IV Fr, 104, 217-220], the FWHM of the X-ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6, 1153-1167; (1998). J.Appl. Phys. 84, 5855-5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two-dimensional CRL is proposed which allows one to calculate the two-dimensional CRL through the one-dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.

Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics.

Fresnel zone plates with apodized apertures [apodization FZPs (A-FZPs)] have been developed to realise Gaussian beam optics in the hard X-ray region. The designed zone depth of A-FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian-like smooth-shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian-like focusing spot profile. Optical properties of two types of A-FZP, i.e. a circular type and a one-dimensional type, have been evaluated by using a microbeam knife-edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A-FZPs are introduced.

Angular coherence in ultrasound imaging: Theory and applications.

The popularity of plane-wave transmits at multiple transmit angles for synthetic transmit aperture (or coherent compounding) has spawned a number of adaptations and new developments of ultrasonic imaging. However, the coherence properties of backscattered signals with plane-wave transmits at different angles are unknown and may impact a subset of these techniques. To provide a framework for the analysis of the coherence properties of such signals, this article introduces the angular coherence theory in medical ultrasound imaging. The theory indicates that the correlation function of such signals forms a Fourier transform pair with autocorrelation function of the receive aperture function. This conclusion can be considered as an extended form of the van Cittert Zernike theorem. The theory is validated with simulation and experimental results obtained on speckle targets. On the basis of the angular coherence of the backscattered wave, a new short-lag angular coherence beamformer is proposed and compared with an existing spatial-coherence-based beamformer. An application of the theory in phase shift estimation and speed of sound estimation is also presented.

A theoretical study of the on-axis average intensity of generalized spiraling Bessel beams in a turbulent atmosphere

In this paper, we study the effect of turbulent atmosphere for a new type of Bessel-like beams family by considering a generalized spiraling Bessel beam (GSBB) created by illuminating a curved fork-shaped hologram with a Laguerre–Gaussian beam. Based on the extended Huygens–Fresnel integral formula in the paraxial approximation, by means of the Rytov method and using the expression of the hard aperture function into a finite sum of complex Gaussian functions, an analytical expression of the on-axis average intensity for the considered beams family is derived. Some numerical simulations for the GSBB propagating in atmospheric turbulence are given and discussed by studying the influences of some factors as the beam topological charge, the beam waist, the wavelength and the turbulent strength.

Ion-photon entanglement and quantum frequency conversion with trapped Ba+ ions.

Trapped ions are excellent candidates for quantum nodes, as they possess many desirable features of a network node including long lifetimes, on-site processing capability, and production of photonic flying qubits. However, unlike classical networks in which data may be transmitted in optical fibers and where the range of communication is readily extended with amplifiers, quantum systems often emit photons that have a limited propagation range in optical fibers and, by virtue of the nature of a quantum state, cannot be noiselessly amplified. Here, we first describe a method to extract flying qubits from a Ba+ trapped ion via shelving to a long-lived, low-lying D-state with higher entanglement probabilities compared with current strong and weak excitation methods. We show a projected fidelity of ≈89% of the ion-photon entanglement. We compare several methods of ion-photon entanglement generation, and we show how the fidelity and entanglement probability varies as a function of the photon collection optic's numerical aperture. We then outline an approach for quantum frequency conversion of the photons emitted by the Ba+ ion to the telecommunication range for long-distance networking and to 780 nm for potential entanglement with rubidium-based quantum memories. Our approach is significant for extending the range of quantum networks and for the development of hybrid quantum networks compromised of different types of quantum memories.

Propagation of the finite Olver beams through an apertured misaligned ABCD optical system

In this paper, an analytical propagation expression of Finite Olver Beams passing through a misaligned ABCD optical system is derived using the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions. Some numerical results are presented in the work for reason to illustrate the effect of misalignement on the distribution characteristics of the Finite Olver Beams passing through the misaligned optical system with a rectangular aperture.

Effects of a turbulent atmosphere on an apertured Lommel-Gaussian beam

In this paper, based on the generalized Huygens-Fresnel diffraction integral, the expansion of the hard aperture function into a finite sum of complex Gaussian functions and the Rytov theory method, we develop an approximate analytical expression of the on-axis intensity of Lommel–Gaussian beams passing through a turbulent atmosphere. The corresponding closed-forms for the unapertured Lommel–Gaussian, the aperture Lommel, the apertured/unapertured Bessel–Gaussian, the apertured Bessel and the apertured/unapertured fundamental Gaussian beams are derived in the work as special cases. Some of these theoretical results provide more accordance with other studies elaborated in the literature. Some numerical calculations are carried out to illustrate the effects of some parameters, such as the waist width, the wavelength, and the turbulence strength, on the on–axis intensity of Lommel–Gaussian at a z-plane of a turbulent atmosphere.

Highly uniform parallel microfabrication using a large numerical aperture system

In this letter, we report an improved algorithm to produce accurate phase patterns for generating highly uniform diffraction-limited multifocal arrays in a large numerical aperture objective system. It is shown that based on the original diffraction integral, the uniformity of the diffraction-limited focal arrays can be improved from ∼75% to &amp;gt;97%, owing to the critical consideration of the aperture function and apodization effect associated with a large numerical aperture objective. The experimental results, e.g., 3 × 3 arrays of square and triangle, seven microlens arrays with high uniformity, further verify the advantage of the improved algorithm. This algorithm enables the laser parallel processing technology to realize uniform microstructures and functional devices in the microfabrication system with a large numerical aperture objective.