Subjective refraction: the mechanism underlying the routine

The routine of subjective refraction is usually understood, explained and taught in terms of the relative positions of line or point foci and the retina. This paper argues that such an approach makes unnecessary and sometimes invalid assumptions about what is actually happening inside the eye. The only assumption necessary in fact is that the subject is able to guide the refractionist to (or close to) the optimum power for refractive compensation. The routine works even in eyes in which the interval of Sturm does not behave as supposed; it would work, in fact, regardless of the structure of the eye. The idealized subjective refraction routine consists of two steps: the first finds the best sphere (the stigmatic component) and the second finds the remaining Jackson cross-cylinder (the antistigmatic component). The model makes use of the concept of symmetric dioptric power space. The second part of the refraction routine can be performed with Jackson cross-cylinders alone. However, it is usually taught and practiced using spheres, cylinders and Jackson cross-cylinders in a procedure that is not easy to understand and learn. Recognizing that this part of the routine is equivalent to one involving Jackson cross-cylinders only allows one to teach and understand the procedure more naturally and easily.     

Reduction of artefact in scatter plots of spherocylindrical data

Round-off of spherocylindrical powers, to multiples of 0.25 D (for example) in the case of sphere and cylinder, and 1 or 5 degrees in the case of axis, represents a type of distortion of the data. The result can be artefacts in graphical representations, which can mislead the researcher. Lines and clusters can appear, some caused by moiré effects, which have no deeper significance. Furthermore artefacts can obscure meaningful information in the data including bimodality and other forms of departure from normality. A process called unrounding is described which largely eliminates these artefacts; each rounded power is replaced by a power chosen randomly from the powers that make up what is called the error cell of the rounded power.     

Mapping of error cells in clinical measure to symmetric power space

During the refraction procedure, the power of the nearest equivalent sphere lens, known as the scalar power, is conserved within upper and lower bounds in the sphere (and cylinder) lens powers. Bounds are brought closer together while keeping the circle of least confusion on the retina. The sphere and cylinder powers and changes in these powers are thus dependent. Changes are depicted in the cylinder-sphere plane by error cells with one pair of parallel sides of negative gradient and the other pair aligned with the graph axis of cylinder power. Scalar power constitutes a vector space, is a meaningful ophthalmic quantity and is represented by the semi-trace of the dioptric power matrix. The purpose of this article is to map to error cells for the following: coordinates of the dioptric power matrix, its principal powers and meridians and its entries from error cells surrounding powers in sphere, cylinder and axis. Error cells in clinical measure for conserved scalar power now contain more compensatory lens powers. Such cells and their respective mappings in terms of most scientific and alternate clinical quantities now image consistently not only to the cells from where they originate but also to each other.     

Comparison of glistenings in intraocular lenses with three different materials: 12‐year follow‐up

Purpose: To compare the degree of lens glistenings associated with three intraocular lenses (IOLs) of different materials and examine the relationship between the dioptric power of the optics and lens glistenings in a long‐term study. Setting: St. Erik Eye Hospital, Stockholm, Sweden. Methods: Forty‐six eyes of 46 patients underwent standard phacoemulsification and implantation with a heparin‐surface‐modified (HSM) polymethylmethacrylate (PMMA) IOL, a silicone IOL or a hydrophobic acrylic IOL. Evaluations of the patients and the glistenings were conducted 11.3–13.4 years postoperatively. The glistenings were examined using Scheimpflug imaging and subsequently analysed using an image analysis program. Results: The median follow‐up time was 12.2 years (range, 11.3–13.4). The hydrophobic acrylic IOL had significantly more lens glistenings than the silicone (p = 0.003) and the PMMA (p = 0.000) IOLs. The silicone IOL had significantly more lens glistenings than the PMMA lens (p = 0.048). The IOL power did not affect the degree of lens glistenings in the hydrophobic acrylic IOL group (p = 0.64). The other groups had too little lens glistenings to evaluate the relationship. Conclusion: In this long‐term follow‐up study, the hydrophobic acrylic IOL had a significantly higher degree of lens glistenings compared to the silicone and PMMA IOLs. The PMMA IOL had almost no lens glistenings. The IOL dioptric power was not significantly correlated with the degree of lens glistenings associated with the hydrophobic acrylic IOL.     

The average eye

For statistical and other purposes one needs to be able to determine an average eye. An average of refractive errors is readily calculated as an average of dioptric power matrices. A refractive error, however, is not so much a property of the eye as a property of the compensating lens in front of the eye. As such, it ignores other aspects of the optical character of the eye. This paper discusses the difficulties of finding a suitable average that fully accounts for the first-order optics of a set of optical systems. It proposes an average based on ray transferences and logarithms and exponentials of matrices. Application to eyes in particular is discussed.     

Artificial intelligence improves accuracy, efficiency, and reliability of a handheld infrared eccentric autorefractor for adult refractometry

AIM: To evaluate the accuracy, efficiency, and reliability of a handheld infrared eccentric autorefractor (hICA) with artificial intelligence (AI) by comparing its refraction measurements to those recorded using hICA and a clinical table-mounted automatic refractor (TAR). METHODS: A cross-sectional study using three optometers, including hICA with or without AI and TAR, for refractometry of adults (aged 19-49 years old) with no signs of ocular disease or trauma in the absence of cycloplegia. Right and left eye refraction data were recorded, including the spherical equivalent (SE), diopter of spherical power (DS), diopter of cylindrical power (DC) decomposed into vectors J0 and J45, and measurement times. To avoid analytical difficulties associated with the interdependence of observations between eyes from the same individual, the Generalized Estimation Equation was used to compare the SE, DS, J0 and J45 measurements, and the times thereof, among the different groups. The intraclass correlation coefficient (ICC) and Spearman’s rank correlation coefficient were used to evaluate correlations among the measurements recorded by the three different instruments. Bland-Altman were used to analyze the precision of the equipment by the agreement. RESULTS: A total of 70 patients (140 eyes; mean age: 31.37y; range: 19-49y) were assessed using refractometry. In a brightly lit environment, there was no significant difference between the mean SE recorded using TAR and that recorded using hICA with AI or without AI (both P>0.05). In an intense-light environment, hICA equipped with AI showed a better detection rate than without AI. Light intensity had a greater effect on dioptric measurements recorded using hICA without AI (P<0.001) than on those recorded using the one equipped with AI (P<0.05). Measurement times varied significantly between the different light intensities and instruments (P<0.05). CONCLUSION: For the normal human eyes, AI may improve the accuracy, efficiency, and reliability of measurements recorded using hICA in various light environments.     

正视眼人群角膜不同范围的非球面性评价

目的初步探索正视眼人群角膜Q值的分布。方法对来我院健康体检的正视眼192人（384眼）进行裸眼远视力、电脑验光、裂隙灯、直接检眼镜和角膜地形图检测，并对结果进行统计学分析。结果本组人群角膜前表面曲率半径R为（7.80±0．23）mm。Q10值为=-0．083±0.098．Q15值为-0.119±0.097．Q20值为-0．149±0.104．Q25值为-0.200±0、107，Q30值为-0．262±0．104；角膜前表面Q值越近中央部越接近0，越靠近周边越向负值增加的方向变化。不同性别角膜不同范围平均Q值无明显差异性（P〉0．05）。Q25与Q30在不同年龄组之间差异有显著性（P〈0．05）．45岁以上组的Q25和Q30值与其他年龄组相比偏大，差别有显著性（P〈0．05）。Q30与角膜前表面曲率半径呈负相关（r=-0.115，P〈0．05）。各范围Q值均与年龄无明显相关性（P〉0．05）。结论正视眼人群角膜前表面中央接近于球形，越到周边越趋于平坦。     

微创超声乳化手术前后角膜前后表面及不同区域范围角膜参数的变化

目的:比较白内障微创超声乳化手术前后角膜前表面屈光力(ASF)、角膜真实净屈光力(TNP)和总角膜屈光力(TCRP)分布特点及角膜前后表面曲率半径比(B/F ratio)差异。方法:前瞻性研究。收集2020-12/2021-05就诊于潍坊眼科医院行2.2mm微切口超声乳化白内障吸除联合人工晶状体植入术的年龄相关性白内障患者156例156眼。术前及术后3mo行Pentacam眼前节生物测量仪检查,收集以角膜顶点和以瞳孔为中心2、4、6mm环上和区域内ASF、TNP和TCRP,以及手术前后B/F ratio。结果:术后3mo,以角膜顶点为中心2mm直径环上和区域内ASF值较术前均无差异(均P>0.05),而4、6mm直径环上和区域内ASF值较术前均有差异(均P<0.05);以瞳孔为中心2mm直径环上及区域内ASF值较术前均无差异(均P>0.05)。以角膜顶点为中心和以瞳孔为中心2、4、6mm直径环上和区域内TNP、TCRP值较术前均有差异(均P<0.05)。术前以角膜顶点为中心和瞳孔为中心在2mm与6mm之间环上和4mm与6mm之间环上TCRP值均有差异(均P<...     

角膜总屈光力的评估方法及其临床应用进展

角膜总屈光力的评估在角膜接触镜的验配和角膜屈光手术的术前评估中至关重要.测算角膜总屈光力的设备多种多样.根据测算原理的不同,角膜总屈光力大致可分为3类：模拟角膜屈光力、基于高斯厚透镜公式的角膜总屈光力和光路追击法获得的角膜总屈光力.角膜屈光术后角膜总屈光力的准确评估在提高预测拟植入人工晶状体屈光力的准确性中起关键作用.目前,对于角膜屈光术后角膜总屈光力的评估缺乏统一标准,很多学者根据各自的研究提出了不同的修正公式.本文着重综述角膜总屈光力尤其是角膜屈光术后眼角膜总屈光力的评估方法及其研究应用进展.     

Effect of Ramadan fasting in tropical summer months on ocular refractive and biometric characteristics

Background: Islamic Ramadan is the month of fasting, in which intake of food and drink is restricted from sunrise until sunset. The objective of the present study was to find out the effect of altered eating habits during Ramadan fasting on ocular refractive and biometric properties. Methods: In this prospective case series, 40 eyes of 22 healthy volunteers with a mean age of 60.55 ± 12.20 years were enrolled. Patients with any systemic disorder and eyes with pathology or previous surgery were excluded. One month before Ramadan (at 8.00 am), during Ramadan fasting (at 8.00 am and 4.00 pm) and one month later during the non‐fasting period (at 8.00 am), ocular refractive and biometric characteristics were measured using an autokeratorefractometer (Auto‐Kerato‐Refractometer KR‐8900; Topcon Co, Tokyo, Japan) and contact ultrasonic biometry (Nidek Echoscan US 800; Nidek Co, Tokyo, Japan). Results: Anterior chamber depth was significantly increased during fasting compared with baseline measurements and returned to baseline one month after Ramadan (3.22 ± 0.07 mm and 4.33 ± 0.17 mm for non‐fasting and fasting, respectively; p < 0.001). The anterior chamber depth measurements were significantly larger at 8.00 am during fasting compared with 4.00 pm (p = 0.01). Axial length was significantly decreased during fasting and returned to baseline one month after Ramadan (23.09 ± 0.14 mm and 22.65 ± 0.18 mm, for non‐fasting and fasting, respectively; p < 0.001). Intraocular lens power calculations were significantly increased during fasting and returned to baseline one month after Ramadan (SRK‐T formula: 21.46 ± 0.27 D and 22.92 ± 0.46 D, for non‐fasting and fasting, respectively; p < 0.001). There were no significant differences in spherical equivalent, corneal astigmatism, mean keratometry and flatter and steeper corneal radii of curvature between time intervals. Conclusions: Ramadan fasting is associated with statistically significant alterations in anterior chamber depth and axial length that result in both statistically and clinically significant changes in intraocular lens power calculations. Therefore, relying on measurements taken during this month might lead to refractive errors after cataract surgery.     

Stability of the Barrett True-K formula for intraocular lens power calculation after SMILE in Chinese myopic eyes

AIM: To compare the Barrett True-K Formula with other formulas integrated in Lenstar 900 to predict intraocular lens (IOL) power after small-incision lenticule extraction (SMILE). METHODS: A theoretical prospective study was performed to predict the ratio of equivalent IOL power before and after SMILE using the SRK/T (Sanders, Retzlaff, Kraff/theoretical), Holladay 1, Haigis, and Barrett True-K formulas and compare the stability of their predictions. The study included 54 eyes (54 cases) with a manifest refraction spherical equivalent (MRSE) of –4.99±1.45 D. They were divided into two groups: 27 eyes with axial length of 24-26 mm in group A, and 27 eyes with axial length >26 mm in group B. All subjects enrolled in this study were examined with the Lenstar 900 before and 6mo after SMILE including measurements of axial length, corneal curvature, and anterior chamber depth (ACD). RESULTS: The prediction of equivalent IOL power of the two groups was more stable for the Barrett True-K formula, especially in long axial-length eyes (group B). The respective percentages for the SRK/T, Holladay 1, Haigis, and Barrett True-K formulas were 7.4%, 7.4%, 85.19%, and 88.89% for a margin of error within 0.5D; 25.92%, 51.84%, 100%, and 100% for a margin of error within 1.0D in group A; 33.33%, 40.74%, 44.44%, and 81.48% for a margin of error within 0.5D; and 44.44%, 59.26%, 66.66%, and 92.59% for a margin of error within 1.0D in group B. The respective percentages for Barrett True-K formulas were 100% for a margin of error within 2.0D in group B. CONCLUSION: Theoretically, the Barrett True-K formula provides more stable predictions than other formulas for cataract eyes after SMILE.     

Comparing methods to view corneal topography data

Background: Graphical display of the many thousands of data points generated by corneal topography systems has progressed from three-dimensional wire representations, through curvature and power maps, to three-dimensional subtraction models. Standard colour-coded corneal ‘topographic’ maps may be misinterpreted as representing corneal profile instead of a form of corneal power. A variety of two- and three-dimensional output methods for displaying corneal topography data are demonstrated. Method: Axial colour-coded isodioptric maps were obtained with the MasterVue Ultra corneal topography system. Separate software was written to access the data files to enable construction of alternative display forms, that is, instantaneous power maps and various colour-coded three-dimensional models. Results: The relative advantages and disadvantages of various methods for viewing corneal topography measurements are demonstrated for data taken from the clinical records of two subjects. Conclusion: Newer methods for displaying corneal topography data enable the visualisation of the differences between representations of power and those of profile. The different display methods have their own advantages and limitations which make them more appropriate in certain applications and less so in others.     

准分子激光原位角膜磨镶术后OrbscanⅡ估算术前角膜屈光力

目的 比较OrbscanⅡ测量准分子激光原位角膜磨镶术(LASIK)前后周边角膜后表面曲率半径改变,初步确立新的角膜前后表面曲率半径比率R,利用术后周边后表面角膜曲率半径和比率R估算术前角膜总屈光力。方法 回顾分析OrbscanⅡ测量151只眼术前及术后3个月角膜7～10 mm区后表面曲率半径值的变化,计算角膜0～～7 mm区前表面曲率半径与角膜7～10 mm区后表面曲率半径比率R,利用比率R推算30只眼术前角膜总屈光力,并验证计算性角膜总屈光值与测量性角膜总屈光值的一致性。LASIK手术前后角膜7～10 mm后表面曲率半径变化和计算性角膜总屈光力与术前OrbscanⅡ测得角膜总屈光力比较采用配对t检验。结果 LASIK术前后角膜7～10 mm区后表面曲率半径差值为（-0.005±0.154）mm(t=0.417,P=0.677),术前角膜0～7 mm区前表面曲率半径与角膜7 ～ 10 mm区后表面曲率半径比率R为1.167±0.030,利用比率R推算的角膜总屈光力均值为(43.49±1.79)D,OrbscanⅡ测得实际角膜总屈光力均值为(43.77±1.53)D,两者差值均值为（-0.28±1.00）D(t=-1.523,P=0.139)。结论 LASIK手术前后周边区域角膜后表面曲率半径改变无实际临床意义,计算所得新角膜前后表面曲率半径比率R可准确的推算LASIK术者术前角膜总屈光力,为LASIK术后丢失术前资料患者双K法计算人工晶状体度数提供重要条件。     

Determining the power of a negative lens field expander

In 1984, Kozlowski, Mainster and Avila derived a formula for the power of the lens needed in the negative lens field expander. Their method is based on the principle of telescopic magnification. In this technical note, we use the principle of spectacle magnification and obtain the power of the same lens. Both methods are presented for comparison. Practitioners may choose either method in determining the power of the negative lens field expander for their low vision patients, but the spectacle magnification method has the advantages of simplicity and familiarity to ophthalmic practitioners.     

Objective assessment of the effect of pupil size upon the power distribution of multifocal contact lenses

AIM: To analytically assess the effect of pupil size upon the refractive power distributions of different designs of multifocal contact lenses. METHODS: Two multifocal contact lenses of center-near design and one multifocal contact lens of center-distance design were used in this study. Their power profiles were measured using the NIMO TR1504 device (LAMBDA-X, Belgium). Based on their power profiles, the power distribution was assessed as a function of pupil size. For the high addition lenses, the resulting refractive power as a function of viewing distance (far, intermediate, and near) and pupil size was also analyzed. RESULTS: The power distribution of the lenses was affected by pupil size differently. One of the lenses showed a significant spread in refractive power distribution, from about ?3 D to 0 D. Generally, the power distribution of the lenses expanded as the pupil diameter became greater. The surface of the lens dedicated for each distance varied substantially with the design of the lens. CONCLUSION: In an experimental basis, our results show how the lenses power distribution is affected by the pupil size and underlined the necessity of careful evaluation of the patient’s visual needs and the optical properties of a multifocal contact lens for achieving the optimal visual outcome.     

青光眼小梁切除术对角膜屈光力影响的研究

目的 探讨青光眼小梁切除术对角膜屈光力的影响。方法 使用角膜地形图仪对青光眼小梁切除手术前后的角膜形态改变进行比较分析。共检查５０例病人５２只眼,其中三角殂巩膜瓣组２６只眼,长方形巩膜瓣组２６只眼。结果 分别对两组手术前的角膜表面非对称指数,角膜表面规则指数,模拟角膜计读数,角膜最小曲率值,角膜表面柱镜值与手术后１周及１个月时的角膜ＳＡＩ,ＳＲＩ,ＳｉｍＫ,ＭｉｎＫ,ＣＹＬ等数值比较,均无显著性差     

Evaluation of the Keratometric Index by the Pentacam

Objective: To calculate the total corneal power and the keratometric index based on actual measurements of the anterior and posterior corneal surfaces and the central corneal thickness by Pentacam and evaluate the accuracy of this keratometric index in estimating total and posterior corneal powers. Methods: This was a series case study. Four hundred and nineteen patients (a total of 419 eyes) who had undergone preoperative examination and laser in situ keratomileusis (LASIK) surgery or cataract surgery from February to October 2017 at the Xiangtan Central Hospital and Eye Hospital, Wenzhou Medical University were chosen for the study. The radius of the best-fit sphere for the anterior corneal surface (Ra) and posterior corneal surface (Rp), and central corneal thickness (CCT) were obtained. The ratio of Ra to Rp (AP ratio), anterior corneal power, posterior corneal power and keratometric index were calculated, and the total corneal power in each eye was calculated using the Gaussian optics formula. A paired-samples t-test was used to compare the difference in K values. Results: The means for Ra, Rp, Rsimk, CCT and SimK were 7.73±0.27 mm, 6.34±0.24 mm, 7.73±0.27 mm, 537±33 μm, and 43.65±1.52 D, respectively. The mean calculated AP ratio was 1.220±0.026. The mean calculated keratometric index (Ncal) was 1.328±0.001. Conclusions: The Pentacam-derived keratometric index improves the predictive accuracies of total and posterior corneal powers.