Equivalent Aperture Research Articles

A Fast Calculation Approach for the Shielding Effectiveness of an Enclosure With Numerous Small Apertures

In this paper, we present an efficient and accurate approach to predict the shielding effectiveness (SE) of an enclosure with numerous small apertures, which involves two methods: the equivalent model of aperture array and waveguide equivalent circuit model. First, the equivalent model of aperture array is derived from the numerical simulation that simplifies the aperture array into a single aperture, then the equivalent single aperture's impedance is calculated and the equivalent circuit model is applied to calculate the SE of the enclosure. The result shows a better agreement with the measurement than the original waveguide equivalent circuit model. In comparison with aperture's admittance model, our method can be applied to the square, circular, and rectangular apertures with nonuniform small aperture distribution. The proposed method can also significantly reduce the simulation time and improve the efficiency of simulation compared with the generalized modal method of moments and CST. Finally, we discuss the applicability of this method.

MIMO through-wall radar 3-D imaging of a human body in different postures

This paper focuses on three-dimensional (3-D) imaging for the human body with different postures to enhance the situation awareness ability of through-wall radar. First, we design a two-dimensional MIMO array where the receiving antennas are uniformly and sparsely arranged in horizontal and vertical directions and four time-division multiplexing transmitting elements are placed at the four array corners. As a result, the equivalent aperture is closed to four times the size of the physical array. Second, an identical time-delay wall compensation algorithm attached to back-projection algorithm is presented to easily and approximately correct the image distortion caused by wall penetration, which employs an identical time-delay offset in the whole 3-D pixel-to-pixel imaging process to partially balance out multiple different focusing time-delay errors corresponding to multiple transmit-receive channels in each pixel. Finally, we develop a human body model with three typical postures in the FDTD simulation. Based on the MIMO array and the time-delay compensation algorithm, the simulated images created via the back-projection algorithm clearly provide the identifiable posture characteristics.

Wafer-level fabrication of multi-element glass lenses: lens doublet with improved optical performances.

This Letter reports on the fabrication of glass lens doublets arranged in arrays and realized at wafer level by means of micro-fabrication. The technique is based on the accurate vertical assembly of separately fabricated glass lens arrays. Since each one of these arrays is obtained by glass melting in silicon cavities, silicon is employed as a spacer in order to build a well-aligned and robust optical module. It is shown that optical performance achieved by the lens doublet is better than for a single lens of equivalent numerical aperture, thanks to lower optical aberrations. The technique has good potential to match the optical requirements of miniature imaging systems.

Contact Algorithm for Determining Aperture Evolution of Rock Fracture during Shearing

AbstractA contact algorithm to determine the aperture evolution of a rock fracture during shearing is reported. The algorithm was based on a theoretical normal closure model and semianalytical dilation model and required only the three-dimensional topography data of the two fracture surfaces at the initial stage before shearing. It allowed the prediction of the aperture distribution of a fracture under normal stress and various shear displacements, which is difficult to observe in coupled shear-flow tests. To ensure the precision of the surface topography data, a laser-scanning profilometer system was used for surface topography measurement. The contact algorithm was then used to predict the aperture evolution of a marble fracture during shearing. The results of aperture variation under normal stress and shear displacement were analyzed and compared with an equivalent aperture derived from back-calculation of flow test results. The results indicated that the contact algorithm is efficient in predicting ap...

Performance determination of a novel dynamic membrane reactor for slightly contaminated surface water treatment

A novel lab-scale bio-diatomite dynamic membrane reactor (BDDMR) using a module made of stainless steel mesh with an equivalent aperture of 80μm was proposed to treat the slightly contaminated surface water. This work presents complete information on the impurities removal performance and mechanisms involved in this process. The BDDMR was very effective at reducing particle number and removing turbidity, chemical oxygen demand (CODMn), dissolved organic carbon, UV absorbance at 254nm (UV254), NH3-N and trihalomethane formation potential with a hydraulic retention time of 4 h. The filtration resistance of each of the selected fluxes was investigated, which indicated that the resistance of high flux increased faster than that of lower flux. Three individual effects responsible for removing pollutants, such as microbial biodegradation, bio-diatomite adsorption and bio-diatomite dynamic membrane were determined. Furthermore, dissolved organic matter fractionation and molecular weight distribution were applied to reveal the pollutant removal mechanisms of the BDDMR.

A New Geometrical Model of Fluid Flow in Rock Fractures for Valid Application of the Cubic Law

The cubic law (CL) is one of the most commonly applied physical laws for flow through rock fractures and fractured media, but many studies indicate that the CL is often not adequate. We investigate the establishment conditions of valid applying the “cubic law” to flow in fractures. A dimensional analysis of the N-S equations yields three conditions for the applicability of cubic law, as a leading order approximation in a local fracture segment with parallel walls. These conditions may not be met in many natural rock fractures as whole and demonstrate that the “cubic law” should be exactly applied in local segments (local cubic law, LCL). In this way, a new 2D discrete equivalent model for natural rough fractures is introduced, and its equivalent aperture and flow formulation are derived. By comparing the developed model and experimental results of different fractures, good accuracy was found, and the model was validated. The model could be useful for theory studies of flows through real rock fractures.

Simulating the human eye in measurements of speckle from laser-based projection displays.

In quantitative measurement of the speckle observed in laser projection displays, it is essential how accurately one simulates the human eye. Based on the eye model given by Westheimer, we succeeded in simulating the optical transfer function of the eye model using that for the circular aperture. The equivalent circular aperture diameter is dependent on the eye model used in the simulation and its viewing conditions, but particularly for the eye models given by Westheimer and Williams, they substantially agreed, yielding approximately 1.2 mm at green under a 3 mm pupil diameter viewing condition.

Particle velocity gradient based acoustic mode beamforming for short linear vector sensor arrays.

In this paper, a subtractive beamforming algorithm for short linear arrays of two-dimensional particle velocity sensors is described. The proposed method extracts the highly directional acoustic modes from the spatial gradients of the particle velocity field measured at closely spaced sensors along the array. The number of sensors in the array limits the highest order of modes that can be extracted. Theoretical analysis and numerical simulations indicate that the acoustic mode beamformer achieves directivity comparable to the maximum directivity that can be obtained with differential microphone arrays of equivalent aperture. When compared to conventional delay-and-sum beamformers for pressure sensor arrays, the proposed method achieves comparable directivity with 70%-85% shorter apertures. Moreover, the proposed method has additional capabilities such as high front-back (port-starboard) discrimination, frequency and steer direction independent response, and robustness to correlated ambient noise. Small inter-sensor spacing that results in very compact apertures makes the proposed beamformer suitable for space constrained applications such as hearing aids and short towed arrays for autonomous underwater platforms.

A Global-Local Synthesis Approach for Large Non-Regular Arrays

A method is proposed for the synthesis of large planar non-regular arrays assuming constant magnitude for the excitation of the elements. The approach, which combines global and local optimization, is based on distinguishing aperture-type and non-coherent parts of the array factor. The following constraints are considered: minimal separation of the antennas, maximum size of the array and fixed mainbeam width. The level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an Lp-norm. Possible applications of this model lie in the field of radio astronomy, satellite communications and radar systems. The proposed optimization strategy consists of three successive steps designed to be independent of each other. Starting with an equivalent continuous aperture, the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array, while the third step performs a local optimization of individual elements of the array. This last step heavily relies on computations of the gradient of the cost function, which can be done quickly using an FFT-based procedure. The method is illustrated for several large-scale examples by considering as inputs four different types of non-regular arrays.

A Model for Water Flow Through Rock Fractures Based on Friction Factor

Rock fracture roughness and tortuosity caused by contact asperities produce extra resistance for fluid flow in comparison with the channel consisting of two smooth parallel plates. To characterise the role of roughness and tortuosity in water flow through rock fractures, the existing studies of the effect of fracture roughness and contact area (tortuosity) on fluid flow through rock fractures were firstly reviewed. Then, an explicit flow model was derived using the friction factor predictor previously proposed according to the flow data of sandstone fractures. Regarding the introduced relative roughness of rock fracture as the correction variable, the developed flow model can be considered as a corrected form of classic cubic law, where the relative roughness is defined as the ratio of the averaged peak asperity height to equivalent hydraulic aperture. Sensitivity analysis shows that the cubic law can overestimate the flow rate by 10 % when the relative roughness increases to 70.7. With further increase in relative roughness up to 300, which usually represents tight rock fractures, the flow rate is only approximately 64 % of that predicted by cubic law. The verification of this friction factor to granite and limestone fractures shows that the used friction factor predictor is in good accordance with the experimental data.

A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant

Both atmospheric extinction coefficient and refractive index structure constant (Cn2) are important parameters to describe laser beam propagation in the atmosphere. The typical measurement methods for these two parameters are separated. Recently an integrated measurement method has been developed with the aperture constraint condition. In this study, a variable aperture method is proposed to simultaneously evaluate the atmospheric extinction coefficient and Cn2 needless to consider the aperture constraint condition. The projection optics with CCD is employed to partially receive atmosphere modulated laser speckle images. Because the extinction coefficient and Cn2 are implicit in the far-field receiving power at a certain aperture, they can be estimated through at least twice measurements of long term speckle at different equivalent aperture on the CCD image. The uncertainty analysis is also carried out. The theoretical and experimental results demonstrate that this technique is feasible, which provides an effective and economical way to understand the complicated behavior of laser beam propagation in the atmosphere.

Accurate method for synthesis of shaped‐beam non‐uniform reflectarray antenna

This study presents an accurate method to synthesise a shaped-beam flat reflectarray (RA) antenna based on the phase synthesis of its equivalent aperture. For this purpose particle swarm optimisation is used to determine the optimal phase distribution on the reflective surface of the antenna. Furthermore, by dividing the equivalent aperture of the antenna into small parts and by appropriate approximation of the induced current in each part, the radiation fields have been evaluated via the sum of the simple integrals. In this approach the relation of the amplitude and phase of the reflection co-efficient of the RA elements with the radiation fields of the antenna can be obtained. Therefore the effect of the RA elements can directly be considered in the optimisation process. Also, in the proposed method the effects of the feed antenna including the angle, polarisation, amplitude and phase of the radiated fields from the feed are fully considered in the synthesis procedure. To verify the synthesis method a RA with flat reflective surface has been designed and manufactured that shows a good agreement with the simulation results obtained from commercial full-wave electromagnetic software, CST Microwave Studio.

Anisotropy in capillary invasion and fluid flow through induced sandstone and shale fractures

Understanding the physics of flows in a single fracture is the basis for modeling subsurface transport problems in fractured media. Capillary pressure curve and equivalent aperture have been accepted as tools for characterizing capillary invasion and single-phase flow in a single fracture. Numerical modeling is used to determine the capillary pressure curve and the equivalent aperture for different flow directions in sandstone and shale fractures. Invasion percolation method is used to model the invasion process of dense non-aqueous phase liquid in a water saturated sandstone fracture from different directions. Finite element method is applied to model the flows of brine and electric current in the fractures along different directions. The numerical results are calibrated against the experimental data including capillary pressure measurement and single-phase flow tests in the fractures. Results from the invasion percolation modeling show that the capillary pressure curve is independent of invasion direction. The study on the flows of brine and electric current in the fractures illustrates that the sandstone fracture displays a higher anisotropy in hydraulic and electrical conductivities than the shale fracture. Furthermore, it is found that the anisotropy is correlated with the directional roughness, harmonic mean, and range of fracture aperture.

Calculation of the light intensity distribution reflected by a planar corner-cube retroreflector array with the size of centimeter and above

The light intensity distribution (LID) reflected by a planar corner-cube retroreflector array with the size of centimeter and above (PCCRA) is calculated based on the Collins formula, coordinate transformation matrixes and vector algebra. The expression can be used for the PCCRAs with different parameters and different complex optical systems described by ABCD matrix. The expression indicates that the LID of a PCCRA is much different from a single corner-cube retroreflector (CCR) with equivalent aperture. Computer simulations are applied to explain the expression clearly. The results show that the LID of the PCCRA is more homogeneous than the single CCR with equivalent aperture under circumstances of both normal incident light and oblique incident light. In addition, the expression is proved by comparing the simulation result of the PCCRA only comprising a single CCR and the previous experimental result.

Lumped mass transfer coefficient for divergent radial solute transport in fractured aquifers

• A lumped mass transfer coefficient is obtained for transport in fractured aquifers. • The mass transfer coefficient is obtained for various geometries. • The mass transfer coefficient is a function of scale and injection rate. • Field scale simulation without including dispersion in fracture is not valid. • Ignoring dispersion in modeling a lab test may be valid at high injection rates. Dispersion plays an important role in transport of contaminants and tracers in fractured aquifers. In this work we develop a model for the lumped mass transfer coefficient by including dispersion in the fracture network for slab-, cylindrical- and spherical-shapes of the aggregates for the immobile zone. Coupled transport equations of mobile and immobile zones are solved to develop a first-order lumped mass transfer coefficient. An equivalent fracture aperture, uniform rock matrix block size and constant volumetric water contents (mobile and immobile zones) with no adsorption/desorption are used to represent the aquifer. Results reveal that geometry of the rock matrix blocks and dispersivity have important effects on the upscaled mass transfer coefficient. It is found that field scale simulations of transport processes without including the dispersion in fractures are not valid for the whole range of practical injection rates (10 4 < Pe < 10 6 ). However, modeling of laboratory scale experiments (less than one meter in length) without including dispersion in the mobile zone may be valid at high injection rates (Pe > 10 5 ). It is confirmed that the upscaled lumped mass transfer coefficient is a function of scale and the rate of injection of the tracer. These findings will find applications in modeling of transport processes of contaminated sites remediation and waste disposal.

Numerical modeling of steady-state flow of a non-Newtonian power-law fluid in a rough-walled fracture

Numerical simulations of power-law fluid flow in a rough fracture of regular or irregular topography were carried out using the finite-volume method under the assumptions of the lubrication theory approximation. The model was verified by comparing its results with analytical results available for regular 1D sinusoidal profiles across or along the flow. For a regular profile with sinusoidal variation of the aperture in both directions, the model confirmed that a geometric average can be used as a first approximation, as long as the variation in the profile is not too large. For all fracture topographies studied, reducing the exponent, i.e. making the fluid more shear-thinning, resulted in increasing equivalent hydraulic aperture. The normalized equivalent hydraulic aperture decreased with the normalized standard deviation of the fracture aperture for all fracture topographies studied, except a fracture with a large-scale feature representing a zone of overlap in the middle of the fracture. The validity of the assumptions made in the numerical simulations, in particular the lubrication theory approximation, is discussed and the directions for future work are outlined in conclusion.

Experimental study on a resonance mesh coating fabricated using a UV-lithography technique

In order to achieve high optical transparency and Ka-band bandpass filtering simultaneously, a resonance mesh coating sample is fabricated using a UV-lithography technique. Optical transmission is measured using an Ocean Optics QE65000 spectrometer. And Ka-band bandpass filtering is measured using an Agilent E8363B PNA series network analyzer. Experimental results indicate that the optical transmission of the resonance mesh coating is 63.4% higher than that of non-meshed Frequency Selective Surfaces (FSS) with equivalent aperture parameters, and the transmittance loss of the coating is lower than 0.21 dB while the coating has a Ka-band resonance frequency of 32 GHz. It can therefore be concluded that the resonance mesh coating can be used as a dual-mode spatial filter to achieve high optical transparency and Ka-band bandpass filtering.

Friction Factor of Water Flow Through Rough Rock Fractures

Fluid flow through rock joints occurs in many rock engineering applications. As the fluid flows through rough-walled rock fractures, pressure head loss occurs due to friction drag of the wall and local aperture changes. In this study, the friction factor was experimentally investigated by performing flow tests through sandstone fractures with joint roughness coefficient ranging from 5.5 to 15.4 under changing normal stress from 0.5 to 3.5 MPa. According to the experimental results, the friction factor was formulated as a function of two-independent variables—Reynolds number and relative roughness. Relative roughness is defined as the ratio of maximum asperity height to equivalent hydraulic aperture. The experimental results show that the proposed predictor of the friction factor fits the data with a coefficient of determination R2 > 0.93. Sensitivity analyses indicate that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2. For Reynolds numbers greater than unity, the difference of friction factor induced by relative roughness is smaller. Inclusion of joint roughness in calculating the friction resistance to fluid flow in rough rock joints and the influence of normal stress to the joints is a major step towards more accurate predictions for fluid flow in underground joint networks. This study provides a significant improvement in fundamental understanding of fluid flow in the jointed strata.

Research the AVG Curve Based on the Method of Flat Bottom Hole

In order to accurately reduce the equivalent defect error and draw the AVG curve, the relational expression between the sound pressure and the beam path was deduced, which was based on the ultrasonic sound field theory, the complex-variable function and the quadric surface integration. Then this curve was implemented by using the hardware and the software which were based on the above theory. In addition, it was analyzed the factors of attenuation coefficient and fitting the curve--Lagrange interpolation, to reduce the method error. Finally, the analysis of testing data shows that: the AVG curve which is made by flat-bottomed hole can accurately measure the equivalent aperture and reduce the data error, after giving full consideration to the attenuation coefficient factors and curve fitting.

Experimental studies of a plane-cone resonator for high-power, transverse-flow &lt;inline-formula&gt;&lt;math display="inline" overflow="scroll"&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;CO&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/inline-formula&gt; laser

A practical plane-cone resonator for the high-power, transverse-flow CO 2 laser has been designed. The output characteristics of the plane-cone resonator are researched experimentally and compared with a traditional plane-concave resonator. The output mode is an approximate TEM 03 mode with a resonator length of 3 m and an equivalent aperture radius of 30 mm. The beam divergence angles of the plane-concave resonator and the plane-cone resonator are 2.6 and 2.1 mrad, respectively. In the experiments that studied the misalignment characteristics, the miss rates of the output beam are 16% and 8%, respectively, when the misaligned angles of the output mirrors are both 0.41 mrad. Also, the miss rates are 20% and 5%, respectively, when the misaligned angles of the reflectors are both 0.41 mrad. The results indicate that this plane-cone resonator has a better anti-misaligned stability than plane-concave resonators.