AIM:To compare the visual outcomes and corneal higherorder aberrations(HOAs)of patients with high or low myopic astigmatism after small incision lenticule extraction(SMILE).METHODS:A total of 157 eyes of 157 patients ...AIM:To compare the visual outcomes and corneal higherorder aberrations(HOAs)of patients with high or low myopic astigmatism after small incision lenticule extraction(SMILE).METHODS:A total of 157 eyes of 157 patients who underwent SMILE were included in this retrospective,nonrandomized,comparative study.All the eyes which were with the rule astigmatism were divided into high astigmatism group(HAG;astigmatism≤-2.00 D,73 eyes)and low astigmatism group(LAG;astigmatism≥-1.00 D,84 eyes).Visual and refractive examinations were performed,HOAs of the anterior surface,posterior surface,and total cornea of the eyes were evaluated preoperatively and 6mo postoperatively.RESULTS:At the postoperative 6-month follow-up,uncorrected distance visual acuity of 20/20 or better was achieved in 97%and 100%eyes in HAG and LAG respectively and 74%and 100%eyes were within-0.50 D.Vector analysis revealed no significant differences in the correction index(P=0.066),angle of error(P=0.091)or flattening index(P=0.987)between two groups.The magnitude of error was-0.37±0.31 D in HAG and-0.04±0.19 D in LAG(P<0.001).Index of success(IOS)was 0.22±0.09 in the HAG and 0.50±0.46 in the LAG(P<0.001).HOAs of most anterior,posterior and total cornea significantly increased after SMILE,especially the spherical aberration and coma.For HAG,the SMILE procedure induced significantly higher anterior,posterior and total cornea horizontal coma and total corneal total HOAs compared with LAG(P<0.001)and these surgically induced HOAs predominantly originated from the anterior surface of the cornea.CONCLUSION:SMILE surgery induces more HOAs and a mild under-correction of astigmatism in eyes with high astigmatism.The increment in HOAs after SMILE is related to preoperative astigmatism.展开更多
BACKGROUND Myopia and high myopia are global public health concerns.Patients with high myopia account for 0.5%-5.0%of the global population.AIM To examine diopters,axial length(AL),higher-order aberrations,and other o...BACKGROUND Myopia and high myopia are global public health concerns.Patients with high myopia account for 0.5%-5.0%of the global population.AIM To examine diopters,axial length(AL),higher-order aberrations,and other ocular parameters in Chinese children with myopia,to analyze the influence of structural parameters associated with myopia on visual quality,and to provide a theoretical basis for the prevention and treatment of childhood myopia and high myopia.METHODS This study included 195 children aged 6–17 years with myopia.The AL was measured with an ultrasonic ophthalmic diagnostic instrument,and the aberrations,corneal curvature(minimum K1,maximum K2,and average Km),central corneal thickness,anterior chamber depth,and anterior chamber angle were measured using a Sirius three-dimensional anterior segment analyzer.Using a standard formula,the corneal radius of curvature R(337.3/Km)and AL/R values were obtained.RESULTS The diopter of high myopia compared with low-middle myopia was correlated with age and AL(r=-0.336,-0.405,P<0.001),and AL of high myopia was negatively correlated with K1,K2,and Km(r=-0.673,-0.661,and-0.680,respectively;P<0.001),and positively correlated with age and the anterior chamber depth(r=0.214 and 0.275,respectively;P<0.05).AL/R was more closely related to diopter than AL in children with myopia,and 94.4%of children with myopia had an AL/R of>3.00.CONCLUSION The ocular structural parameters of children change because of different diopters.AL/R is more specific and sensitive than AL in evaluating the refractive status of myopia in children.An AL/R of>3.00 may be used as a specific index of myopia in children.There are differences in AL/R between high myopia and low-middle myopia,which can be used for the classification of ametropia.The degree of myopia has a certain influence on higher-order aberrations.展开更多
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...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.展开更多
AIM: To investigate the relationship between higher- order aberration (HOA) and myopic progression in schoolchildren. ·METHODS: Between April 23 2011 and August 29, 2011 in the children’s myopia outpatient clini...AIM: To investigate the relationship between higher- order aberration (HOA) and myopic progression in schoolchildren. ·METHODS: Between April 23 2011 and August 29, 2011 in the children’s myopia outpatient clinic of the West China Hospital of Sichuan University, 148 eyes of 74 schoolchildren were reviewed. HOAs for a 6 -mm pupil were measured with an aberrometer. Myopic progression rate was defined according to the change in spherical equivalent refraction (SER) divided by the time span (years). Subjects with myopic progression rate of ≥0.50 diopters (D) were classified as the ’fast’group and the subjects with myopic progression rate of 【0.50D were classified as the’slow’group. A retrospective study was conducted to compare HOA between the two groups, using root mean square (RMS) values and Zernike coefficients. ·RESULTS: The RMS values of HOA (t =2.316, P =0.02), HOA without Z 4 0 (t =2.224, P =0.03),third-order aberrations (t’ =2.62, P =0.01), and coma (t’ =2.49, P =0.01) were significantly higher in the fast group than those in the slow group. The individual Zernike coefficients of Z 3 -1 (t = -2.072, P =0.04) and Z 5 1 (Z =-2.627, P =0.01) displayed statistically significant differences between the two groups. Significant correlations were found between the RMS values of HOA (r =0.193, P =0.019), RMS values of HOA without Z 4 0 (r =0.23, P =0.005), RMS values of coma(r =0.235,P =0.004),RMS values of third-order aberrations (r =0.243, P =0.003), and the progression rate. · CONCLUSION: Our results provide evidence of a relationship between HOA and myopic progression. In a future prospective longitudinal study, we aim to verify whether HOA is a risk factor for myopic progression.展开更多
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 wavefron...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.展开更多
AIM: To study the distribution of ocular higher-order aberrations(HOAs) and mesopic pupil size in individuals screened for refractive surgery. · METHODS: Ocular HOAs and mesopic pupil size were studied in 2 458 e...AIM: To study the distribution of ocular higher-order aberrations(HOAs) and mesopic pupil size in individuals screened for refractive surgery. · METHODS: Ocular HOAs and mesopic pupil size were studied in 2 458 eyes of 1 240 patients with myopia, myopic astigmatism and compound myopic astigmatism and 215 eyes of 110 patients with hyperopia, hyperopic astigmatism and compound hyperopic astigmatism using the Zywave aberrometer (Busch& Lomb). All patients had correctable refractive errors without a history of refractive surgery or underlying diseases. Root-mean-square values of HOAs, total spherical aberration, total coma and mesopic pupil size were analyzed. Ocular HOAs were measured across a ≥ 6.0 mm pupil, and pupil size measurements were performed under the mesopic condition. · RESULTS: The mean values of HOAs, total spherical aberration and total coma in the myopic group were 0.369 μm, ±0.233, 0.133±0.112μm and 0.330±0.188μm, respectively. In the hyperopic group the mean values of HOAs, total spherical aberration and total coma were 0.418μm±0.214, 0.202±0.209μm and 0.343±0.201μm, respectively. Hyperopes showed greater total HOAs (P <0.01) and total spherical aberration (P <0.01) compared to myopes. In age-matched analysis, only the amount of total spherical aberration was higher in the hyperopic group (P =0.05). Mesopic pupil size in the myopic group was larger (P ≤0.05). · CONCLUSION: The results suggested that significant levels of HOAs were found in both groups which are important for planning refractive surgeries on Iranians. There were significantly higher levels of total spherical aberration in hyperopes compared to myopes. Mesopic pupil size was larger in myopic group.展开更多
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 si...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.展开更多
Objective To evaluate the effects of preoperative soft contact lens (SCL) wear on higher-order aberrations(HOAs)correction after wavefront-guided and conventional laser in situ keratomileusis (LASIK). Methods A prospe...Objective To evaluate the effects of preoperative soft contact lens (SCL) wear on higher-order aberrations(HOAs)correction after wavefront-guided and conventional laser in situ keratomileusis (LASIK). Methods A prospective randomized double-masked comparative study was conducted in 180 eyes of 90 patients scheduled for LASIK, including 92 eyes of 46 patients with previous SCL wear. The patients were divided into four groups: no SCL-conventional group, SCL-conventional group, no SCL-wavefront group and SCL-wavefront group. Preoperative and postoperative examinations included uncorrected visual acuity (UCVA), best spectacle-corrected visual acuity (BSCVA), contrast sensitivity and HOAs. Results The UCVA and BSCVA were 20/20 in all patients at 6 months postoperatively. And 36.3%, 22.7%, 18.1% and 35.4% gained one line or more of BSCVA in no SCL-wavefront group, SCL-wavefront group, no SCL-conventional group and SCL-conventional group, respectively. Both the safety index and efficacy index surpassed one in 4 groups and were highest in no SCL-wavefront group. The increase in root-mean-square (RMS) values of HOAs was significantly lower in no SCL-wavefront group and higher in SCL-wavefront group. At 6 months postoperatively, the increase in RMS of HOAs (RMSh) were 0.67, 1.58, 1.17 and 1.28 in no SCL-wavefront group, SCL-wavefront group, no SCL-conventional group and SCL-conventional group, respectively. Conclusion Preoperative contact lens wear has significant influence on the efficacy of HOAs correction in wavefront-guided LASIK. Patients with contact lens wear preoperatively should be cautious when scheduled for wavefront-guided LASIK.展开更多
Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes...Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes from 75 postoperative subjects were included in this prospective study.Three consecutive corneal aberrometric measurements were obtained with the Scheimpfug-Placido topographer by two experienced operators to assess intra-and inter-observer reproducibility.The within-subject standard deviation(Sw),test-retest repeatability(TRT)and the intraclass correlation coefcient(ICC)were calculated.Results:For intraobserver repeatability of anterior and total corneal aberrations,all ICCs were more than 0.922,except for trefoil(0.722 to 0.768).The ICCs of total root mean square(RMS),coma Z(3,±1),and spherical aberration Z(4,0)were over 0.810 while higher-order RMS,trefoil Z(3,±3),and astigmatism II Z(4,±2)were below 0.634 for posterior corneal surface aberrations.All Sw values for all types of aberrations were equal to or below 0.07μm.Regarding interobserver reproducibility,all TRT values were no more than 0.12μm,0.05μm,and 0.11μm for anterior,posterior,and total corneal aberrations,respectively.The ICC values ranged from 0.875 to 0.989,from 0.686 to 0.976 and over 0.834 for anterior,posterior,and total corneal aberrations,respectively.Conclusions:The repeatability of measurements of anterior and total corneal aberrations with the Sirius system in corneas after SMILE surgery was high,except for trefoil.There was some variability in posterior corneal aberrometric measurements.High reproducibility of corneal aberrometric measurements was observed between measurements of both examiners,except for trefoil,with poor to moderate reproducibility.展开更多
Background The advent of wavefront technology in the past five years has provided some insight into the optical outcomes of cataract surgery. The Tecnis Z9001 intraocular lens （Tecnis IOL, AMO） with a modified prola...Background The advent of wavefront technology in the past five years has provided some insight into the optical outcomes of cataract surgery. The Tecnis Z9001 intraocular lens （Tecnis IOL, AMO） with a modified prolate anterior surface was claimed to reduce or even eliminate ocular spherical aberration to improve the visual quality. The purpose of this study was to determine whether Tecnis IOLs can improve the quality of vision as evaluated by measuring visual acuity, wavefront aberration, and contrast sensitivity. Methods In an intraindividual prospective study, 20 patients with bilateral cataract were randomly assigned to receive a modified prolate anterior surface IOL （Tecnis Z9001, AMO） in one eye and a biconvex spherical surface IOL （CeeOn 911A, AMO） in the other. After 3 months, the following were investigated： best corrected visual acuity, pupil diameter, photopic and mesopic contrast sensitivity, and wavefront aberration of the whole eye （ocular）, cornea, and internal plane. Results The differences in the best corrected visual acuity and pupil diameter between the two groups were not statistically significant. Negative 4th-order spherical aberration （Z4^0） was found in the Tecnis group, whereas positive Z4^0 found in the CeeOn group for the internal and ocular plane. Statistically significant differences were found at the ocular higher-aberrations between the two IOLs. Contrast sensitivity testing showed significantly better results in the Tecnis group at visual angles higher than 1.0 degree under photopic conditions and at visual angles higher than 1.6 degree under mesopic conditions both without glare and with glare in comparison with the CeeOn group. Conclusions The Tecnis Z9001 IOL with a modified prolate anterior surface produces negative spherical aberration and consequently reduces the higher-order aberrations in pseudophakic eyes. This leads to enhanced contrast sensitivity and improved functional vision compared to conventional spherical IOLs.展开更多
Background:Intraocular lens(IOL)calcification is a serious condition that can only be treated by removing the clouded lens.Since explantation bears the risk of complications,it is often deferred until the patient find...Background:Intraocular lens(IOL)calcification is a serious condition that can only be treated by removing the clouded lens.Since explantation bears the risk of complications,it is often deferred until the patient finds the symptoms intolerable.Usually,as the IOL opacifies,visual acuity is minimally affected early on.In this study,we assessed the impact of IOL opacification on optical quality.Methods:We analyzed ten opacified explanted IOLs(Oculentis GmbH).Wavefront aberrations were obtained with a SHSOphthalmic device(Optocraft GmbH),which features a Hartmann-Shack sensor.The root mean square(RMS)of higher-order aberrations(HOAs)was compared.The effect of calcification on image quality was assessed through the Strehl ratio(SR).We detected light scattering with a C-Quant(Oculus GmbH)and expressed it as a straylight parameter.Results:At 2 mm,3mm and 4 mm,the mean RMS(±standard deviation)was 0.033μm(±0.026μm),0.044μm(±0.027),and 0.087μm(±0.049),respectively.The mean SR value was 0.81±0.15 at 3 mm,with four IOLs showing a nearly diffraction-limited performance,but in two explants,opacification precluded reliable measurements.Increased straylight was found in all opacified IOLs with a mean value of 150.2±56.3 deg^(2)/sr at 3 mm.Conclusions:We demonstrated that IOL opacification induces HOAs.However,the RMS remained low,which resulted only in a slight reduction of the SR-derived optical quality.On the other hand,we found a severe straylight elevation in the opacified lenses,which may result in dysphotopsia,such as glare,and subjective complaints,despite good visual acuity.展开更多
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&...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±0.19 pm(CXL-Plus;P<0.0001)and changed from 0.71±0.28 to 0.73±0.36 pm(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=0752).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.展开更多
Restoration of phase aberrations is crucial for addressing atmospheric turbulence in light propagation.Traditional restoration algorithms based on Zernike polynomials(ZPs)often encounter challenges related to high com...Restoration of phase aberrations is crucial for addressing atmospheric turbulence in light propagation.Traditional restoration algorithms based on Zernike polynomials(ZPs)often encounter challenges related to high computational complexity and insufficient capture of high-frequency phase aberration components,so we proposed a Principal-Component-Analysis-based method for representing phase aberrations.This paper discusses the factors influencing the accuracy of restoration,mainly including the sample space size and the sampling interval of D/r_(0),on the basis of characterizing phase aberrations by Principal Components(PCs).The experimental results show that a larger D/r_(0)sampling interval can ensure the generalization ability and robustness of the principal components in the case of a limited amount of original data,which can help to achieve high-precision deployment of the model in practical applications quickly.In the environment with relatively strong turbulence in the test set of D/r_(0)=24,the use of 34 terms of PCs can improve the corrected Strehl ratio(SR)from 0.007 to 0.1585,while the Strehl ratio of the light spot after restoration using 34 terms of ZPs is only 0.0215,demonstrating almost no correction effect.The results indicate that PCs can serve as a better alternative in representing and restoring the characteristics of atmospheric turbulence induced phase aberrations.These findings pave the way to use PCs of phase aberrations with fewer terms than traditional ZPs to achieve data dimensionality reduction,and offer a reference to accelerate and stabilize the model and deep learning based adaptive optics correction.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
Background To comprehensively evaluate the agreement of component corneal aberrations from the newly updated wavefront analysis software of a swept-source optical coherence tomographer(SS-OcT)and a referential Placido...Background To comprehensively evaluate the agreement of component corneal aberrations from the newly updated wavefront analysis software of a swept-source optical coherence tomographer(SS-OcT)and a referential Placido-topography combined OcT device in elderly cataract patients.Methods Retrospective study including 103 eyes from 103 elderly patients scheduled for cataract surgery that were measured on the same day with a SS-OcT(Heidelberg Engineering,Germany)device and a Placido-topography combined OCT device(CsO,Italy).Anterior,total,and posterior corneal wavefront aberrations were evaluated for their mean differences and limits of agreement(LoA)via Bland-Altman plots.Vector analysis was additionally employed to compare corneal astigmatism measurements in dioptric vector space.Results Mean differences of all corneal aberrometric parameters did not exceed O.05 um.Total corneal aberrations were not significantly different from 0 except for vertical coma(-0.04μm;P=0.003),spherical aberration(-0.01μm,P<0.001),and root mean square(RMS)higher-order aberration(HOA)(0.03μm,P=0.04).The 95%LoA for total corneal aberration parameters between both devices were-0.46 to 0.42μm for horizontal astigmatism,-0.37 to 0.41μm for oblique astigmatism,-0.19 to 0.17μm for oblique trefoil,-0.33 to 0.25μm for vertical coma,-0.20 to 0.22μm for horizontal coma,-0.22 to 0.20 um for horizontal trefoil,-0.11 to 0.08μm for spherical aberration,and-0.22 to 0.28 um for RMs HOA.Vector analysis revealed no statistically significant mean differences for anterior,total,and posterior corneal astigmatism in dioptric vector space.Conclusion In eyes undergoing cataract surgery with a regular elderly cornea,corneal wavefront analysis from the SS-OcT device showed functional equivalency to the reference device.Nevertheless,clinically relevant higher-order aberration parameters should be interpreted with caution for surgical decision-making.展开更多
This article briefly reviews the topic of complex network synchronization,with its graph-theoretic criterion,showing that the homogeneous and symmetrical network structures are essential for optimal synchronization.Fu...This article briefly reviews the topic of complex network synchronization,with its graph-theoretic criterion,showing that the homogeneous and symmetrical network structures are essential for optimal synchronization.Furthermore,it briefly reviews the notion of higher-order network topologies and shows their promising potential in application to evaluating the optimality of network synchronizability.展开更多
Information spreading has been investigated for many years,but the mechanism of why the information explosively catches on overnight is still under debate.This explosive spreading phenomenon was usually considered dri...Information spreading has been investigated for many years,but the mechanism of why the information explosively catches on overnight is still under debate.This explosive spreading phenomenon was usually considered driven separately by social reinforcement or higher-order interactions.However,due to the limitations of empirical data and theoretical analysis,how the higher-order network structure affects the explosive information spreading under the role of social reinforcement has not been fully explored.In this work,we propose an information-spreading model by considering the social reinforcement in real and synthetic higher-order networks,describable as hypergraphs.Depending on the average group size(hyperedge cardinality)and node membership(hyperdegree),we observe two different spreading behaviors:(i)The spreading progress is not sensitive to social reinforcement,resulting in the information localized in a small part of nodes;(ii)a strong social reinforcement will promote the large-scale spread of information and induce an explosive transition.Moreover,a large average group size and membership would be beneficial to the appearance of the explosive transition.Further,we display that the heterogeneity of the node membership and group size distributions benefit the information spreading.Finally,we extend the group-based approximate master equations to verify the simulation results.Our findings may help us to comprehend the rapidly information-spreading phenomenon in modern society.展开更多
Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reac...Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reactor core. Both the deterministic method and the Monte Carlo(MC) method can be used to solve the higher-order modes. However, MC method, compared to the deterministic method, faces challenges in terms of computational efficiency and α mode calculation stability, whereas the deterministic method encounters issues arising from homogenization-related geometric and energy spectra adaptation.Based on the higher-order mode diffusion calculation code HARMONY, we developed a new higher-order mode calculation code, HARMONY2.0, which retains the functionality of computing λ and α higher-order modes from HARMONY1.0, but enhances the ability to treat complex geometries and arbitrary energy spectra using the MC-deterministic hybrid two-step strategy. In HARMONY2.0, the mesh homogenized multigroup constants were obtained using OpenMC in the first step,and higher-order modes were then calculated with the mesh homogenized core diffusion model using the implicitly restarted Arnoldi method(IRAM), which was also adopted in the HARMONY1.0 code. In addition, to improve the calculation efficiency, particularly in large higher-order modes, event-driven parallelization/domain decomposition methods are embedded in the HARMONY2.0 code to accelerate the inner iteration of λ∕α mode using OpenMP. Furthermore, the higher-order modes of complex geometric models, such as Hoogenboom and ATR reactors for λ mode and the MUSE-4 experiment facility for the prompt α mode, were computed using diffusion theory.展开更多
The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.Th...The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.展开更多
文摘AIM:To compare the visual outcomes and corneal higherorder aberrations(HOAs)of patients with high or low myopic astigmatism after small incision lenticule extraction(SMILE).METHODS:A total of 157 eyes of 157 patients who underwent SMILE were included in this retrospective,nonrandomized,comparative study.All the eyes which were with the rule astigmatism were divided into high astigmatism group(HAG;astigmatism≤-2.00 D,73 eyes)and low astigmatism group(LAG;astigmatism≥-1.00 D,84 eyes).Visual and refractive examinations were performed,HOAs of the anterior surface,posterior surface,and total cornea of the eyes were evaluated preoperatively and 6mo postoperatively.RESULTS:At the postoperative 6-month follow-up,uncorrected distance visual acuity of 20/20 or better was achieved in 97%and 100%eyes in HAG and LAG respectively and 74%and 100%eyes were within-0.50 D.Vector analysis revealed no significant differences in the correction index(P=0.066),angle of error(P=0.091)or flattening index(P=0.987)between two groups.The magnitude of error was-0.37±0.31 D in HAG and-0.04±0.19 D in LAG(P<0.001).Index of success(IOS)was 0.22±0.09 in the HAG and 0.50±0.46 in the LAG(P<0.001).HOAs of most anterior,posterior and total cornea significantly increased after SMILE,especially the spherical aberration and coma.For HAG,the SMILE procedure induced significantly higher anterior,posterior and total cornea horizontal coma and total corneal total HOAs compared with LAG(P<0.001)and these surgically induced HOAs predominantly originated from the anterior surface of the cornea.CONCLUSION:SMILE surgery induces more HOAs and a mild under-correction of astigmatism in eyes with high astigmatism.The increment in HOAs after SMILE is related to preoperative astigmatism.
基金Supported by Scientific Research Project of Heilongjiang Health Commission,China,No.2020-141.
文摘BACKGROUND Myopia and high myopia are global public health concerns.Patients with high myopia account for 0.5%-5.0%of the global population.AIM To examine diopters,axial length(AL),higher-order aberrations,and other ocular parameters in Chinese children with myopia,to analyze the influence of structural parameters associated with myopia on visual quality,and to provide a theoretical basis for the prevention and treatment of childhood myopia and high myopia.METHODS This study included 195 children aged 6–17 years with myopia.The AL was measured with an ultrasonic ophthalmic diagnostic instrument,and the aberrations,corneal curvature(minimum K1,maximum K2,and average Km),central corneal thickness,anterior chamber depth,and anterior chamber angle were measured using a Sirius three-dimensional anterior segment analyzer.Using a standard formula,the corneal radius of curvature R(337.3/Km)and AL/R values were obtained.RESULTS The diopter of high myopia compared with low-middle myopia was correlated with age and AL(r=-0.336,-0.405,P<0.001),and AL of high myopia was negatively correlated with K1,K2,and Km(r=-0.673,-0.661,and-0.680,respectively;P<0.001),and positively correlated with age and the anterior chamber depth(r=0.214 and 0.275,respectively;P<0.05).AL/R was more closely related to diopter than AL in children with myopia,and 94.4%of children with myopia had an AL/R of>3.00.CONCLUSION The ocular structural parameters of children change because of different diopters.AL/R is more specific and sensitive than AL in evaluating the refractive status of myopia in children.An AL/R of>3.00 may be used as a specific index of myopia in children.There are differences in AL/R between high myopia and low-middle myopia,which can be used for the classification of ametropia.The degree of myopia has a certain influence on higher-order aberrations.
文摘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.
基金Sichuan Province Scientific Plan Project,China (No. 2010SZ0087)
文摘AIM: To investigate the relationship between higher- order aberration (HOA) and myopic progression in schoolchildren. ·METHODS: Between April 23 2011 and August 29, 2011 in the children’s myopia outpatient clinic of the West China Hospital of Sichuan University, 148 eyes of 74 schoolchildren were reviewed. HOAs for a 6 -mm pupil were measured with an aberrometer. Myopic progression rate was defined according to the change in spherical equivalent refraction (SER) divided by the time span (years). Subjects with myopic progression rate of ≥0.50 diopters (D) were classified as the ’fast’group and the subjects with myopic progression rate of 【0.50D were classified as the’slow’group. A retrospective study was conducted to compare HOA between the two groups, using root mean square (RMS) values and Zernike coefficients. ·RESULTS: The RMS values of HOA (t =2.316, P =0.02), HOA without Z 4 0 (t =2.224, P =0.03),third-order aberrations (t’ =2.62, P =0.01), and coma (t’ =2.49, P =0.01) were significantly higher in the fast group than those in the slow group. The individual Zernike coefficients of Z 3 -1 (t = -2.072, P =0.04) and Z 5 1 (Z =-2.627, P =0.01) displayed statistically significant differences between the two groups. Significant correlations were found between the RMS values of HOA (r =0.193, P =0.019), RMS values of HOA without Z 4 0 (r =0.23, P =0.005), RMS values of coma(r =0.235,P =0.004),RMS values of third-order aberrations (r =0.243, P =0.003), and the progression rate. · CONCLUSION: Our results provide evidence of a relationship between HOA and myopic progression. In a future prospective longitudinal study, we aim to verify whether HOA is a risk factor for myopic progression.
文摘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.
文摘AIM: To study the distribution of ocular higher-order aberrations(HOAs) and mesopic pupil size in individuals screened for refractive surgery. · METHODS: Ocular HOAs and mesopic pupil size were studied in 2 458 eyes of 1 240 patients with myopia, myopic astigmatism and compound myopic astigmatism and 215 eyes of 110 patients with hyperopia, hyperopic astigmatism and compound hyperopic astigmatism using the Zywave aberrometer (Busch& Lomb). All patients had correctable refractive errors without a history of refractive surgery or underlying diseases. Root-mean-square values of HOAs, total spherical aberration, total coma and mesopic pupil size were analyzed. Ocular HOAs were measured across a ≥ 6.0 mm pupil, and pupil size measurements were performed under the mesopic condition. · RESULTS: The mean values of HOAs, total spherical aberration and total coma in the myopic group were 0.369 μm, ±0.233, 0.133±0.112μm and 0.330±0.188μm, respectively. In the hyperopic group the mean values of HOAs, total spherical aberration and total coma were 0.418μm±0.214, 0.202±0.209μm and 0.343±0.201μm, respectively. Hyperopes showed greater total HOAs (P <0.01) and total spherical aberration (P <0.01) compared to myopes. In age-matched analysis, only the amount of total spherical aberration was higher in the hyperopic group (P =0.05). Mesopic pupil size in the myopic group was larger (P ≤0.05). · CONCLUSION: The results suggested that significant levels of HOAs were found in both groups which are important for planning refractive surgeries on Iranians. There were significantly higher levels of total spherical aberration in hyperopes compared to myopes. Mesopic pupil size was larger in myopic group.
文摘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.
文摘Objective To evaluate the effects of preoperative soft contact lens (SCL) wear on higher-order aberrations(HOAs)correction after wavefront-guided and conventional laser in situ keratomileusis (LASIK). Methods A prospective randomized double-masked comparative study was conducted in 180 eyes of 90 patients scheduled for LASIK, including 92 eyes of 46 patients with previous SCL wear. The patients were divided into four groups: no SCL-conventional group, SCL-conventional group, no SCL-wavefront group and SCL-wavefront group. Preoperative and postoperative examinations included uncorrected visual acuity (UCVA), best spectacle-corrected visual acuity (BSCVA), contrast sensitivity and HOAs. Results The UCVA and BSCVA were 20/20 in all patients at 6 months postoperatively. And 36.3%, 22.7%, 18.1% and 35.4% gained one line or more of BSCVA in no SCL-wavefront group, SCL-wavefront group, no SCL-conventional group and SCL-conventional group, respectively. Both the safety index and efficacy index surpassed one in 4 groups and were highest in no SCL-wavefront group. The increase in root-mean-square (RMS) values of HOAs was significantly lower in no SCL-wavefront group and higher in SCL-wavefront group. At 6 months postoperatively, the increase in RMS of HOAs (RMSh) were 0.67, 1.58, 1.17 and 1.28 in no SCL-wavefront group, SCL-wavefront group, no SCL-conventional group and SCL-conventional group, respectively. Conclusion Preoperative contact lens wear has significant influence on the efficacy of HOAs correction in wavefront-guided LASIK. Patients with contact lens wear preoperatively should be cautious when scheduled for wavefront-guided LASIK.
基金the Medical and Health Science and Technology Program of Zhejiang Province(2019KY111)Foundation of Wenzhou City Science&Technology Bureau(Y2020037)+1 种基金EYE&ENT Hospital of Fudan University High-level Talents Program(2021318)Clinical Research Plan of SHDC(SHDC2020CR1043B)。
文摘Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes from 75 postoperative subjects were included in this prospective study.Three consecutive corneal aberrometric measurements were obtained with the Scheimpfug-Placido topographer by two experienced operators to assess intra-and inter-observer reproducibility.The within-subject standard deviation(Sw),test-retest repeatability(TRT)and the intraclass correlation coefcient(ICC)were calculated.Results:For intraobserver repeatability of anterior and total corneal aberrations,all ICCs were more than 0.922,except for trefoil(0.722 to 0.768).The ICCs of total root mean square(RMS),coma Z(3,±1),and spherical aberration Z(4,0)were over 0.810 while higher-order RMS,trefoil Z(3,±3),and astigmatism II Z(4,±2)were below 0.634 for posterior corneal surface aberrations.All Sw values for all types of aberrations were equal to or below 0.07μm.Regarding interobserver reproducibility,all TRT values were no more than 0.12μm,0.05μm,and 0.11μm for anterior,posterior,and total corneal aberrations,respectively.The ICC values ranged from 0.875 to 0.989,from 0.686 to 0.976 and over 0.834 for anterior,posterior,and total corneal aberrations,respectively.Conclusions:The repeatability of measurements of anterior and total corneal aberrations with the Sirius system in corneas after SMILE surgery was high,except for trefoil.There was some variability in posterior corneal aberrometric measurements.High reproducibility of corneal aberrometric measurements was observed between measurements of both examiners,except for trefoil,with poor to moderate reproducibility.
文摘Background The advent of wavefront technology in the past five years has provided some insight into the optical outcomes of cataract surgery. The Tecnis Z9001 intraocular lens （Tecnis IOL, AMO） with a modified prolate anterior surface was claimed to reduce or even eliminate ocular spherical aberration to improve the visual quality. The purpose of this study was to determine whether Tecnis IOLs can improve the quality of vision as evaluated by measuring visual acuity, wavefront aberration, and contrast sensitivity. Methods In an intraindividual prospective study, 20 patients with bilateral cataract were randomly assigned to receive a modified prolate anterior surface IOL （Tecnis Z9001, AMO） in one eye and a biconvex spherical surface IOL （CeeOn 911A, AMO） in the other. After 3 months, the following were investigated： best corrected visual acuity, pupil diameter, photopic and mesopic contrast sensitivity, and wavefront aberration of the whole eye （ocular）, cornea, and internal plane. Results The differences in the best corrected visual acuity and pupil diameter between the two groups were not statistically significant. Negative 4th-order spherical aberration （Z4^0） was found in the Tecnis group, whereas positive Z4^0 found in the CeeOn group for the internal and ocular plane. Statistically significant differences were found at the ocular higher-aberrations between the two IOLs. Contrast sensitivity testing showed significantly better results in the Tecnis group at visual angles higher than 1.0 degree under photopic conditions and at visual angles higher than 1.6 degree under mesopic conditions both without glare and with glare in comparison with the CeeOn group. Conclusions The Tecnis Z9001 IOL with a modified prolate anterior surface produces negative spherical aberration and consequently reduces the higher-order aberrations in pseudophakic eyes. This leads to enhanced contrast sensitivity and improved functional vision compared to conventional spherical IOLs.
基金supported by an unrestricted research grant from the Klaus Tschira FoundationHeidelberg,Germany.T.Yildirim is funded by the Physician-Scientist Program of the Heidelberg University,Faculty of Medicine.
文摘Background:Intraocular lens(IOL)calcification is a serious condition that can only be treated by removing the clouded lens.Since explantation bears the risk of complications,it is often deferred until the patient finds the symptoms intolerable.Usually,as the IOL opacifies,visual acuity is minimally affected early on.In this study,we assessed the impact of IOL opacification on optical quality.Methods:We analyzed ten opacified explanted IOLs(Oculentis GmbH).Wavefront aberrations were obtained with a SHSOphthalmic device(Optocraft GmbH),which features a Hartmann-Shack sensor.The root mean square(RMS)of higher-order aberrations(HOAs)was compared.The effect of calcification on image quality was assessed through the Strehl ratio(SR).We detected light scattering with a C-Quant(Oculus GmbH)and expressed it as a straylight parameter.Results:At 2 mm,3mm and 4 mm,the mean RMS(±standard deviation)was 0.033μm(±0.026μm),0.044μm(±0.027),and 0.087μm(±0.049),respectively.The mean SR value was 0.81±0.15 at 3 mm,with four IOLs showing a nearly diffraction-limited performance,but in two explants,opacification precluded reliable measurements.Increased straylight was found in all opacified IOLs with a mean value of 150.2±56.3 deg^(2)/sr at 3 mm.Conclusions:We demonstrated that IOL opacification induces HOAs.However,the RMS remained low,which resulted only in a slight reduction of the SR-derived optical quality.On the other hand,we found a severe straylight elevation in the opacified lenses,which may result in dysphotopsia,such as glare,and subjective complaints,despite good visual acuity.
文摘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±0.19 pm(CXL-Plus;P<0.0001)and changed from 0.71±0.28 to 0.73±0.36 pm(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=0752).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.
文摘Restoration of phase aberrations is crucial for addressing atmospheric turbulence in light propagation.Traditional restoration algorithms based on Zernike polynomials(ZPs)often encounter challenges related to high computational complexity and insufficient capture of high-frequency phase aberration components,so we proposed a Principal-Component-Analysis-based method for representing phase aberrations.This paper discusses the factors influencing the accuracy of restoration,mainly including the sample space size and the sampling interval of D/r_(0),on the basis of characterizing phase aberrations by Principal Components(PCs).The experimental results show that a larger D/r_(0)sampling interval can ensure the generalization ability and robustness of the principal components in the case of a limited amount of original data,which can help to achieve high-precision deployment of the model in practical applications quickly.In the environment with relatively strong turbulence in the test set of D/r_(0)=24,the use of 34 terms of PCs can improve the corrected Strehl ratio(SR)from 0.007 to 0.1585,while the Strehl ratio of the light spot after restoration using 34 terms of ZPs is only 0.0215,demonstrating almost no correction effect.The results indicate that PCs can serve as a better alternative in representing and restoring the characteristics of atmospheric turbulence induced phase aberrations.These findings pave the way to use PCs of phase aberrations with fewer terms than traditional ZPs to achieve data dimensionality reduction,and offer a reference to accelerate and stabilize the model and deep learning based adaptive optics correction.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
文摘Background To comprehensively evaluate the agreement of component corneal aberrations from the newly updated wavefront analysis software of a swept-source optical coherence tomographer(SS-OcT)and a referential Placido-topography combined OcT device in elderly cataract patients.Methods Retrospective study including 103 eyes from 103 elderly patients scheduled for cataract surgery that were measured on the same day with a SS-OcT(Heidelberg Engineering,Germany)device and a Placido-topography combined OCT device(CsO,Italy).Anterior,total,and posterior corneal wavefront aberrations were evaluated for their mean differences and limits of agreement(LoA)via Bland-Altman plots.Vector analysis was additionally employed to compare corneal astigmatism measurements in dioptric vector space.Results Mean differences of all corneal aberrometric parameters did not exceed O.05 um.Total corneal aberrations were not significantly different from 0 except for vertical coma(-0.04μm;P=0.003),spherical aberration(-0.01μm,P<0.001),and root mean square(RMS)higher-order aberration(HOA)(0.03μm,P=0.04).The 95%LoA for total corneal aberration parameters between both devices were-0.46 to 0.42μm for horizontal astigmatism,-0.37 to 0.41μm for oblique astigmatism,-0.19 to 0.17μm for oblique trefoil,-0.33 to 0.25μm for vertical coma,-0.20 to 0.22μm for horizontal coma,-0.22 to 0.20 um for horizontal trefoil,-0.11 to 0.08μm for spherical aberration,and-0.22 to 0.28 um for RMs HOA.Vector analysis revealed no statistically significant mean differences for anterior,total,and posterior corneal astigmatism in dioptric vector space.Conclusion In eyes undergoing cataract surgery with a regular elderly cornea,corneal wavefront analysis from the SS-OcT device showed functional equivalency to the reference device.Nevertheless,clinically relevant higher-order aberration parameters should be interpreted with caution for surgical decision-making.
基金Hong Kong Research Grants Council under the GRF(9043664).
文摘This article briefly reviews the topic of complex network synchronization,with its graph-theoretic criterion,showing that the homogeneous and symmetrical network structures are essential for optimal synchronization.Furthermore,it briefly reviews the notion of higher-order network topologies and shows their promising potential in application to evaluating the optimality of network synchronizability.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12305043 and 12165016)the Natural Science Foundation of Jiangsu Province(Grant No.BK20220511)+1 种基金the Project of Undergraduate Scientific Research(Grant No.22A684)the support from the Jiangsu Specially-Appointed Professor Program。
文摘Information spreading has been investigated for many years,but the mechanism of why the information explosively catches on overnight is still under debate.This explosive spreading phenomenon was usually considered driven separately by social reinforcement or higher-order interactions.However,due to the limitations of empirical data and theoretical analysis,how the higher-order network structure affects the explosive information spreading under the role of social reinforcement has not been fully explored.In this work,we propose an information-spreading model by considering the social reinforcement in real and synthetic higher-order networks,describable as hypergraphs.Depending on the average group size(hyperedge cardinality)and node membership(hyperdegree),we observe two different spreading behaviors:(i)The spreading progress is not sensitive to social reinforcement,resulting in the information localized in a small part of nodes;(ii)a strong social reinforcement will promote the large-scale spread of information and induce an explosive transition.Moreover,a large average group size and membership would be beneficial to the appearance of the explosive transition.Further,we display that the heterogeneity of the node membership and group size distributions benefit the information spreading.Finally,we extend the group-based approximate master equations to verify the simulation results.Our findings may help us to comprehend the rapidly information-spreading phenomenon in modern society.
基金supported by the National Natural Science Foundation of China(No.U2267207)Science and Technology on Reactor System Design Technology Laboratory(No.KFKT-05-FWHTWU-2023004).
文摘Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reactor core. Both the deterministic method and the Monte Carlo(MC) method can be used to solve the higher-order modes. However, MC method, compared to the deterministic method, faces challenges in terms of computational efficiency and α mode calculation stability, whereas the deterministic method encounters issues arising from homogenization-related geometric and energy spectra adaptation.Based on the higher-order mode diffusion calculation code HARMONY, we developed a new higher-order mode calculation code, HARMONY2.0, which retains the functionality of computing λ and α higher-order modes from HARMONY1.0, but enhances the ability to treat complex geometries and arbitrary energy spectra using the MC-deterministic hybrid two-step strategy. In HARMONY2.0, the mesh homogenized multigroup constants were obtained using OpenMC in the first step,and higher-order modes were then calculated with the mesh homogenized core diffusion model using the implicitly restarted Arnoldi method(IRAM), which was also adopted in the HARMONY1.0 code. In addition, to improve the calculation efficiency, particularly in large higher-order modes, event-driven parallelization/domain decomposition methods are embedded in the HARMONY2.0 code to accelerate the inner iteration of λ∕α mode using OpenMP. Furthermore, the higher-order modes of complex geometric models, such as Hoogenboom and ATR reactors for λ mode and the MUSE-4 experiment facility for the prompt α mode, were computed using diffusion theory.
文摘The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.
