Actual Amplitude Research Articles

A comparison in university students of the amplitude of accommodation determined subjectively

Background: Historically, the push-up and the minus lens methods have been used for the measurements of the amplitude of accommodation, and the differences between the results of these methods are well known.Aim: The purpose of this study was to compare three methods for determining the monocular amplitude of accommodation and consider whether agreement exists between such methods.Setting: The study was conducted at the Optometry Clinic, University of Limpopo.Method: Thirty-four (N = 34) African optometry students participated in this study. There were 20 female and 14 male students. The age range of the participants was 20–34 years. Amplitude of accommodation was measured via the subjective push-up, push-down and minus lens methods only on the right eyes of the sample.Results: The highest average amplitude of accommodation was obtained with the push-up method (10.20 D ± 0.96 D), while the minus lens method produced the smallest mean amplitude of accommodation (9.66 D ± 0.75 D). A higher correlation was found between the push-up and push-down methods (r = 0.80, p = 0.06). The smallest correlation was observed between the push-up and the minus lens methods (r = 0.60, p = 0.062). There were no statistically significant differences between the amplitude of accommodation in male and female students for all three methods (p > 0.005).Conclusion: It seems easier to recognise the point where one can identify a target in pushdown amplitude than the point of first sustained blur in the push-up method. The push-up method tends to overestimate the actual amplitude of accommodation because of the effects of depth of focus. The less evaluated method in the literature is the push-away method; however, further research is necessary to answer the question of which (if any) method is more accurate.

Calibration of Sub-Threshold Evoked EPSPs in Dendritic Spines using Voltage-Sensitive Dyes

Dendritic spines are specialized structures in the brain that receive excitatory synaptic inputs. Activation of synaptic receptors on spines leads to current influx that depolarizes the activated spine, the parent dendrite and the neuron's somatic and axonal compartments. Local membrane potential fluctuations affect voltage-dependent channels producing calcium influx in an interplay of electrical and biochemical signaling. We combine 2-photon glutamate uncaging with 2-photon voltage-sensitive dye (VSD) imaging to study changes in membrane potential in individual spines. We compare two methods of calibrating these signals in spines that may be spatially distant from the somatic compartment. Subthreshold calibration signals have limited amplitude, and actual amplitudes can fall short of the expected values due to patch clamp limitations and space clamp effects, both leading to over-estimated EPSP amplitudes. Backpropagating action potentials have large amplitude but an average attenuation decay rate must be incorporated leading to some uncertainty. We measure the small but significant nonlinearity in dye response that would lead to under-estimated EPSP amplitudes if not accounted for. Calibrated evoked spine EPSP (spEPSP) amplitudes, along with somatic EPSP (soEPSP) amplitudes are input to a compartmental model (NEURON) to predict spine neck resistance (Rneck) values that are consistent with our measurements. While highly variable, predicted Rneck is centered on 200MOhm and is consistent with independent estimates based on FRAP experiments using a cytosolic dye in the absence of the VSD.

Decoherence, control and attosecond probing of XUV-induced charge migration in biomolecules. A theoretical outlook.

The sudden ionization of a molecule by an attosecond pulse is followed by charge redistribution on a time scale from a few femtoseconds down to hundreds of attoseconds. This ultrafast redistribution is the result of the coherent superposition of electronic continua associated with the ionization thresholds that are reached by the broadband attosecond pulse. Thus, a correct theoretical description of the time evolution of the ensuing wave packet requires the knowledge of the actual ionization amplitudes associated with all open ionization channels, a real challenge for large and medium-size molecules. Recently, the first calculation of this kind has come to light, allowing for interpretation of ultrafast electron dynamics observed in attosecond pump-probe experiments performed on the amino acid phenylalanine [Calegari et al., Science 2014, 346, 336]. However, as in most previous theoretical works, the interpretation was based on various simplifying assumptions, namely, the ionized electron was not included in the description of the cation dynamics, the nuclei were fixed at their initial position during the hole migration process, and the effect of the IR probe pulse was ignored. Here we go a step further and discuss the consequences of including these effects in the photoionization of the glycine molecule. We show that (i) the ionized electron does not affect hole dynamics beyond the first femtosecond, and (ii) nuclear dynamics has only a significant effect after approximately 8 fs, but does not destroy the coherent motion of the electronic wave packet during at least few additional tens of fs. As a first step towards understanding the role of the probe pulse, we have considered an XUV probe pulse, instead of a strong IR one, and show that such an XUV probe does not introduce significant distortions in the pump-induced dynamics, suggesting that pump-probe strategies are suitable for imaging and manipulating charge migration in complex molecules. Furthermore, we show that hole dynamics can be changed by shaping the attosecond pump pulse, thus opening the door to the control of charge dynamics in biomolecules.

Fast and precise voltage sag detection method for dynamic voltage restorer (DVR) application

Voltage sag detection method has a significant impact on the performance of dynamic voltage restorer (DVR). This paper proposes a fundamental voltage amplitude detection method which is applicable in both single/three-phase systems for DVR applications. Advantages of the proposed method include application in distorted power grid without any low-pass filter, precise and reliable detection, simple computation and implementation without using a phased locked loop and lookup table. The proposed method has been simulated and implemented experimentally and tested under various conditions considering all possible cases such as different amounts of voltage sag depth (VSD), different amounts of point-on-wave (POW) at which voltage sag occurs, harmonic distortion, line frequency variation, and phase jump (PJ). A detailed procedure to design the threshold band for comparator is presented. According to the achieved results and detailed analysis, maximum ripple of the calculated fundamental voltage amplitude is ±0.3% in normal condition of line frequency and ±1% in the case of ±1Hz variation of 60Hz line frequency. In addition, the error between the actual fundamental voltage amplitude and the calculated one is almost zero in normal condition of line frequency and maximum of ±0.25% in the case of line frequency variation with excessive-harmonic distortion. Furthermore, detection time (DT) of the proposed method is analyzed in detail for different amounts of VSD, POW and PJ. The best and worst detection time of the proposed method were measured 1 and 8.8ms, respectively. Finally, the proposed method has been compared with other methods available in the literature.

Calibrating oscillation response of a piezo-stage using optical tweezers.

In optical tweezers, a piezo-stage (PZT) is widely used to precisely position samples for force clamp, calibrating optical trap and stretching DNA. For a trapped bead in solution, the oscillation response of PZT is vital for all kinds of applications. A coupling ratio, actual amplitude to nominal amplitude, can be calibrated by power spectral density during sinusoidal oscillations. With oscillation frequency increasing, coupling ratio decreases in both x- and y-directions, which is also confirmed by the calibration with light scattering of scanning two aligned beads on slide. Those oscillation responses are related with deformability of chamber and the intrinsic characteristics of PZT. If we take nominal amplitude as actual amplitude for sinusoidal oscillations at 50 Hz, the amplitude is overestimated ~2 times in x-direction and ~3 times in y-direction. That will lead to huge errors for subsequent calibrations.

ANALYSIS OF ELECTROMAGNETIC PROCESS IN COMBINED INDUCTOR SYSTEMS, AS TOOLS FOR STRAIGHTENING OF MODERN CAR

The field in combined inductor systems exists only over workpiece, it occurs at only a low-frequency circular magnetic field. In this paper electromagnetic processes in tools of the magnetic pulse attraction (the combined inductor systems) are analyzed. Investigation based on numerical estimations, using previously obtained analytical relations for the excited fields and forces. Calculations are necessary for the successful implementation of straightening metal coatings bodies car. A distribution of relative intensity of magnetic fields to surfaces of sheet workpiece in the centre of a working zone is obtained. The distribution of amplitude tangential component intensity of resulting magnetic field of the surface of sheet metal along the centre of a rectangular coil is received. Feature of the combined induction system is non-uniformly distributed forces of attraction in the work area. The results showed that the calculated working area on the outer surface of sheet workpiece magnetic field strength will be less than 5% of the field strength of a circular low-frequency source. Calculations have shown the effectiveness of the proposed instrument magnetic pulse straightening metal coating bodies car. The actual amplitude of distributed attraction forces are ~ 7.7 MPa.

Accuracy of Three-Dimensional Shape Measurement Using a Triangulation Method Sensor with Optical Skid

On-machine measurement is used in ultra-processing machining, but it is seldom used in precision machining. For on-machine measurement, it is necessary that the sensor not be easily affected by the moving error or environment vibration in the field of precision machining. A triangulation method sensor with the optical skid method made using a new design concept is proposed to remove the moving error and vibration. The optical skid method used two laser spots with different sizes: the small spot diameter is the stylus and the large spot diameter is the skid [1]. The difference between these two signals reflects the surface shape. The developed sensor comprises an optical source and two optical receiving systems. Each optical receiving system has an imaging lens and a detector. Instead of two laser spots of different sizes, two detectors with different sizes of receiving area serve as the optical skid. Results confirmed the possibility of reducing the influence of the vibration using the developed sensor. In on-machine measurements, measurement of the surface profile with long wavelength is often necessary. If the spot diameter of the skid is not much larger than the surface profile wavelength, then the smoothing effect of the skid is reduced. Therefore, the amplitude of the measured profile by the skid sensor is smaller than actual amplitude of the workpiece. This paper presents a method of reconstructing the surface profile from the measurement results and the obtained effects of the reconstruction method from simulations and experiments.

SU‐E‐J‐150: Four‐Dimensional Cone‐Beam CT Algorithm by Extraction of Physical and Motion Parameter of Mobile Targets Retrospective to Image Reconstruction with Motion Modeling

Purpose:To develop 4D‐cone‐beam CT (CBCT) algorithm by motion modeling that extracts actual length, CT numbers level and motion amplitude of a mobile target retrospective to image reconstruction by motion modeling.Methods:The algorithm used three measurable parameters: apparent length and blurred CT number distribution of a mobile target obtained from CBCT images to determine actual length, CT‐number value of the stationary target, and motion amplitude. The predictions of this algorithm were tested with mobile targets that with different well‐known sizes made from tissue‐equivalent gel which was inserted into a thorax phantom. The phantom moved sinusoidally in one‐direction to simulate respiratory motion using eight amplitudes ranging 0–20mm.Results:Using this 4D‐CBCT algorithm, three unknown parameters were extracted that include: length of the target, CT number level, speed or motion amplitude for the mobile targets retrospective to image reconstruction. The motion algorithms solved for the three unknown parameters using measurable apparent length, CT number level and gradient for a well‐defined mobile target obtained from CBCT images. The motion model agreed with measured apparent lengths which were dependent on the actual target length and motion amplitude. The gradient of the CT number distribution of the mobile target is dependent on the stationary CT number level, actual target length and motion amplitude. Motion frequency and phase did not affect the elongation and CT number distribution of the mobile target and could not be determined.Conclusion:A 4D‐CBCT motion algorithm was developed to extract three parameters that include actual length, CT number level and motion amplitude or speed of mobile targets directly from reconstructed CBCT images without prior knowledge of the stationary target parameters. This algorithm provides alternative to 4D‐CBCT without requirement to motion tracking and sorting of the images into different breathing phases which has potential applications in diagnostic CT imaging and radiotherapy.

Influence of structural flexibility on the wake vortex pattern of airfoils undergoing harmonic pitch oscillation

Reported herein is an investigation of the influence of the structural flexibility of sinusoidally pitching airfoils on the pattern of vorticity shed into the wake. For rigid airfoils, it is well known that, depending on the oscillation frequency and amplitude, this pattern takes the form of the classical or reverse von Karman vortex street. The pattern may be characterized by the vortex circulation (Γ o ), vortex-to-vortex streamwise and cross-stream spacing (a and b, respectively), and vortex core radius (R). In the present work, these four parameters are obtained from particle image velocimetry measurements in the wake of airfoils consisting of a rigid “head” and flexible “tail” at chord Reynolds number of 2010 for different tail flexibilities. The results show that flexible airfoils exhibit the switch from classical to reverse von Karman vortex street (i.e., change in the sign of b) at a reduced frequency of oscillation lower than their rigid counterpart. At a given oscillation frequency, the Strouhal number at which this switch occurs is smallest for a given airfoil structural flexibility; which becomes stiffer with increasing frequency. Using Strouhal number based on the actual trailing edge oscillation amplitude, reasonable scaling is found of the dependence of not only b but also Γ o , a and R on the motion and structure parameters for all airfoils investigated. These results are complemented with analyses using a vortex array model, which together with the identified scaling of the wake vortex parameters, provide basis for the computation of the net thrust acting on the airfoil.

Is the wear coefficient dependent upon slip amplitude in fretting? Vingsbo and Söderberg revisited

More than 25 years ago, Vingsbo and Söderberg published a seminal paper regarding the mapping of behaviour in fretting contacts (O. Vingsbo, S. Söderberg, On fretting maps, Wear, 126 (1988) 131–147). In this paper, it was proposed that in the gross-slip fretting regime, the wear coefficient increased by between one and two orders of magnitude as the fretting displacement amplitude increased from around 20µm to 300µm (defined as the limits of the gross-slip regime).Since the publication of this paper, there have been many papers published in the literature regarding fretting in the gross-sliding regime where such a strong dependence of wear coefficient upon fretting displacement has not been observed, with instead, the wear coefficient being shown to be almost independent of fretting amplitude. Indeed, many researchers have demonstrated that there is a good correlation between wear volume and frictional energy dissipated in the contact for many material combinations, with the additional insight that a threshold in energy dissipated in the contact exists, below which no wear is observed (experimental data relating to fretting of a high-strength steel is presented in the current paper which supports this concept).It is argued that in deriving a wear coefficient in fretting, there are two key considerations which have not always been addressed: (i) the far-field displacement amplitude is not an adequate substitute for the slip amplitude (the former is the sum of the latter together with any elastic deformation in the system between the contact and the point at which the displacement is measured); and (ii) there is a threshold in the fretting duration, below which no wear occurs and above which the rate of increase in wear volume with increasing duration is constant (this constant may be termed the wear coefficient, ktrue). Not addressing these two issues results in the derivation of a nominal wear coefficient (knominal) which is always less than ktrue. A simple analysis is presented which indicates thatknominalktrue=1−A−Bwhere A is associated with erroneously utilising the far-field displacement amplitude in place of the contact slip amplitude in the calculation of the wear coefficient and B is associated with the failure to recognise that there is a threshold in fretting duration below which no wear occurs.A and B are shown to depend upon the tractional force required to initiate sliding (itself dependent upon the applied load and coefficient of friction), the system stiffness, the applied displacement amplitude, the threshold fretting duration below which no wear occurs and the number of fretting cycles in the test. Using typical values of these parameters, the ratio of knominal to ktrue has been shown to be strongly dependent upon the applied displacement amplitude over the range addressed by Vingsbo and Söderberg (with the ratio rapidly decreasing by an order of magnitude over this range). As such, it is argued that ktrue shows no strong dependence on slip amplitude in fretting, and that the strong dependence of knominal upon displacement amplitude presented by Vingsbo and Söderberg does not imply a change in ktrue as is often inferred.The routine recording of force–displacement loops in fretting is a major experimental advancement which has taken place since the publication of the paper by Vingsbo and Söderberg. It is argued that this technique must be routinely used to allow the correct interpretation of wear data in terms of the actual slip amplitude (or energy dissipated); moreover, a range of conditions should be experimentally examined to allow the threshold fretting duration below which no wear has occurred to be evaluated and its significance assessed.

Relationship between second- and third-order acoustic nonlinear parameters in relative measurement

The higher-order acoustic nonlinear parameters are considered effective damage indices in the field of nondestructive evaluation (NDE). They are defined by using the displacement amplitudes of the fundamental frequency and the harmonics, which are called the absolute nonlinear parameters. Generally, however, it is difficult to measure the very small displacement amplitudes of high-frequency harmonics. Therefore, the simplified parameters using the detected wave signal amplitudes, which are known as the relative nonlinear parameters, have been widely used, although their applications are limited to the relative comparison of before and after damage of a single material under consistent experimental circumstances. In this paper, in order to make clear the concept of relative parameter, we presented first that the relative ratio of the simplified parameters is identical to that of the absolute parameters when the detected signal amplitudes are linearly proportional to the actual displacement amplitudes with respect to the fundamental frequency and the harmonics. In addition, the new relationship between the relative ratio of simplified second-order parameter and the relative ratio of simplified third-order parameter was derived from the relationship between the absolute second- and third-order parameters. This new relationship was successfully verified based on experimental results obtained from Al 6061-T6 processed for different heat treatment times, where it was confirmed in advance that the PZT detection signal amplitudes at the fundamental frequency and its second- and third-order harmonics were linearly proportional to the displacement amplitudes.

Implications of ongoing neural development for the measurement of the error-related negativity in childhood.

Event-related potentials (ERPs) have been proposed as biomarkers capable of reflecting individual differences in neural processing not necessarily detectable at the behavioral level. However, the role of ERPs in developmental research could be hampered by current methodological approaches to quantification. ERPs are extracted as an average waveform over many trials; however, actual amplitudes would be misrepresented by an average if there was high trial-to-trial variability in signal latency. Low signal temporal consistency is thought to be a characteristic of immature neural systems, although consistency is not routinely measured in ERP research. The present study examined the differential contributions of signal strength and temporal consistency across trials in the error-related negativity (ERN) in 6-year-old children, as well as the developmental changes that occur in these measures. The 234 children were assessed annually in kindergarten, 1st, and 2nd grade. At all assessments signal strength and temporal consistency were highly correlated with the average ERN amplitude, and were not correlated with each other. Consistent with previous findings, ERN deflections in the averaged waveform increased with age. This was found to be a function of developmental increases in signal temporal consistency, whereas signal strength showed a significant decline across this time period. In addition, average ERN amplitudes showed low-to-moderate stability across the three assessments whereas signal strength was highly stable. In contrast, signal temporal consistency did not evidence rank-order stability across these ages. Signal strength appears to reflect a stable individual trait whereas developmental changes in temporal consistency may be experientially influenced.

Order Tracking Analysis Using Generalized Fourier Transform With Nonorthogonal Basis

The nonorthogonal basis generalized Fourier transform is used as orders extraction technique during machinery speed-up and slow-down tests due to nonstationary nature of vibration signals in these tests. The kernels of this transform have time-dependent frequency which is related to the operating speed of the machine. Since these kernels may belong to different groups or shafts, they are generally nonorthogonal. The actual amplitudes and phases of the orders can be found by solving the system of linear equations resulting from decomposition process which is proposed in this work as an improvement to the time variant discrete Fourier transform (TVDFT) method. The proposed scheme is proved to be efficient and the processing time is very small as compared to other schemes such as the Vold–Kalman order tracking (VKOT) method. The accuracy and efficiency of the proposed scheme are investigated using simulated vibration signal and also actual signals.

Stress evolution during ultrasonic Al ribbon bonding

The present study reveals the stress distribution in the substrate during ultrasonic bonding. The deformations of the Si substrate, Al ribbon, and Al pad were numerically analyzed using a finite element method. Experimental observation of the interface using a highspeed video camera was also conducted to determine the actual interfacial slip amplitude. This amplitude becomes smaller than that of tool-tip with bonding time. It was suggested from the numerical simulations that frictional adhesion enhanced the friction force, resulting in an increase in the equivalent stress in the ribbon and pad. As a result, very large stresses occur in the substrate during ultrasonic bonding. These stresses evolve with the progress of ultrasonic bonding, i.e., frictional adhesion.

Incipient fault detection and diagnosis based on Kullback–Leibler divergence using principal component analysis: Part II

Most of fault indicators are devoted to detect deviations related to specific features but they fail to detect and estimate unpredictable slight distortions often caused by incipient faults. The Kullback–Leibler divergence is characterised with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work has two main objectives: first estimate the amplitude of incipient faults in multivariate processes based on the divergence and second evaluate, through detection error probabilities, the performance of the divergence in the detection of incipient faults in noisy environments.Throughout all the paper, the Fault-to-Noise Ratio (FNR) has been referred to as a comparative criterion between the fault level and noise; particularly the region around 0 dB of FNR is of interest in the evaluation. A theoretical study is developed to derive an analytical model of the divergence that considers the presence of Gaussian noise and allows obtaining a theoretical estimate of the fault amplitude. After application on a simulated AR process, the fault amplitude estimate turns out to be an overestimation of the actual amplitude, therefore guaranteeing a safety margin for monitoring. Accurate fault severity estimation for an eddy currents application shows the effectiveness of this approach.

SU-E-J-252: A Motion Algorithm to Extract Physical and Motion Parameters of a Mobile Target in Cone-Beam Computed Tomographic Imaging Retrospective to Image Reconstruction

Purpose: A motion algorithm was developed to extract actual length, CT-numbers and motion amplitude of a mobile target imaged with cone-beam-CT (CBCT) retrospective to image-reconstruction. Methods: The motion model considered a mobile target moving with a sinusoidal motion and employed three measurable parameters: apparent length, CT number level and gradient of a mobile target obtained from CBCT images to extract information about the actual length and CT number value of the stationary target and motion amplitude. The algorithm was verified experimentally with a mobile phantom setup that has three targets with different sizes manufactured from homogenous tissue-equivalent gel material embedded into a thorax phantom. The phantom moved sinusoidal in one-direction using eight amplitudes (0–20mm) and a frequency of 15-cycles-per-minute. The model required imaging parameters such as slice thickness, imaging time. Results: This motion algorithm extracted three unknown parameters: length of the target, CT-number-level, motion amplitude for a mobile target retrospective to CBCT image reconstruction. The algorithm relates three unknown parameters to measurable apparent length, CT-number-level and gradient for well-defined mobile targets obtained from CBCT images. The motion model agreed with measured apparent lengths which were dependent on actual length of the target and motion amplitude. The cumulative CT-number for a mobile target was dependent on CT-number-level of the stationary target and motion amplitude. The gradient of the CT-distribution of mobile target is dependent on the stationary CT-number-level, actual target length along the direction of motion, and motion amplitude. Motion frequency and phase did not affect the elongation and CT-number distributions of mobile targets when imaging time included several motion cycles. Conclusion: The motion algorithm developed in this study has potential applications in diagnostic CT imaging and radiotherapy to extract actual length, size and CT-numbers distorted by motion in CBCT imaging. The model provides further information about motion of the target.

Measures and LMIs for Impulsive Nonlinear Optimal Control

This note shows how to use semi-definite programming to find lower bounds on a large class of nonlinear optimal control problems with polynomial dynamics and convex semialgebraic state constraints and an affine dependence on the control. This is done by relaxing an optimal control problem into a linear programming problem on measures, also known as a generalized moment problem. The handling of measures by their moments reduces the problem to a convergent series of standard linear matrix inequality relaxations. When the optimal control consists of a finite number of impulses, we can recover simultaneously the actual impulse times and amplitudes by simple linear algebra. Finally, our approach can be readily implemented with standard software, as illustrated by a numerical example.

THz emission from argon implanted silicon surfaces

THz emission from semiconductor surfaces is influenced by the sign and strength of the surface field as well as the relaxation dynamics of the photoinduced carriers. In this paper, an experimental study on argon implanted silicon surfaces is presented. Moderately doped silicon wafers were implanted with 100 keV argon ions with fluences ranging from 1011 to 5×1014cm−2. The THz emission from silicon is strongly enhanced after ion implantation, while the actual THz amplitude depends on the ion dose. For small fluences the increase of the THz amplitude is dedicated to Fermi level pinning due to the introduction of midgap states. In case of highly damaged surfaces where ellipsometry confirms the formation of amorphous zones the THz amplitude starts to decrease. The results demonstrate that for small damage levels THz emission is mainly sensitive to the changed electronic properties whereas for highly damaged surfaces it mostly reacts on the altered generation profile that stems from the changed optical properties of a damaged surface region.

On the nonlinear and time-varying acoustic modeling of the simplified intake or exhaust silencing system

The intake or exhaust noise of an internal combustion engine is usually predicted by the linear, time-invariant source model in frequency domain with reasonable precision. However, the actual finite amplitude pulsation involves the nonlinear, time-varying characteristics that are prominent in time-domain. To overcome the discrepancy between two source models, an approximate nonlinear and time-varying frequency domain source model can be employed by appending the nonlinear or time-varying terms to the linear, time-invariant source model. Proper selection of the nonlinear describing terms varying with time is important for the realistic and precise prediction of the radiated sound. For the selection of such terms, flow and motional characteristics in the valve and orifice of a simplified fluid machine comprised of very large reservoir, valve, and duct is considered. Effects of each describing term and the combined terms are investigated by comparing the sound spectrum predicted from nonlinear source model to that from linear source model. In the comparison, the sound spectrum calculated by the method of characteristics is used as a reference. It is found that the source model using only the velocityrelated terms yields the best result among all the models using various combinations of the terms with different characteristics. The best model yields a difference from the linear source model within ±5 dB in overall sound level. Change of acoustic loads results in a difference of 20–27 dB in linear source model from the reference data; however, maximum 10–22 dB deviations are observed in using the various nonlinear source models. It is concluded that more than 4 describing terms should be employed in the nonlinear model to obtain a realistic result of the radiated sound from the intake or exhaust system.

Analysis of near-field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized illumination

The near-field focusing properties of actual hybrid amplitude–phase binary subwavelength Fresnel zone plates (HBSFZPs) are studied theoretically. The analysis based on the exact vector angular spectrum method is done for a radially polarized beam incident on the HBSFZPs. The results show that the near-field subwavelength focusing with a long depth of focus can be obtained using an HBSFZP, which is very useful for near-field subwavelength photolithography and high-resolution microscopy. The position of the actual focus in the near-field focusing HBSFZPs depends on the evanescent wave rather than the propagating wave. The etch depth has an important influence on focusing properties of HBSFZPs.