Higher order aberration comparison between two aspherical intraocular lenses: MC6125AS and Akreos advanced optics

AIM: To compare higher order aberrations in two aspherical intraocular lenses(IOLs): Akreos advanced optics(AO) and Dr. Schmidt Microcrystalline 6125 aspheric anterior surface(MC6125AS) with each other. METHODS: Forty eyes of 39 patients underwent phacoemulsification and Akreos AO and MC6125 AS were implanted in their eyes in a random manner. Three months post-operatively, higher order aberrations including spherical aberration, coma aberration, and total aberrations were measured and compared.RESULTS: The total aberration was 0.24±0.17 in eyes with Dr. Schmidt and 0.20 ±0.01 in eyes with Akreos AO(P =0.361). The mean of coma aberration was 0.17 ±0.21 and 0.09 ±0.86 in Dr. Schmidt and Akreos lenses,respectively(P =0.825). Total spherical aberration was almost the same in both groups(mean: 0.05, P =0.933).Best corrected visual acuity in Akreos AO(0.10±0.68) and Dr. Schmidt(0.09±0.67) did not differ significantly(P =0.700). CONCLUSION: There is no statistically significant difference in the higher order aberrations between these two aspherical lenses.

Visual function and higher order aberration after implantation of aspheric and spherical multifocal intraocular lenses:a meta-analysis

AIMTo assess the visual outcomes of aspheric multifocal intraocular lenses (IOLs) compared with spherical multifocal IOL after cataract surgery.

Effect of incision types for Artisan phakic intraocular lens implantation on ocular higher order aberrations

AIM： To evaluate the effect of incision types for Artisan phakic intraocular lens （PIOL） implantation on ocular higher-order aberrations （HOAs）.METHODS： A retrospective review was conducted of the patients who had undergone Artisan PIOL implantation for the correction of myopia and followed up for at least 6mo. Patients are classified into 2 groups considering the incision type： cornea group with patients undergone clear corneal incision; sclera group with patients undergone sclera tunnel incision. All patients with postoperative astigmatism of under 1 diopter （D） were included to minimize the effect of residual astigmatism on postoperative HOAs. Visual acuity, special equivalents, astigmatism, predictability （±1 D from target refraction）, HOAs （coma, trefoil, spherical aberration）, and corneal endothelial counts were analyzed preoperatively and 6mo postoperatively.RESULTS： At the postoperative 6mo, all patients of both groups achieved uncorrected visual acuity of 16/20 or better, and significantly decreased the spherical equivalents compared with preoperative values. The predictability of refractive correction was 96% in the former, and 94% in the latter. Unlike the sclera group, preoperative astigmatism decreased significantly in cornea group at postoperative 6mo. The HOAs increased significantly at postoperative 6mo compared to the preoperative values in both groups, and the root mean square （RMS） total and trefoil wavefront aberration of cornea group were significantly higher than those of sclera group.CONCLUSION： Although corneal incision significantly reduces preexisting astigmatism, the postoperative 6mo of total RMS and trefoil aberration change may deteriorate the visual quality after Artisan PIOL implantation.

Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.

Effects of higher-order aberrations on contrast sensitivity in normal eyes of a large myopic population

AIM：To study the relation between higher-order aberrations（HOAs）and contrast sensitivity（CS）in normal eyes among a population of laser in situ keratomileusis（LASIK）candidates.METHODS：In 6629 eyes of 3315 LASIK candidates,CS were measured under dark environment at the spatial frequencies of 1.5,3,6,12 and 18 cycles per degree（c/d）,respectively,using an Optec 6500 visual function tester.Meanwhile,ocular HOAs were measured for a 6.0 mm pupil with a Hartmann-Shack wavefront analyzer.RESULTS：In the study,the subjects with an average spherical equivalent of-4.86±2.07 D were included.HOAs decreased from the third to the sixth order aberrations with predominant aberrations of third-order coma,trefoil and fourth-order spherical aberration.At low and moderate spatial frequencies,CS was negatively correlated with the third-order coma and trefoil aberrations,and decreased with increasing Z31,but increased with increasing Z3-3and Z5-1.At high spatial frequencies,CS decreased with increasing Z3-3and increased with increasing Z5-1.CONCLUSION：At a large pupil size of 6.0 mm,the thirdorder aberrations,but not the total aberrations,are the main factors affecting CS.Vertical coma is negatively correlated with CS.

Record-Breaking Frequency of 44 GHz Based on the Higher Order Mode of Surface Acoustic Waves with LiNbO_(3)/SiO_(2)/SiC Heterostructures

Surface acoustic wave (SAW) technology has been extensively explored for wireless communication, sensors, microfluidics, photonics, and quantum information processing. However, due to fabrication issues, the frequencies of SAW devices are typically limited to within a few gigahertz, which severely restricts their applications in 5G communication, precision sensing, photonics, and quantum control. To solve this critical problem, we propose a hybrid strategy that integrates a nanomanufacturing process (i.e., nanolithography) with a LiNbO_(3)/SiO_(2)/SiC heterostructure and successfully achieve a record-breaking frequency of about 44 GHz for SAW devices, in addition to large electromechanical coupling coefficients of up to 15.7%. We perform a theoretical analysis and identify the guided higher order wave modes generated on these slow-on-fast SAW platforms. To demonstrate the superior sensing performance of the proposed ultra-high-frequency SAW platforms, we perform micro-mass sensing and obtain an extremely high sensitivity of approximately 33151.9 MHz·mm2·μg−1, which is about 1011 times higher than that of a conventional quartz crystal microbalance (QCM) and about 4000 times higher than that of a conventional SAW device with a frequency of 978 MHz.

Comparison of correcting myopia and astigmatism with SMILE or FS-LASIK and postoperative higher-order aberrations

AIM:To compare the effect of myopia and astigmatism correction and postoperative change in higher-order aberration as results of receiving small-incision lenticule extraction(SMILE)and femtosecond laser-assisted in situ keratomileusis(FS-LASIK).METHODS:A prospective and non-randomized controlled study was conducted.The subjects are divided into two groups according to different operations received:229 eyes of 116 patients in the SMILE group and 168 eyes of 86 patients in the FS-LASIK group.All subjects were followed up for 3 mo by monitoring their uncorrected visual acuity(UCVA),best-corrected visual acuity(BCVA),spherical equivalent,higher-order aberrations,and the preoperative and postoperative complications.RESULTS:At 1 wk,1,and 3 mo post-surgery,224 eyes(97.8%),227 eyes(99.1%)and 229 eyes(100%)had UCVA≥20/20 in the SMILE group,while 165 eyes(98.2%),167 eyes(99.4%)and 167 eyes(99.4%)had UCVA≥20/20 in the FS-LASIK group,respectively(χ^(2)=0.146,2.135,and 1.124;all P>0.05).BCVA reduction was not observed in both groups at 1 and 3 mo of post-surgery(χ^(2)=0.734 and 1.898,P>0.05).There was no statistically significant difference in the spherical equivalent between the two groups at 1 and 3 mo post-surgery,though the percentage of the spherical equivalent within±0.50 D at 3 mo postsurgery was 98%in the SMILE group,which was higherthan that of the FS-LASIK group(92%,χ^(2)=1.872,P>0.05).The root mean square(RMS)values of total high-order aberration,coma,and spherical aberration of the two groups increased significantly in the early postoperative period and decreased after 3 mo,but the values were still higher than the preoperative levels(P<0.05);there was no significant difference between the two groups in the RMS values of total higher-order aberrations and specific higherorder aberrations(P>0.05).The incidence of complications in the SMILE group was lower than that in the FS-LASIK group(χ^(2)=14.52,P<0.05).CONCLUSION:SMILE and FS-LASIK can effectively treat myopia,significantly improve visual acuity,and increase the total high-order aberration,spherical aberration,and coma.The incidence of complications after SMILE is relatively low.

Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

Study on the Corneal Higher-Order Aberrations and Correlation in Patients with Different Degrees of Myopia Suitable for Wavefront-Guided FS-LASIK

Background: Individualized corneal refractive surgery requires an understanding of the basis of higher-order aberrations before surgery. To investigate the characteristics and distribution of anterior surface wavefront aberrations in patients suitable for corneal refractive surgery. Methods: A total of 121 myopic patients (121 eyes, 18 - 45 years old) who underwent corneal refractive surgery were recruited from January to May 2016 at Affiliated Hospital, Yanbian University. Patients were randomly selected by the Pentacam anterior segment analysis system with a spherical equivalent (SE) of -0.25 to -10.00 D. The corneal anterior aberrations (total higher-order aberration;spherical aberration;Coma;Trefoil) and Q and K values were detected, and a correlation analysis of the relevant parameters was carried out. Results: The root-mean-square (RMS) of the third to sixth order aberrations of the corneal anterior wavefront aberrations at a 6 mm analysis diameter showed a decreasing trend in patients suitable for the corneal refractive surgery, and the RMS of the third order aberrations accounted for 62.92% of the total HOAs. The coma ratio (coma/total cornea higher-order aberrations) was increased with the increasing diopters, while the spherical aberration ratio (spherical aberration/total cornea higher-order aberrations) was not changed. In addition, the spherical aberration was 0.203 ± 0.082 μm (range: 0.061 to 0.503 μm), and the Q30 was -0.19 ± 0.03 (range: -0.58 to 0.31). There were significant differences in the coma aberrations of preoperative corneal anterior surface (3, 1) between the low, middle and high myopia groups (P = 0.013). The spherical equivalent was positively correlated with the corneal coma of the anterior corneal surfaces (R =?-0.241, P = 0.009), and the Q value was positively correlated with the total higher-order aberrations (R = 0.326, P Conclusions: Individual wavefront aberrations on the anterior surfaces of the cornea are comparatively different, and the Zernike coefficients are related to the degree of myopia. Spherical aberrations are the most overriding aberrations of the cornea.

Changes in higher order aberrations after central corneal regularization-a comparative two-year analysis of a semiautomated topography-guided photorefractive keratectomy combined with corneal cross-linking

Background:The optical quality in progressive keratoconus deteriorates due to ectasia and distortion of the corneal shape and optics.While corneal cross-linking(CXL)aims at stopping disease progression,“CXL-Plus”combines CXL with excimer laser ablation to improve visual function.Central Corneal Regularization(CCR)represents a therapeutic excimer laser modality specifically designed to smoothen the ectatic corneal shape and to reduce higher order aberrations(HOA).We set out to compare CXL-Plus,consisting of CXL combined with CCR,with CXL by itself for patients with progressive keratoconus.Methods:Retrospective 2-year matched group analysis of patients who either underwent CXL-Plus(n=28)or CXL as a sole procedure(n=28)for progressive keratoconus.Main outcome parameters were HOA,visual function and tomographic results 12 and 24 months postoperatively.Results:After 12 months,the total HOA root mean square wavefront error was reduced from 0.79±0.30 to 0.40±0.19μm(CXL-Plus;p<0.0001)and changed from 0.71±0.28 to 0.73±0.36μm(CXL;p=0.814).Uncorrected distance visual acuity improved from 0.70±0.35 to 0.36±0.29 logMAR(CXL-Plus;p=0.0002)and from 0.65±0.39 to 0.46±0.37 logMAR(CXL;p=0.067),translating to gains of three or more lines in 50%(CXL-Plus)and 36%(CXL)of patients.The steepest keratometry value(Kmax)regressed by 5.84 D(CXL-Plus;p<0.0001)and 0.66 D(CXL;p=0.752).For none of the investigated parameters a statistically significant change could be shown between 12 and 24 months.Conclusions:CXL-Plus in the form of a CCR reduces HOA and Kmax more effectively than CXL as a sole procedure.

Comparison of high order aberration after conventional and customized ablation in myopic LASIK in different eyes of the same patient

Purpose: To verify whether there exists any difference in higher order aberrations after undergoing myopic LASIK (laser in situ keratomileusis) with conventional ablation and customized ablation in different eyes of the same patient. Methods: This was a prospective randomized study of 54 myopic eyes (27 patients) that underwent LASIK using the Nidek EC-5000 ex-cimer laser system (Nidek, Gamagori, Japan). Topography-guided customized aspheric treatment zone (CATz) was used in the first eye of the patient (study group) and the other eye of the same patient was operated on with conventional ablation (control group). Higher order aberrations [root-mean-square (RMS) in the 5-mm zone] of both groups were observed with the Nidek OPD-Scan aberrometer before and 3 months after LASIK. Preoperative mean refractive error was similar between two eyes of the same patient (t=?0.577, P>0.05). Results: Preoperatively, higher order aberrations (RMS in the 5-mm zone) in the CATz ablation and conventional groups were (0.3600±0.0341) μm and (0.2680±0.1421) μm, respectively. This difference was not statistically significant (t=1.292, P>0.05). Three months after LASIK, higher order aberrations (RMS in 5-mm zone) in the CATz ablation and conventional groups were (0.3627±0.1510) μm and (0.3991±0.1582) μm, respectively. No statistically significant difference was noted between pre- and postoperative higher order aberrations in the CATz group (t=?0.047, P>0.05). However, a statistically significant increase in higher order aberrations was observed after conventional ablation (t=?5.261, P<0.05). A statistically sig-nificant difference was noted in the increase of higher order aberrations after LASIK between groups (t=?2.050, P=0.045). Con-clusion: LASIK with conventional ablation and topography-guided CATz ablation resulted in the same BSCVA (best specta-cle-corrected visual acuity) 3 month after LASIK. Higher order aberrations were increased, but the increase of higher order ab-errations after customized ablation treatment was less than that after conventional ablation.

Comparison of two types of visual quality analyzer for the measurement of high order aberrations

AIM： To compare the difference and agreement of KR- lW and iTrace for measurement of high order aberrations.METHODS： KR-1W and iTrace were respectively used in a group of healthy people （40 volunteers, 32 eyes） to measure the high order aberration （HOA） of corneal, internal and total ocular. The clinical difference and agreement of two instruments were respectively evaluated by paired-samples 1-test and Bland-Altman analysis. RESULTS： The paired-samples t-test showed that the corneal HOA measured by the two instruments had no statistical differences （P〉0.05）; but the internal and total ocular HOA had significant statistical differences （P〈 0.05）, and the mean results measured by iTrace were higher than that of KR-1W. However, Bland-Altman analysis revealed that the HOA of corneal and internal were all in 95% limits of agreement; and just one point of total ocular HOA was beyond the 95% limits of agreement. CONCLUSION： KR-1W and iTrace were consistent well in the measurement of corneal, internal and total ocular HOA, especially for the cornea.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.

Opti mal higher order learning adaptive control approach for a class of SISO nonlinear systems

In this paper, an optimal higher order learning adaptive control approach is developed for a class of SISO nonlinear systems. This design is model-free and depends directly on pseudo-partial-derivatives derived on-line from the input and output information of the system. A novel weighted one-step-ahead control criterion function is proposed for the control law. The convergence analysis shows that the proposed control law can guarantee the convergence under the assumption that the desired output is a set point. Simulation examples are provided for nonlinear systems to illustrate the better performance of the higher order learning adaptive control.

Existence of Positive Solutions for Higher Order Boundary Value Problem on Time Scales

In this paper, we investigate the existence of positive solutions of a class higher order boundary value problems on time scales. The class of boundary value problems educes a four-point （or three-point or two-point） boundary value problems, for which some similar results are established. Our approach relies on the Krasnosel＇skii fixed point theorem. The result of this paper is new and extends previously known results.

EXACT BOUNDARY CONTROLLABILITY FOR HIGHER ORDER QUASILINEAR HYPERBOLIC EQUATIONS

By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.

HIGHER ORDER SPECTRAL ANALYSIS IN FAULT DIAGNOSIS OF ROTORS

The nonlinear properties of rotating machinery vibration signals are presented. The relationship between faults and quadratic phase coupling is discussed. The mechanism that gives rise to quadratic phase coupling is analyzed, and the coupling models are summarized. As a result, higher order spectra analysis is introduced into fault diagnosis of rotors. A brief review of the properties of higher order spectra is presented. Furthermore, the bicoherence spectrum is employed to extract the features that signify the machinery condition. Experiments show that bicoherence spectrum patterns of different faults are quite different, so it is proposed to identify the faults in rotors.

On the Variational Problems of the Functionals with Derivatives of Higher Orders and Undetermined Boundary

According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.