Third-order aberration analysis of tilted-pupil optical systems

The aberration field of an optical system with a tilted pupil is explored through expanding the vector expressions of the third-order wavefront aberrations. First, the vector forms of the wavefront aberrations are modified to obtain the aberration expressions with the pupil tilted; full field displays of coma and astigmatism in this situation are given. Then, the third-order aberration formulas with the pupil decentered and tilted simultaneously are derived and discussed. Finally, an example is taken to certify the validity of aberration distribution properties.

Broadband third-order optical nonlinearities of layered franckeite towards mid-infrared regime

The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.

Multidimensional images and aberrations in STEM

Recent advances in scanning transmission electron microscopy(STEM)have led to increased development of multidimensional STEM imaging modalities and novel image reconstruction methods.This interest arises because the main electron lens in a modern transmission electron microscope usually has a diffraction-space information limit that is significantly better than the real-space resolution of the same lens.This state-of-affairs is sometimes shared by other scattering methods in modern physics and contributes to a broader excitement surrounding multidimensional techniques that scan a probe while recording diffraction-space images,such as ptychography and scanning nano-beam diffraction.However,the contrasting resolution in the two spaces raises the question as to what is limiting their effective performance.Here,we examine this paradox by considering the effects of aberrations in both image and diffraction planes,and likewise separate the contributions of pre-and post-sample aberrations.This consideration provides insight into aberration-measurement techniques and might also indicate improvements for super-resolution techniques.

Stimulated Raman scattering microscopy with phase-controlled light focusing and aberration correction for rapid and label-free, volumetric deep tissue imaging

We report a novel stimulated Raman scattering(SRS)microscopy technique featuring phase-controlled light focusing and aberration corrections for rapid,deep tissue 3D chemical imaging with subcellular resolution.To accomplish phasecontrolled SRS(PC-SRS),we utilize a single spatial light modulator to electronically tune the axial positioning of both the shortened-length Bessel pump and the focused Gaussian Stokes beams,enabling z-scanning-free optical sectioning in the sample.By incorporating Zernike polynomials into the phase patterns,we simultaneously correct the system aberrations at two separate wavelengths(~240 nm difference),achieving a~3-fold enhancement in signal-to-noise ratio over the uncorrected imaging system.PC-SRS provides>2-fold improvement in imaging depth in various samples(e.g.,polystyrene bead phantoms,porcine brain tissue)as well as achieves SRS 3D imaging speed of~13 Hz per volume for real-time monitoring of Brownian motion of polymer beads in water,superior to conventional point-scanning SRS 3D imaging.We further utilize PC-SRS to observe the metabolic activities of the entire tumor liver in living zebrafish in cellsilent region,unraveling the upregulated metabolism in liver tumor compared to normal liver.This work shows that PCSRS provides unprecedented insights into morpho-chemistry,metabolic and dynamic functioning of live cells and tissue in real-time at the subcellular level.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

Phase aberration correction in ultrasonic phased array non-destructive testing systems

Phase aberration correction for medical ultrasound systems has attracted a great deal of attention. Since phased array techniques are now widely employed for industrial non-destructive testing （NDT） applications in various fields, the problem of phase aberrations in the process of NDT testing is considered. The technique of cross-covariance for phase aberration correction is presented. The performance of the technique for phase aberration correction is tested by means of echo signals obtained in practical non-destructive testing experiment. The results show that the technique has the better accuracy of phase correction.

Effect of Varieties on Tea Pigment and Chromatic Aberration of Black Tea Infusion

Effects of varieties on the content of tea pigment, L＊, a＊ and b＊ value of chromatic aberration of black tea infusion was studied. The correlation relationship between content of TF, TR, TB and L＊, a＊, b＊ value was extremely significant at P＆lt;0.05. Fresh tea leaves with plucking standard of 1 bud and 2 leaves could man-ufacture black tea with higher content of tea pigment, higher a＊ and b＊ value but lower L＊ value, than those of plucking standard of 1 bud and 3 leaves. But the discrepancy of certain parameter of the two plucking standards changed with vari-eties. Varieties’ quality potential could be concealed by improper plucking standards. Six varieties were divided into four groups on the basis of gross tea polyphenols in fresh tea leaves （GTP）, consumption of tea polyphenols to gross tea polyphenols ratio （CTP/GTP） and gross tea pigment to consumption of tea polyphenols ratio （GP/CTP）. Hybrid performed the very suitability of black tea manufacturing. To en-sure high quality of made black tea, suitable variety should be chosen and reason-able plucking standard also should be taken into consideration.

MicroRNA aberrations:An emerging field for gallbladdercancer management

Gallbladder cancer(GBC) is infrequent but most lethal biliary tract malignancy characterized by an advanced stage diagnosis and poor survival rates attributed to absence of specific symptoms and effective treatment options. These necessitate development of early prognostic/predictive markers and novel therapeutic interventions. Micro RNAs(mi RNAs) are small, noncoding RNA molecules that play a key role in tumor biology by functioning like tumor suppressor- or oncogenes and their aberrant expression are associated with the pathogenesis of several neoplasms with overwhelming clinical implications. Since mi RNA signature is tissue specific, here, we focused on current data concerning the mi RNAs abberations in GBC pathogenesis. In GBC, mi RNAs with tumor suppressor activity(mi R-135-5p, mi R-335, mi R-34 a, mi R-26 a, mi R-146b-5p, Mir-218-5p, mi R-1, mi R-145, mir-130a) were found downregulated, while those with oncogenic property(mi R-20 a, mi R-182, mir-155) were upregulated. The expression profile of mi RNAs was significantly associated with GBC prognosis and prediction, and forced over-expression/ inhibition of these mi RNAs was shown to affect tumor growth and development. Further, differential expression of mi RNAs in the blood samples of GBC patients suggest mi RNAs as promising noninvasive biomarker. Thus, mi RNAs represent potential candidate for GBC management, though many hurdles need to be overcome before mi RNAs therapy can be clinically applied to GBC prevention and treatment.

High order aberration and straylight evaluation after cataract surgery with implantation of an aspheric,aberration correcting monofocal intraocular lens

·AIM: To evaluate the quality of vision in respect to high order aberrations and straylight perception after implantation of an aspheric, aberration correcting,monofocal intraocular lens(IOL).·METHODS: Twenty-one patients(34 eyes) aged 50 to83 y underwent cataract surgery with implantation of an aspheric, aberration correcting IOL(Tecnis ZCB00,Abbott Medical Optics). Three months after surgery they were examined for uncorrected(UDVA) and corrected distance visual acuity(CDVA), contrast sensitivity(CS)under photopic and mesopic conditions with and without glare source, ocular high order aberrations(HOA, Zywave II) and retinal straylight(C-Quant).· RESULTS: Postoperatively, patients achieved a postoperative CDVA of 0.0 log MAR or better in 97.1% of eyes. Mean values of high order abberations were +0.02±0.27(primary coma components) and-0.04 ±0.16(spherical aberration term). Straylight values of the C-Quant were 1.35±0.44 log which is within normal range of age matched phakic patients. The CS measurements under mesopic and photopic conditions in combination with and without glare did not show any statistical significance in the patient group observed(P ≥0.28).· CONCLUSION: The implantation of an aspherical aberration correcting monofocal IOL after cataractsurgery resulted in very low residual higher order aberration(HOA) and normal straylight.

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.

Visual and optical performance of eyes with different corneal spherical aberration implanted with aspheric intraocular lens

AIM: To compare the visual and optical performance of eyes with different corneal spherical aberration (SA) implanted with spherical aberration-free intraocular lens (IOLs). METHODS: Thirty-six patients with different corneal SA had phacoemulsification with implantation of spherical aberration-free IOLs. Patients were divided into 3 groups according to the value of preoperative corneal SA. Eyes with corneal SA <0.10 mu m were assigned to group A, those with 0.10 <= corneal SA <0.20 mu m to Group B, and those with 0.20 <= corneal SA <0.35 mu m to Group C. Best-corrected visual acuity (BCVA), contrast sensitivity, corneal SA, total ocular aberrations, and depth of focus were recorded 3 months postoperatively. Distance-corrected near and intermediate visual acuity was studied to measure depth of focus. RESULTS: BCVA and contrast sensitivity were similar between groups. There were no significant differences in distance-corrected near or intermediate visual acuity. Corneal SA was similar before and 3 months after surgery in the 3 groups. With a 5.0mm pupil diameter, root mean square values for total ocular higher-order aberrations (HOAs) were lower in groups A and B than in group C. Total ocular SA was lower in group A than in groups B and C. SA was also lower in group B than in group C. Coma and trefoil were similar between the groups. CONCLUSION: Implantation of spherical aberration-free IOLs in eyes with different corneal SA results in similar visual performance at BCVA, contrast sensitivity and depth of focus.

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.

Relationship between higher-order aberrations and myopia progression in schoolchildren: a retrospective study

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.

Conformal optical design with combination of static and dynamic aberration corrections

Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aberrations are induced which vary with the field-of-regard （FOR） angle. A system for correcting optical aberrations created by a conformal dome has an outer surface and an inner surface. Optimizing the inner surface is regard as static aberration correction. A deformable mirror is placed at the position of the secondary mirror in the two-mirror all reflective imaging system, which is the dynamic aberration correction. An ellipsoidal MgF2 conformal dome with a fineness ratio of 1.0 is designed as an example. The FOR angle is 0°-30°, and the design wavelength is 4μm. After the optimization at 7 zoom positions by using the design tools Code V, the root-mean-square （RMS） spot size is reduced to approximately 0.99 to 1.48 times the diffraction limit. The design results show that the performances of the conformal optical systems can be greatly improved by the combination of the static correction and the dynamic correction.

The correlation and overlaps between PD-L1 expression and classical genomic aberrations in Chinese lung adenocarcinoma patients: a single center case series

Objective:To investigate the correlation and overlaps between PD-L1 expression and classical genomic aberrations in Chinese lung adenocarcinoma(LADC)patients.Methods:We reviewed 428 consecutive,surgically resected cases of LADC from October 2015 to December 2016 from our center.PD-L1 expression was evaluated based on tumor proportion score(TPS).Correlation and co-occurrence of PD-L1 expression level with those of classical driver genes,such as EGFR,ALK,ROS-1,and KRAS and with clinical variables and disease-free survival(DFS)were analyzed.Results:Seventy of the 428 cases(16.4%)showed TPS≥1%,and 21 cases(4.9%)showed TPS≥50%.PD-L1 positive expression was significantly associated with male gender,smoking,advanced TNM stage,and solid histologic subtype.Both TPS≥1% and ≥50%were correlated with the absence of an EGFR mutation(P<0.001)and the presence of ALK rearrangement(P=0.024).KRAS mutation was associated with TPS≥50%(P=0.035).PD-L1 positivity commonly overlapped with the alterations of classical driver oncogenes(58.5%with TPS≥1% and 42.9% with TPS≥50%).Approximately three-quarters of PD-L1 positive cases co-occurred with classical therapeutic-gene aberrations in cases with stage III/IV cancer or cancer progression.LADC could be divided into four subgroups based on the expression profile of current routine biomarkers for potential therapeutic strategies.Conclusions:PD-L1 expression is not only closely correlated with classic gene alterations but also commonly overlaps with the aberrations of classical driver oncogenes in Chinese LADC patients.These findings provide a useful overview of clinical strategies that rely on the profile of routinely used molecular biomarkers.

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.

Aberration changes of the corneal anterior surface following discontinued use of rigid gas permeable contact lenses

AIM: To record aberrations with a corneal topographic device on the anterior surface of the cornea at different time-points prior to wearing and following discontinued use of rigid gas permeable (RGP) contact lenses. The effect of wearing RGP on the anterior surface of the cornea was discussed to provide guidance for clinical refractive error correction.METHODS: The study objects were 24 eyes from 24 patients. All patients underwent identical examination procedures prior to lens use, as well as afterwards, including slit-lamp examination, non-contact tonometer measurement, computer optometry and corneal curvature measurement, subjective refraction test, and corneal topography analysis. The patients wore contact lenses everyday for 1 month and then discontinued. Corneal topographies were recorded at certain time points of 30 minutes, 1 day, 3, 7 and 14 days following use.RESULTS: Total corneal aberration at each time point following discontinued use of RGP contact lenses was less than the time point prior to use. Detailed results were as follows: root mean square (RMS) (pre)=(1.438± 0.328)μm, RMS (30 minutes) =(1.076 ±0.355)μm, RMS (1 day) =(1.362 ±0.402)μm, RMS (3 days) =(1.373 ±0.398)μm, RMS (7 days) =(1.387 ±0.415)μm, and RMS (14 days) = (1.430±0.423)μm. Results showed that at 30 minutes after discontinued use of RGP contact lenses, almost all 2 ndand 3 rd-order aberrations change. Quadrafoil Z10 and spherical Z12 of the 4 th-order were also changed. Alterations to Z5, Z6, and Z12 at 1 day after discontinued use were significant differences compared with the time period prior to RGP use: Z5 and Z6 decreased, and Z12 increased slightly. Z5 and Z6 remained decreased at 3 days after discontinued use, but Z9 and Z10 continued to increase and Z12 returned to levels prior to RGP use. At 14 days after discontinued use, all aberrations were notsignificantly different from the values prior to use.CONCLUSION: The use RGP contact lenses greatly reduced total aberration of the anterior surface of the cornea. Changes to 2 ndand 3 rd-order aberrations (including Z3, Z4, Z5, Z6, Z7, and Z8) were more significant. Following discontinued use of RGP contact lenses, the majority of lower order aberrations returned to original levels in a short period of time. During this process, a transient higher order aberration appeared, but all changes disappeared within 14 days after discontinued use of RGP contact lenses.

Personalized aspheric intraocular lens implantation based on corneal spherical aberration: a review

With the evolution of cataract surgery from visual rehabilitation to refractive surgery, aspheric intraocular lenses(IOLs) are being increasingly used in the field of ophthalmology. This increased use can be attributed to negative or zero spherical aberrations with unique optical designs, which counteract some of the positive spherical aberrations of the cornea. These alterations reduce the total spherical aberration of human eyes and improve the visual acuity in patients with cataract postoperatively. At present, various types of aspheric IOLs are used worldwide. Although the implantation of aspheric IOL is beneficial to the patients who need correction of spherical aberrations, much controversy is still associated with ocular residual spherical aberrations that facilitate the best visual quality for patients postoperatively. In order to provide reference for future clinical work and scientific research, this report reviews the relationship between the ocular residual spherical aberration of human eyes and visual quality.

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.