Acoustic Frequency Range Research Articles

Microphone array analysis for simultaneous condition detection, localization, and classification in a pipe.

An acoustic method for simultaneous condition detection, localization, and classification in air-filled pipes is proposed. The contribution of this work is threefold: (1) a microphone array is used to extend the usable acoustic frequency range to estimate the reflection coefficient from blockages and lateral connections; (2) a robust regularization method of sparse representation based on a wavelet basis function is adapted to reduce the background noise in acoustical data; and (3) the wavelet components are used to localize and classify the condition of the pipe. The microphone array and sparse representation method enhance the acoustical signal reflected from blockages and lateral connections and suppress unwanted higher-order modes. Based on the sparse representation results, higher-level wavelet functions representing the impulse response are used to localize the position of the sensor corresponding to a blockage or lateral connection with higher spatial resolution. It is shown that the wavelet components can be used to train and to test a support vector machine (SVM) classifier for the condition identification more accurately than with a time domain SVM classifier. This work paves the way for the development of simultaneous condition classification and localization methods to be deployed on autonomous robots working in buried pipes.

Differential Effects of Binaural Pitch Fusion Range on the Benefits of Voice Gender Differences in a "Cocktail Party" Environment for Bimodal and Bilateral Cochlear Implant Users.

Some cochlear implant (CI) users are fitted with a CI in each ear ("bilateral"), while others have a CI in one ear and a hearing aid in the other ("bimodal"). Presently, evaluation of the benefits of bilateral or bimodal CI fitting does not take into account the integration of frequency information across the ears. This study tests the hypothesis that CI listeners, especially bimodal CI users, with a more precise integration of frequency information across ears ("sharp binaural pitch fusion") will derive greater benefit from voice gender differences in a multi-talker listening environment. Twelve bimodal CI users and twelve bilateral CI users participated. First, binaural pitch fusion ranges were measured using the simultaneous, dichotic presentation of reference and comparison stimuli (electric pulse trains for CI ears and acoustic tones for HA ears) in opposite ears, with reference stimuli fixed and comparison stimuli varied in frequency/electrode to find the range perceived as a single sound. Direct electrical stimulation was used in implanted ears through the research interface, which allowed selective stimulation of one electrode at a time, and acoustic stimulation was used in the non-implanted ears through the headphone. Second, speech-on-speech masking performance was measured to estimate masking release by voice gender difference between target and maskers (VGRM). The VGRM was calculated as the difference in speech recognition thresholds of target sounds in the presence of same-gender or different-gender maskers. Voice gender differences between target and masker talkers improved speech recognition performance for the bimodal CI group, but not the bilateral CI group. The bimodal CI users who benefited the most from voice gender differences were those who had the narrowest range of acoustic frequencies that fused into a single sound with stimulation from a single electrode from the CI in the opposite ear. There was no similar voice gender difference benefit of narrow binaural fusion range for the bilateral CI users. The findings suggest that broad binaural fusion reduces the acoustical information available for differentiating individual talkers in bimodal CI users, but not for bilateral CI users. In addition, for bimodal CI users with narrow binaural fusion who benefit from voice gender differences, bilateral implantation could lead to a loss of that benefit and impair their ability to selectively attend to one talker in the presence of multiple competing talkers. The results suggest that binaural pitch fusion, along with an assessment of residual hearing and other factors, could be important for assessing bimodal and bilateral CI users.

Experimental study of acoustic agglomeration coupled with water droplets on eliminating cable fire smoke

Acoustic agglomeration to eliminate fire smoke is one of the most promising technologies at this stage, and we effectively solve technical stumbling blocks such as narrow acoustic frequency range, sound pressure level injury, and long agglomeration time using acoustic waves coupled with water droplets. According to the mechanism and experimental research, acoustic waves coupled with water droplets technology can broaden the optimal agglomeration frequency range, reduce the influence of acoustic power, and effectively improve agglomeration efficiency. Water droplets with a concentration of 40 g/m 3 were added at the acoustic frequency of 1.5 kHz and the acoustic power of 10 W to achieve the safe escape threshold for personnel within 30 s of working while reducing the damage to the human ear caused by the high sound pressure level. • A new method to eliminate fire smoke is proposed. • The addition of water droplets can expand the range of agglomeration frequencies. • 50% reduction in required agglomeration time. • The addition of water droplets can reduce the acoustic power input. • Reduces damage to the human ear from high sound pressure levels.

Satellite remote sensing of environmental variables can predict acoustic activity of an orthopteran assemblage.

Passive acoustic monitoring (PAM) is a promising method for biodiversity assessment, which allows for longer and less intrusive sampling when compared to traditional methods (e.g., collecting specimens), by using sound recordings as the primary data source. Insects have great potential as models for the study and monitoring of acoustic assemblages due to their sensitivity to environmental changes. Nevertheless, ecoacoustic studies focused on insects are still scarce when compared to more charismatic groups. Insects’ acoustic activity patterns respond to environmental factors, like temperature, moonlight, and precipitation, but community acoustic perspectives have been barely explored. Here, we provide an example of the usefulness of PAM to track temporal patterns of acoustic activity for a nocturnal assemblage of insects (Orthoptera). We integrate satellite remote sensing and astronomically measured environmental factors at a local scale in an Andean Forest of Colombia and evaluate the acoustic response of orthopterans through automated model detections of their songs for nine weeks (March and April of 2020). We describe the acoustic frequency range and diel period for the calling song of each representative species. Three species overlapped in frequency and diel acoustics but inhabit different strata: canopy, understory, and ground surface level. Based on the acoustic frequency and activity, we identified three trends: (i) both sampled cricket species call at lower frequency for shorter periods of time (dusk); (ii) all sampled katydid species call at higher frequency for longer time periods, including later hours at night; and (iii) the diel acoustic activity span window seems to increase proportionally with dominant acoustic frequency, but further research is required. We also identified a dusk chorus in which all the species sing at the same time. To quantify the acoustic response to environmental factors, we calculated a beta regression with the singing activity as a response variable and moon phase, surface temperature and daily precipitation as explanatory variables. The response to the moon phase was significant for the katydids but not for the crickets, possibly due to differences in diel activity periods. Crickets are active during dusk, thus the effects of moonlight on acoustic activity are negligible. The response to precipitation was significant for the two crickets and not for the katydids, possibly because of higher likelihood of rain interrupting crickets’ shorter diel activity period. Our study shows how the local survey of orthopteran acoustic assemblages, with a species taxonomic resolution coupled with remote-sensing environmental measurements can reveal responses to environmental factors. In addition, we demonstrate how satellite data might prove to be a useful alternative source of environmental data for community studies with geographical, financial, or other constraints.

A theoretical framework for acoustically produced luminescence: From thermometry to ultrasound pressure field mapping

Acoustically produced luminescence (APL) can be used for fast and easy mapping of ultrasound pressure fields, allowing quantitative investigation of these fields for a wide range of acoustic frequencies and pressures. APL offers a fast and inexpensive alternative for the conventional point-by-point hydrophone scanning. This can benefit industrial and medical ultrasound applications that experience stringent certification and safety requirements on pressure field characterization. APL was shown to originate from absorption-mediated heating by ultrasound irradiation of a membrane material, which consists of a polymer binder and a luminescent material (or phosphor). This heating induces local thermoluminescence emission, which is proportional to the ultrasound pressure. However, a precise framework describing the physics of the APL process, allowing the retrieval of acoustic field information from the measured light emission has been lacking. Here, we present a full theoretical model of the APL phenomenon, allowing the reconstruction of both the pressure and temperature fields from the measured luminescence. The developed theoretical model is verified using finite-element modeling and experimental validation. We then demonstrate how APL can be used to obtain a 3D reconstruction of an ultrasound pressure field, in a fast and easy way. Finally, the general model demonstrated here can also prove useful for other applications, e.g. in luminescence-based thermometry using persistent phosphors.

Manipulation of Low-Frequency Sound with a Tunable Active Metamaterial Panel

We propose the design of a flat active wall panel and demonstrate its effectiveness in modulating the wall impedance, which can lead to the total absorption of incident sound waves in the low-frequency range of 50--120 Hz, or alter its reflection phase. Such an acoustic frequency range is usually the most difficult to handle for passive acoustic components, owing to the long wavelength, and consequently, the bulky size of the materials required. The active panel is actuated by a piezoelectric transducer, with its vibrational displacement amplified by a specially designed mechanical amplifier. Through both simulations and impedance-tube experiments, we show that simply tuning the active panel's displacement amplitude can vary its impedance from that of the hard wall, to impedance matching with air (leading to total absorption), to zero (leading to reflection phase reversal). No feedback loop is necessary for the active-panel device; only an initial adjustment during installation is necessary. We simulate the room-acoustics application for a 1 \ifmmode\times\else\texttimes\fi{} 1 ${\mathrm{m}}^{2}$ wall panel that occupies only 1/48 of the total wall area of the room and show that it can introduce switchable elements to the audio experience.

Sensitivity enhancement effect of Fabry–Pérot etalon acoustic sensor based on acoustic reflection structure

The traditional acoustic signal detection structure uses a diaphragm or a short optical fiber as its acoustically sensitive moving unit. However, the acoustically sensitive moving unit limits the acoustic pressure detection range, sensitivity range, or detectable frequency range. In order to improve this limitation, this study presents a high sensitivity acoustic signal detection structure based on Fabry–Pérot etalon (FPE). The FPE is composed of two Plano-Concave Lenses, and the reflectivity of its cavity mirrors exceeds 99%. According to the COMSOL 5.6 simulation, 1 Pa acoustic pressure can cause a change in the refractive index of 2.6511 × 10−9 and a drift of the resonance frequency of 1.5464 × 10−6nm. An acoustic signal detection system based on phase modulation spectrum technology is constructed. The experimental results of this study show that the high Q value of FPE is 107. In the range of 31.5 Hz–10 kHz, the acoustic detection system has a frequency response with a sensitivity of 2.5873 V/Pa and a total harmonic distortion (THD) of 0.97%. Using an acoustic reflector to converge the acoustic pressure, and then optimize the FPE acoustic detection structure, the sensitivity can be increased by 2.24 times, which is consistent with the simulation results. The excellent performance of the acoustic reflector structure will benefit the future research of photo-acoustic imaging.

Experimental validation of sonic speed theory for wet steam

In order to obtain the sonic speed of the wet steam under different thermal conditions, and verify the accuracy and the precision of Petr’s wet steam sonic theory, experimental measurements were carried out. Also, the effects of acoustic frequency, pressure, wetness, and droplet size on the sonic speed of wet steam were studied based on Petr’s wet steam sonic theory. Results indicate that deviations between the experimental results and Petr’s wet steam sonic theory is in the range of −4%–4%, which is within the experimental measurement error of ±5%. The variation range of the ratio of the actual sonic speed a to the frozen speed af is 0.89–1. When the sonic speed ratio ( a/ af) is close to 1, it means that the sonic speed of wet steam is close to the frozen speed, and the faster the sound wave propagates in the wet steam. In the acoustic frequency range of 102–105 Hz, the sonic speed of wet steam increases with increase of acoustic frequency, pressure, and water droplet size, and decreases with increasing wetness.

Acoustic Performance and Flame Retardancy of Ammonium Polyphosphate/Diethyl Ethylphosphonate Rigid Polyurethane Foams.

Flame-retardant water-blown rigid polyurethane foams (RPUFs) modified by ammonium polyphosphate (APP) and diethyl ethylphosphonate (DEEP) were synthesized by a one-pot free-rising method. We performed scanning electron microscopy (SEM), compression strength tests, acoustic absorption measurements and thermogravimetric analysis, as well as limited oxygen index, vertical burning and cone calorimeter tests to investigate the mechanical properties, acoustic performance and flame retardancy of the foams. SEM confirmed that the open-cell structures of the foams were successfully constructed with the introduction of a cell-opening agent. Upon using 20 php APP, the average acoustic absorption coefficient of the foam reached 0.535 in an acoustic frequency range of 1500–5000 Hz. The results of thermogravimetric analysis demonstrated that the incorporation of APP and DEEP can effectively restrain mass loss of RPUFs during pyrolysis. In particular, the compressive strength of a foam composite containing 5 php APP and 15 php DEEP increased to 188.77 kPa and the LOI value reached 24.9%. In a vertical burning test and a cone calorimeter test, the joint use of APP and DEEP endowed RPUFs with a V-0 rating and they attained a THR value of 23.43 MJ/m2. Moreover, the addition of APP improved the acoustic absorption performance of the foam, verified by acoustic absorption measurements. Considering potential applications, the formulation containing 15 php APP and 5 php DEEP could be used in the preparation of a new flame-retardant acoustic absorption rigid polyurethane foam.

Introduction of innovative technologies in friction units of heavy-duty tribosystems and monitoring of their condition

The article describes studies of heavy-duty metal-polymer tribosystems: wheel-brake pad and pyatnik-podpyatnik of rolling stock, as well as spline couplings of the MI-26 helicopter tail rotor transmission. Tests of the wheel - brake pad system were carried out on an inertial stand with two-way braking at loads and speeds close to real operating conditions. Methods for modifying polymers, fillers, and nanoscale additives have been developed for the Pyatnik - podpyatnik tribosystem of rolling stock. To increase the wear resistance of work surfaces two-layer carbon fibers were applied to the spline couplings. DLC- coatings. Bench tests of these coatings showed a 4.5-fold reduction in wear when testing full-scale slots with a load of 30,000 kg. H and the number of completed cycles in 1,000,000. Methods for monitoring spline couplings based on the analysis of the frequency spectrum of the acoustic-emission (AE) vibration signal generated during the operation of the friction unit are considered. The results of studying the working state of spline couplings obtained by vibration diagnostics in the acoustic frequency range are presented. The state estimation is based on both the characteristics of the time signal and the transformation of the signal in the frequency domain using modal decomposition of the signal using Hilbert-Huang transformations. It is shown that for the effective for monitoring heavy-duty tribosystems, it is advisable to use neural networks.

Evaluation of Enset Fabric Reinforced Green Composite as Sound Absorber Structure

Noise is an unpleasant sound generated from high level sound source, which is a major concern on the residential areas and disturbed comfort, safe activity performance and human health. Now a days, most people are interested on light weight, having good mechanical strength and biologically degradable as well as compostable products. The aim of this research work was characterized the acoustic properties of new alternative ecological composite materials using low cost and light weight agro waste resources. The sound absorption performance of enset fabric and its composite were determined using two microphone transfer mechanism with impedance tube method. The porosity and void structure of enset fibers were studied by scanning electron microscope (SEM) for analysis of enset fabric/enset fabric composite sound dissipation mechanism. The sound absorption coefficient of enset fabric reinforced green composite had a value of 0.9 at critical frequency of 4500 Hz. The test result revealed that, enset fabric had better sound absorption capacity than commercially used glass fabric and had a promising potential to substitute flax in ecofriendly automobile and construction sectors with a wide range of acoustic absorbing frequencies, 3000 Hz - 6000 Hz.

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks

Abstract The “Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun” mission provides a unique opportunity to study the structure of interplanetary shocks and the associated generation of plasma waves with frequencies between ∼50 and 8000 Hz due to its long duration electric and magnetic field burst waveform captures. We compare wave properties and occurrence rates at 11 quasi-perpendicular interplanetary shocks with burst data within 10 minutes (∼3200 proton gyroradii upstream, ∼1900 downstream) of the shock ramp. A perturbed shock is defined as possessing a large amplitude whistler precursor in the quasi-static magnetic field with an amplitude greater than 1/3 the difference between the upstream and downstream average magnetic field magnitudes; laminar shocks lack these large precursors and have a smooth, step function-like transition. In addition to wave modes previously observed, including ion acoustic, whistler, and electrostatic solitary waves, waves in the ion acoustic frequency range that show rapid temporal frequency change are common. Three shocks had burst captures in the ramp; of these, the two laminar shocks contained a wide range of large amplitude wave modes in the ramp whereas the one perturbed shock contained no such waves. Thus, energy dissipation through wave–particle interactions is more prominent in these two laminar shocks than in the perturbed shock. Based on observations from all 11 shocks, the wave occurrence rates for laminar shocks are higher in the transition region, especially the ramp, than downstream. In contrast, perturbed shocks have approximately 2–3 times the wave occurrence rate downstream than laminar shocks.

Looking Into Surface Plasmon Polaritons Guided by the Acoustic Metamaterials

Acoustic metamaterials are introduced as the structures with the alternating elements possessing effective properties that can be tuned seeking for the dramatic control on wave propagation. Homogenization of the structure under consideration is needed aiming to calculate permittivity of metamaterial. We present theoretical outcomes studying an acoustic composite possessing negative effective parameters in the acoustic frequency range. An acoustic metamaterial with an the alternating nanowires arranged in a building block and embedded in a host material was investigated. Propagation of surface plasmon polaritons at the metamaterial interface was predicted.

Fast and High‐Resolution Ultrasound Pressure Field Mapping Using Luminescent Membranes

AbstractUltrasound is used extensively in medical imaging and therapy, non‐destructive testing, flow sensing, underwater range assessment, and acoustic microscopy. To ensure the accuracy of these techniques, detailed knowledge of the acoustic pressure field produced by the ultrasonic transducer is required. This paper proposes a functional polymer membrane loaded with ultrasound‐activated luminescent microparticles. The semitransparent membrane makes use of the luminescent properties of BaSi2O2N2:Eu2+ to convert ultrasonic pressure into visible light in a fast and straightforward way, through a process termed acoustically produced luminescence (APL). APL is shown to work within a wide range of acoustic frequencies (1–25 MHz) and pressures (50 kPa–4.5 MPa), and enables a quantitative characterization of ultrasound fields with a lateral spatial resolution below 200 µm. At the investigated pressures and frequencies, the light generation mechanism is essentially related to ultrasonic heating rather than mechanical stimulation. These membranes offer effective field mapping possibilities, much faster than conventional time consuming point‐by‐point hydrophone scanning.

Polyacrylamide hydrogel phantoms for performance evaluation of multispectral photoacoustic imaging systems

As photoacoustic imaging (PAI) begins to mature and undergo clinical translation, there is a need for well-validated, standardized performance test methods to support device development, quality control, and regulatory evaluation. Despite recent progress, current PAI phantoms may not adequately replicate tissue light and sound transport over the full range of optical wavelengths and acoustic frequencies employed by reported PAI devices. Here we introduce polyacrylamide (PAA) hydrogel as a candidate material for fabricating stable phantoms with well-characterized optical and acoustic properties that are biologically relevant over a broad range of system design parameters. We evaluated suitability of PAA phantoms for conducting image quality assessment of three PAI systems with substantially different operating parameters including two commercial systems and a custom system. Imaging results indicated that appropriately tuned PAA phantoms are useful tools for assessing and comparing PAI system image quality. These phantoms may also facilitate future standardization of performance test methodology.

Експериментальне дослідження діелектричної проникності та динамічного поверхневого натягу мастильно-охолоджувальних рідин при барботуванні

Subject and Purpose. The maintenance of physical and chemical properties and biological stability of lubricoolants during downtimes, which are bound to happen sometimes and last long, is a hot problem in metalworking industry. The procedure of bubbling for the lubricoolant mixing, saturation with oxygen and inactivation of anaerobic microflora calls for chemical and biological techniques to monitor the lubricoolant condition during the bubbling and after it. Yet the standard methods lack responsiveness and accuracy of the analysis, implying the further refinement of the output values. In the present work, microwave super-high frequency (SHF) dielectrometry is employed for the examination of the dielectric constant and dynamic surface tension of synthetic, semi-synthetic and organic emulsions during the bubbling. Methods and Methodology. The dielectric constant and dynamic surface tension of 5.7 % water-soluble emulsions are measured at frequency f = 37.7 GHz. A frequency sweep in the acoustic frequency range f = 20…25000 Hz is used, for which purpose the end of the 8-mm waveguide is supplied with a piezo сell. Results. It has been revealed that the dielectric constant and dynamic surface tension of lubricoolants depend on the physicochemical characteristics that the lubricoolants acquire during a month-long downtime and after 10-, 20-, and 30-minute bubblings. The dielectric constant and dynamic surface tension demonstrate that the bubbling improves lubricating properties of all the emulsions examined. For this, a 10-minute bubbling is enough for semi-synthetic lubricoolants, and a 20-minute bubbling is needed for synthetic and organic lubricoolants. Conclusion. The microwave dielectrometry method with a frequency sweep in the acoustic frequency range can be used in metalworking industry as an aid to lubricoolant quality control during the downtime or storage.

Геоакустическая эмиссия при прохождении через земную кору высокоэнергетических мюонов космического происхождения

The unresolved problem of traditional seismology to date is the separation from the stream of information recorded by numerous seismic sensors of a strictly defined signal about the approach of a catastrophic earthquake specific in time and space. Such a signal is usually lost against a constant background from a large number of another events. At the turn of the 1980s and 1990s, scientists from the Physics Institute and the Institute of Physics of the Earth developed a preliminary concept for a new promising direction in seismology. Using the signal from elastic vibrations in the acoustic frequency range for earthquake prediction. These signals can be generated by ionization. Ionization is formed at the moment of the passage of high-energy muons through a seismically stressed medium in the deep layers of the earth's crust. It is hoped that this method may be one way to predict earthquakes in the future.

Quartz-enhanced photoacoustic spectroscopy exploiting low-frequency tuning forks as a tool to measure the vibrational relaxation rate in gas species

We demonstrated that quartz-enhanced photoacoustic spectroscopy (QEPAS) is an efficient tool to measure the vibrational relaxation rate of gas species, employing quartz tuning forks (QTFs) as sound detectors. Based on the dependence of the QTF resonance frequency on the resonator geometry, a wide range of acoustic frequencies with narrow detection bandwidth was probed. By measuring the QEPAS signal of the target analyte as well as the resonance properties of different QTFs as a function of the gas pressure, the relaxation time can be retrieved. This approach has been tested in the near infrared range by measuring the CH4 (nν4) vibrational relaxation rate in a mixture of 1% CH4, 0.15 % H2O in N2, and the H2O (ν1) relaxation rate in a mixture of 0.5 % H2O in N2. Relaxation times of 3.2 ms Torr and 0.25 ms Torr were estimated for CH4 and H2O, respectively, in excellent agreement with values reported in literature.

Relationship of gain and phase in the transfer function of swirling flames

Gain and phase are two key characteristics of flame transfer function (FTF) in evaluating unsteady flame response. Few studies have investigated the correlation between gain and phase of FTF compared to the extensive literature on the gain characteristics. In this study, we measured the gain and phase of acoustic-excited swirling flames with different flow rates, fuels, equivalence ratios, and burner structures on a single nozzle premixed swirl burner. We identified, for the first time, the consistent variation of FTF gain and derivative of phase over a wide range of acoustic frequencies, and revealed an essential linear relationship between the extremal frequencies of gain and phase derivative, demonstrating that the gain and phase of FTF are not independent. We further proposed an analytical decomposition of the periodically oscillated swirling flame in which FTF equals the combined complex vector of all the perturbing mechanisms. The synchronized variation characteristics of the gain and phase derivative for different flames and acoustic excitations can be explained using a two vector model based on vector decomposition. The distinct time lags and angular velocities of the perturbing vectors were determined by the different spatial positions of the flame tip and base. The local extrema of the FTF modulus and phase derivative are caused by the phase interference of the sub-vectors. Multiple complex vectors affecting heat release rate should be considered under high frequency.

Structure optimization of quasi one-dimensional acoustic filters with the use of a genetic algorithm

The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order to determine the optimal objective function for the genetic algorithm, the entire space of the possibility of the layers’ distribution for a six-layer structure was analyzed. The spread of the transmission integral values even for the 6-layer structure was significant and ranged from 11.9% to 81.5%. Minimizing the value of the transmission integral as an objective function could lead to a large number of high transmission peaks with a small half width. It allowed the determining of the optimal objective functions for minimizing transmission in a given frequency range, and another allowing for its maximization. The phase diagram of the solution space for the transmission integral from the integral of the absolute value of the transmission functions derivative was determined. Transmission of the most and the least optimal six-layer structures was shown depending on the assumed objective function. Then, the analysis of fifteen and thirty-layer structures was carried out. From the dependence of the objective function values for the best individuals for each generation, it was determined that despite carrying out a thousand iterations, the stable state was determined before reaching 250 iterations of the algorithm, and thus the optimal structure was determined. The transmissions ratio of analyzed structures in the studied frequency range (up to 20 kHz) to full transmission (without structures) in this acoustic frequency range for the analyzed optimal 6, 15 and 30-layer structures were 16.78%, 9.6% and 4.41%, respectively.