特发性黄斑裂孔手术治疗后裂孔愈合和视力恢复的相关因素

目的 探讨特发性黄斑裂孔手术治疗后影响裂孔愈合和视力恢复的相关因素.方法 收集我院行玻璃体切割+内界膜撕除+气体充填手术的特发性黄斑裂孔患者35例(35眼)为研究对象,分别进行术前、术后常规检查,包括裂隙灯显微镜、间接检眼镜、最佳矫正视力(best correct visual acuity,BCVA)、频域光学相干断层扫描(spectral domain optical coherence tomography,SD-OCT),并测量裂孔底径(base diameter,BASE)、裂孔最小径(minimum diameter,MIN)、裂孔高度(height,H)、裂孔两侧外界膜的断端与光感受器脱离起点之间的距离(M、N)、水平方向光感受器内外节缺失区直径(diameter of IS/OS absence,DIOA).采用最小分辨角对数(logMAR)记录矫正视力.根据患眼术后的SD-OCT图像结果,将黄斑裂孔愈合级别分为A、B、C3组.根据患眼术前术后BCVA情况,将术后视力分为:视力提高组、视力不变组、视力下降组.观察黄斑裂孔愈合和视力变化情况,并结合患者年龄、性别、术前黄斑裂孔各测量参数进行相关性分析.结果 35例中黄斑裂孔愈合A组23眼,B组6眼,C组6眼.视力提高组27眼,视力不变组、视力下降组均为4眼.结果显示:(1)黄斑裂孔愈合情况与BASE、H、MIN、黄斑裂孔指数(macular hole index,MHI)、裂孔牵拉指数(tractional hole index,THI)、孔径指数(DHI)、手术前BCVA (logMAR)弱相关(均为P ＜0.05);与黄斑裂孔指数(macular hole healing index,MHCI)显著相关(r=-0.588,P=0.000);与年龄、性别均无相关性(均为P＞O.05).(2)术后BCVA (logMAR)与BASE、MIN弱相关(均为P＜O.05);与THI、DIOA、术前BCVA(logMAR)显著相关(均为P＜0.05);与年龄、性别、H、MHCI、MHI、DHI均无相关性(均为P＞0.05).(3)术前DIOA与术前BCVA (logMAR)显著正相关(r =0.658,P=0.000);术后DIOA与术后BCVA (logMAR)显著正相关(r=0.565,P=0.000);术后BCVA(logMAR)和术后DIOA较术前均有所改善,且差异均有统计学意义(均为P＜0.05).结论 (1)MHCI与裂孔愈合等级的相关性最高,可作为手术前预测术后裂孔愈合情况的一个指标;(2)术前DIOA、术前BCVA(logMAR)、THI与术后视力恢复的相关性最高,可作为预测术后视力恢复情况的指标;(3) BCVA与DIOA具有显著相关性,因此视力改善与否的关键取决于DIOA的大小.     

特发性黄斑前膜手术前后光学相干断层扫描形态变化与视力的关系

目的 评估特发性黄斑前膜手术前后光学相干断层扫描形态变化与视力的关系.方法 回顾性分析在我院行玻璃体切割术+内界膜剥除术的特发性黄斑前膜患者32例(32眼)的临床资料,分析术前、术后光学相干断层扫描图像中黄斑中心凹的形态、中心凹厚度与最佳矫正视力的关系.结果 29例患者视力提高,3例患者视力无提高,最佳矫正视力由术前0.25±0.12提高至术后的0.49±0.28(P ＜0.05),所有患者黄斑中心凹厚度均有所下降,由术前的(385±115) μm降至术后的(241±64) μm(P ＜0.05).最佳矫正视力与黄斑中心凹厚度相关性分析呈负相关性,即黄斑中心凹越厚,视力越差.结论 特发性黄斑前膜手术前后黄斑中心凹形态变化与视力有密切关系,光学相干断层扫描可用于术前评估及术后追踪其转归.     

特发性黄斑裂孔玻璃体切割术后视力恢复及黄斑解剖愈合的相关因素分析

目的 探讨特发性黄斑裂孔玻璃体切割术后影响视力恢复及黄斑解剖愈合的相关因素.方法 49例49眼特发性黄斑裂孔行玻璃体切割联合内界膜剥离术的患者纳入本研究.行最佳矫正视力(best corrected visual acuity,BCVA) (logMAR)检查、裂隙灯显微镜及间接检眼镜等检查,同时采用光学相干断层扫描检测黄斑裂孔基底直径、裂孔边缘高度及裂孔最小径,计算黄斑裂孔指数(macular hole index,MHI)、黄斑裂孔牵拉指数(tractional hole index,THI),对黄斑裂孔愈合情况分类.观察术后6个月时视力恢复及黄斑裂孔愈合情况,并与年龄、病程、术前BCVA、裂孔基底直径、裂孔高度、裂孔最小径、MHI、THI等进行相关性分析.结果 术后BCVA为(0.45±0.29) logMAR,与术前BCVA(0.89±0.34) logMAR相比差异具有统计学意义(t=34.2,P=0.000).术后裂孔基底直径为(432.1±90.7) μm,裂孔边缘高度为(214.0±81.3) μm,裂孔最小径为(195.3 ±86.2)μm,均较术前明显减小,差异均有统计学意义(均为P=0.000);术后49眼中,裂孔完全愈合者31眼(63.3％),部分愈合者14眼(28.6％),未愈合者4眼(8.2％).相关性分析结果表明,术后BCVA (logMAR)与年龄、病程、术前BCVA (logMAR)均无相关性(均为P ＞0.05),而与MHI、THI显著相关(r=0.763,P=0.000;r =0.814,P=0.000);黄斑裂孔愈合类型与裂孔基底直径、裂孔边缘高度、裂孔最小径、MHI、THI均显著相关(均为P＜0.05),而与术前BCVA、病程、年龄无相关性(均为P＞0.05).结论 MHI、THI可作为预测术后视力恢复及黄斑裂孔愈合的指标.     

特发性黄斑裂孔术后有晶状体眼与人工晶状体眼视力恢复比较

目的 比较特发性黄斑裂孔术后有晶状体眼与人工晶状体眼视力的恢复情况.方法 选择术后黄斑裂孔闭合的特发性黄斑裂孔患者45例(45眼),按照患者术后晶状体状况,分为有晶状体眼组(32例32眼)和人工晶状体眼组(13例13眼).所有患眼均行玻璃体切割+内界膜剥离+C3F8填充术,术中使用吲哚菁绿溶液辅助剥离内界膜.术后随访6个月,记录术前、术后两组患者的视力情况及术后有晶状体眼组的晶状体混浊进展情况.结果 人工晶状体眼组术后视力提高率为76.9%.有晶状体眼组术后视力提高率为43.8%,两组相比差异有统计学意义(P=0.028).人工晶状体眼组术后平均最佳矫正视力(LogMAR视力)为0.30±0.20,有晶状体眼组为0.58±0.32,两组相比差异亦有统计学意义(P=0.009).术后有晶状体眼组14眼出现晶状体混浊进展.结论 特发性黄斑裂孔术后晶状体混浊可明显影响患者的视力恢复,白内障摘出联合人工晶状体植入可使特发性黄斑裂孔患者术后得到进一步的视力恢复.     

玻璃体手术治疗特发性黄斑裂孔的临床观察

目的:观察玻璃体切割、内界膜剥除联合玻璃体腔气体填充治疗特发性黄斑裂孔的手术疗效及影响因素。方法:对特发性黄斑裂孔患者22例23眼的临床资料进行回顾分析。患眼术前术后除常规检查外最后由光学相干断层扫描(OCT)确诊及测量黄斑裂孔形态。所有患眼均行玻璃体切割、内界膜剥除联合玻璃体腔气体(空气或惰性气体)填充术。观察患者术后视力和黄斑裂孔闭合率及手术并发症的发生情况。用SPSS 13.0统计软件分析患者年龄、病程、术前最佳矫正视力(BCVA)、黄斑裂孔直径、玻璃体腔填充气体种类与术后BCVA和黄斑裂孔闭合率的相关性。结果:术后OCT检查结果显示患者黄斑裂孔闭合率100%。其中术中使用空气进行玻璃体腔填充的14眼,一期黄斑裂孔闭合11眼(79%);术中使用惰性气体(100mL/L C3F8)进行玻璃体腔填充的9眼,一期黄斑裂孔全部闭合,闭合率100%,二者比较,差异无统计学意义(χ2=2.1214,P>0.05)。术后平均矫正视力0.23±0.12,与术前平均矫正视力0.11±0.05相比较,差异有统计学意义(t=4.023,P<0.05)。术后视力提高者术前黄斑裂孔直径小于术后视力不提高者,差异有统计学意义(t=3.92,P<0.05)。术后BCVA与患者年龄(r=-0.415,P=0.256)、病程(r=0.193,P=0.498)、术前BCVA(r=0.152,P=0.673)无相关性。结论:玻璃体切割、内界膜剥除联合玻璃体腔气体填充术治疗特发性黄斑裂孔疗效确切;黄斑裂孔直径是影响特发性黄斑裂孔术后闭合和视力预后的主要因素;而术前视力、年龄、病程对特发性黄斑裂孔术后闭合和视力预后的影响无相关性。     

特发性黄斑裂孔与外伤性黄斑裂孔玻璃体切割手术治疗预后差异比较

目的 观察玻璃体切割手术治疗特发性黄斑裂孔和外伤性黄斑裂孔的预后差异及其影响因素.方法 对特发性黄斑裂孔72例72只眼,外伤性黄斑裂孔55例55只眼的临床资料进行回顾性分析.所有患眼均接受相同方式的玻璃体切割手术治疗.观察两组患者手术后视力改变和黄斑裂孔闭合形式;对比分析黄斑裂孔直径、手术前视力＜0.1和≥0.1、病程＜4个月和≥4个月与手术后视力改变和黄斑裂孔闭合形式之间的相关性.结果 特发性黄斑裂孔72只眼中,闭合72只眼,占100.0%;外伤性黄斑裂孔 55只眼中,闭合47只眼,占85.5%;黄斑裂孔贴附8只眼,占14.5%.特发性黄斑裂孔的裂孔闭合高于外伤性黄斑裂孔的裂孔闭合,二者比较,差异有统计学意义(χ2=11.177,P=0.001).特发性黄斑裂孔和外伤性黄斑裂孔手术后视力与手术前视力比较,差异均有统计学意义(t=-6.841,-4.093;P值均=0.000).特发性黄斑裂孔和外伤性黄斑裂孔手术后视力提高者组间比较,差异无统计学意义(χ2=3.651,P=0.07).特发性黄斑裂孔手术前视力＜0.1和≥0.1的患眼手术后视力提高者之间比较,差异有统计学意义(x=12.04,P=0.001).外伤性黄斑裂孔手术前视力＜0.1和≥0.1的患眼手术后视力提高者之间比较,差异无统计学意义(χ2=0.371,P=0.486).特发性黄斑裂孔手术后视力提高者手术前黄斑裂孔直径小于手术后视力不提高者,差异有统计学意义(t=2.476,P=0.016).外伤性黄斑裂孔的裂孔闭合者手术前黄斑裂孔直径小于裂孔贴附者手术前黄斑裂孔直径,差异有统计学意义(t=-4.042,P＜0.001).外伤性黄斑裂孔病程＜4个月和≥4个月的患眼,手术后视力改变之间(χ2=0.704)、黄斑裂孔闭合形式之间(χ2=0.166)比较,差异无统计学意义(P=0.401,0.684).结论 特发性黄斑裂孔的裂孔闭合率优于外伤性黄斑裂孔的裂孔闭合率.黄斑裂孔直径和手术前视力是影响特发性黄斑裂孔视力预后的主要因素;而手术前视力和病程对外伤性黄斑裂孔的视力预后无显著影响.     

频域相干光断层扫描观察特发性黄斑裂孔患者手术前后光感受器细胞层改变

目的 探讨特发性黄斑裂孔患者手术前后光感受器细胞层内外节的改变特征.方法 回顾性病例系列研究.收集32例(32只眼)确诊并接受手术治疗的特发性黄斑裂孔患者的临床资料进行回顾性分析,同时对其手术前后的高分辨率频域相干光断层扫描(OCT)图像进行对比研究.患者手术前与后logMAR视力和光感受器细胞层内外节被破坏区域直径比...     

光学相干断层扫描在评估特发性黄斑前膜患者术后视力改善中的应用价值

背景 特发性黄斑前膜(IMEM)发病率高,严重影响患眼的视功能,玻璃体切割术是其治疗的主要方法,但关于其术后视力预测的研究较少. 目的 对IMEM进行玻璃体切割联合膜剥除手术患眼的临床资料进行分析,评价IMEM患者手术前后光学相干断层扫描(OCT)测量的黄斑中心凹厚度(CFT)变化与术后视力改善的关系.方法 采用回顾性研究方法,收集2009年3月至2013年5月在北京大学人民医院确诊为IMEM且行玻璃体切割手术、并完成随访的病例48例49眼的临床资料.患者依据术前OCT图像中视网膜色素上皮(RPE)层、视网膜光感受器内节/外节(IS/OS)及外界膜(ELM)层反光条带是否完整分为完整组(17例18眼)及不完整组(31例31眼),记录患眼手术前OCT测量的CFT值和LogMAR视力,并与术后12周的结果进行比较,分析术眼手术前后CFT值变化与视力改善程度的关系,评价术前OCT测量的CFT值在预测术眼术后视力改善程度方面的应用价值. 结果 术后12周,完整组18眼的OCT图像显示RPE层、IS/OS层及ELM层均仍完整,而不完整组OCT图像RPE层反光条带不连续者由术前的6眼减少到1眼,IS/OS层反光条带不连续者由术前的29眼减少到19眼,ELM层反光条带不连续者由术前的27眼减少到15眼(各层的不连续眼数有重复).术眼视力的增加值随着CFT值的减少而增加,二者间呈显著负相关(R2 =0.298,B=0.001,P=0.000),CFT每减少100 μm,术后LogMAR视力提高1行.完整组患眼术前平均LogMAR最佳矫正视力(BCVA)为0.4±0.19,术后为0.36±0.21,差异无统计学意义(t=0.876,P=0.393).不完整组术前平均logMAR BCVA为0.82±0.41,术后为0.46±0.26,差异有统计学意义(t=6.206,P=0.000).不完整组患眼术后视力的改善程度为0.3,优于完整组的0.0. 结论 IMEM术眼手术前后OCT测量视网膜外层结构的连续性及CFT的变化均与患眼视力改善的程度明显相关,术前视网膜外层结构连续者术后预后较好,而术前视网膜外节结构不连续者术后多数可以得到明显改善,包括结构和视力.术前OCT检查在评价IMEM患者术后视力预后方面有一定价值.     

玻璃体切割联合内界膜移植术治疗大直径特发性黄斑裂孔的疗效评估

背景 大直径特发性黄斑裂孔(IMH)严重损害患眼视力,手术难度较大,如何选择和优化手术方法仍是研究热点. 目的 探讨游离内界膜移植术治疗大直径IMH的有效性和安全性.方法 采用前瞻性系列病例观察研究方法,于2013年1月至2015年11月纳入在河北医科大学第二医院就诊的大直径IMH患者[平均直径为(814.31±112.95)μm]42例42眼.所有患眼均施行玻璃体切割联合游离内界膜移植+体积分数12％C3F8填充术.分别于术前及术后1、3、6、12个月对患者进行最佳矫正视力(BCVA) (LogMAR)、裂隙灯显微镜检查和双目间接检眼镜检查,并采用频域光相干断层扫描(SD-OCT)仪检查手术前后黄斑中心区视网膜变化,评估裂孔闭合率,评估和比较手术前后患眼BCVA、光感受器内段/外段(IS/OS)缺损范围、外界膜缺损范围和中心凹视网膜厚度的变化. 结果 术后12个月患者黄斑裂孔闭合率为97.6％ (41/44).术后1、3、6和12个月患者BCVA较术前均明显改善,手术前后不同时间点BCVA总体比较差异有统计学意义(F=28.032,P＜0.001);术眼术前及术后1、3、6和12个月IS/OS缺损范围分别为(1 112.00±45.44)、(859.00±84.55)、(649.00±52.47)、(486.00±46.88)和(320.00±45.13) μm,总体比较差异有统计学意义(F=38.761,P＜0.001),其中术后1、3、6和12个月术眼IS/OS缺损范围较术前均明显减小,差异均有统计学意义(均P＜0.05);术眼术前和术后1、3、6和12个月外界膜平均缺损范围分别为(1 038.00±39.63)、(748.00±64.12)、(585.00±48.88)、(438.00±42.84)和(265.00±28.97) μm,总体比较差异有统计学意义(F=36.459,P＜0.001),术后1、3、6和12个月外界膜缺损范围较术前均明显减小,差异均有统计学意义(均P＜0.05).术后1个月黄斑中心凹厚度值大于术后3、6、12个月,差异均有统计学意义(均P＜0.05).术后3个月OCT显示黄斑裂孔底部高反射信号物质消失,即移植的游离内界膜分解代谢. 结论玻璃体切割联合游离内界膜移植术治疗大直径IMH是安全、有效的,移植的游离内界膜仅作为临时性胶质细胞增生支架,不会形成永久性瘢痕.     

影响特发性黄斑裂孔微创玻璃体切割手术后视力预后的相关因素研究

目的 探讨影响特发性黄斑裂孔(IMH)微创玻璃体切割手术(TSV)后视力预后的相关因素.方法 前瞻性临床研究.连续接受23G TSV治疗的IMH患者46例50只眼纳入研究.其中,男性8例9只眼,女性38例41只眼；平均年龄(60.7±9.6)岁.均采用Snellen视力表行矫正视力(CVA)检查,同时行验光、裂隙灯显微镜加前置镜、频域(SD)光相干断层扫描(OCT)检查.将小数视力换算成最小分辨角对数(logMAR)视力进行统计学处理.患者CVA 0.02～0.6,平均logMAR CVA 0.95±0.29；平均病程(11.1±7.8)个月；平均光感受器内外节连接(IS/OS)断裂长度(1 566.9±830.5) μm;平均黄斑裂孔底部最大直径(914.0±484.8) μm. IMH 2、3、4期分别为10、19、21只眼.患者均行TSV.以手术后3个月为疗效评价时间点,分析手术后视力与患者年龄、病程、手术前视力、IMH分期、手术前IS/OS断裂长度、黄斑裂孔底部最大直径、手术后中心凹感光细胞层厚度、IS/OS断裂长度的相关性；观察TSV治疗IMH的安全性.结果 手术后3个月,所有患眼黄斑裂孔均闭合,占100.0％.平均logMAR CVA 0.45±0.25;平均中心凹感光细胞层厚度、平均IS/OS断裂长度分别为(183.8±62.6)、(477.5±341.9) μm.手术后平均logMAR CVA与手术前比较,差异有统计学意义(Z=6.571,P＜0.001).平均IS/OS断裂长度较手术前明显缩短,差异有统计学意义(t=12.679,P＜0.001).相关性分析结果显示,手术后logMAR CVA与手术前logMAR CVA(r=0.569)、病程(r=0.465)、手术前后IS/OS断裂长度(r=0.574、0.564)均呈正相关关系(P＜0.001)；与患者年龄、黄斑裂孔 底部最大直径、手术后中心凹感光细胞层厚度无相关关系(r=0.546、0.361、-0.441,P＞0.05).IMH 4期患眼较2、3期患眼手术后logMAR CVA差,其差异有统计学意义(Z=0.455、2.556,P＜0.05).手术后出现并发性白内障17只眼；黄斑前膜8只眼.行白内障摘除手术后视力再次明显提高.未出现眼内感染等与手术相关的并发症.结论 影响IMH患眼TSV后视力预后的主要因素为手术前视力、病程、IS/OS断裂长度.     

Paraneoplastic and non-paraneoplastic retinopathy and optic neuropathy: Evaluation and management

Paraneoplastic syndromes involving the visual system are a heterogeneous group of disorders occurring in the setting of systemic malignancy. Timely recognition of one of these entities can facilitate early detection and treatment of an unsuspected, underlying malignancy, sometimes months before it would have otherwise presented, and gives the patient an increased chance at survival. We outline the clinical features, pathogenesis, and treatment strategies for the retinal- and optic nerve–based paraneoplastic syndromes: cancer-associated retinopathy; melanoma-associated retinopathy; paraneoplastic vitelliform maculopathy; bilateral diffuse uveal melanocytic proliferation; paraneoplastic optic neuropathy; and polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes syndrome. Distinguishing these disorders from their non-paraneoplastic counterparts (e.g., autoimmune-related retinopathy and optic neuropathy, and acute zonal occult outer retinopathy) and determining appropriate systemic evaluation for the responsible tumor can be challenging. In addition, we discuss the utility and interpretation of autoantibody testing.     

Anesthesia and preoperative and postoperative medications

Retrobulbar blocks, although widely used, still have potentially serious complications. Topical anesthesia presents less risk of injury to the globe and less pain but requires careful usage and an experienced surgeon. New techniques, however, allow for an increase in the percentage of patients able to have topical anesthesia. Preoperatively, 2.5% phenylephrine is found to be just as effective as 10% phenylephrine, and, when compared with wound closure and surgeon's experience, the effect of prophylactic medications was found to be negated. Postoperatively, diclofenac is found to be as effective an anti-inflammatory agent as prednisolone. Also, the addition of 10% phenylephrine to 4% pilocarpine drops enhances the effectiveness of pharmacologic treatment of postoperative iridocorneal adhesions. In addition, ophthalmologists should be aware of emerging antibiotic resistance.     

Proximal and accommodative convergence and age

The authors have estimated the phoria for distant and near fixation in two groups of subjects (mean age 27.5 ± 4.4 and 59.2 ± 8.2 years). Different accommodative stimuli were induced by adding minus lenses for distant fixation and plus lenses for near fixation. Statistical analysis of the experimental data indicates that, for distant fixation, the value of phoria per unit of accommodative stimulus is significantly lower in presbyopic than in nonpresbyopic subjects. Also, during near fixation, the accommodative convergence (AC/A ratio) is more reliable in the presbyopic subjects when the accommodative stimulus is progressively reduced. This varying behavior indicates in presbyopic subjects that proximal convergence is of greater relative importance in the determination of the fusion-free position. In nonpresbyopic subjects, accommodative convergence is the more important component.     

Anesthesia and preoperative and postoperative medications

Although certain methods such as retrobulbar blocks are used extensively, improvements in procedure can always be implemented. The use of ultrasound, low concentrations of anesthesia, careful monitoring, and, in the case of risk patients, anesthesia standby are all important considerations to ensure uneventful treatments. Topical anesthesia eliminates needle risk as well as risk of ptosis and bruising. Because it has been demonstrated that bacteria routinely enter the anterior chamber during uncomplicated cataract surgery, certain irrigation solutions are helpful, but still debatable. Postoperatively, diclofenac, flurbiprofen, and timolol have all been proven to be effective in reducing ocular inflammation, reducing incidence of CME, and controlling pressure increase, respectively.     

Segmentation and accuracy in copying and drawing: Experts and beginners

As part of an ongoing investigation into real-world copying and drawing, I recorded the eye-hand drawing strategies of 16 subjects with drawing experiences ranging from expert to novice while they copied a line drawing of a standing nude. The experts produced accurate copies whereas all the beginners produced marked inaccuracies of overall scaling, proportion and shape. Analysis of eye and hand movements showed that the experts alone segmented the original drawing into simple line sections that were copied one at a time using a direct eye-hand strategy not requiring intermediary encoding to visual memory. The results suggest that segmentation into simple lines defines the task-specific process of accurate copying, and that this process is restricted to experts, i.e. acquired through training and practice. Additional preliminary tests also suggest that a similar process may apply to drawing a model from life.     

Sensitivity to first- and second-order motion and form in children and adults

We compared the sensitivity of adults and children aged 3-10 years to first- and second-order motion and form. For first-order stimuli, at all ages sensitivity was better for motion than form, and motion thresholds were better at 6 Hz than at 1.5 Hz. For second-order stimuli, at all ages sensitivity was better for form than motion, and motion thresholds were better at 0.25 cyc/deg than at 1 cyc/deg. Thresholds became adult-like later for motion than for form and later for first-order than second-order stimuli. For first-order stimuli, the changes with age were larger and more protracted.     

Ethics and optometry: concepts and applications

Ethics refers both to the study of behaviour, and moral principals. The related concepts of justice and law are also relevant to optometry. A profession typically claims specialist knowledge and ethical behaviour – putting the interests of clients above its own. However, professional codes fail as ethical directives, and their goals are questioned. Beginning with broad principles, institutional ethics and issues of general health care provision are considered, and applications to optometry are made. Ethical theory can guide us in interacting with our patients, utilising resources and ordering priorities. The conservative approach to consumerism and advertising is defended on the basis of protecting public and professional interests. Ethical behaviour can be fostered, and this process should begin in undergraduate education.     

Nodes and nodal points and lines in eyes and other optical systems

The typical stigmatic optical system has two nodal points: an incident nodal point and an emergent nodal point. A ray through the incident nodal point emerges from the system through the emergent nodal point with its direction unchanged. In the presence of astigmatism nodal points are not possible in most cases. Instead there are structures, called nodes in this paper, of which nodal points are special cases. Because of astigmatism most eyes do not have nodal points a fact with obvious implications for concepts, such as the visual axis, which are based on nodal points. In order to gain insight into the issues this paper develops a general theory of nodes which holds for optical systems in general, including eyes, and makes particular allowance for astigmatism and relative decentration of refracting elements in the system. Key concepts are the incident and emergent nodal characteristics of the optical system. They are represented by 2 × 2 matrices whose eigenstructures define the nature and longitudinal position of the nodes. If a system's nodal characteristic is a scalar matrix then the node is a nodal point. Otherwise there are several possibilities: Firstly, a node may take the form of a single nodal line. Second, a node may consist of two separated nodal lines reminiscent of the familiar interval of Sturm although the nodal lines are not necessarily orthogonal. Third, a node may have no obvious nodal line or point. In the second and third of these classes one can define mid-nodal ellipses. Astigmatic systems exist with nodal points and stigmatic systems exist with no nodal points. The nodal centre may serve as an approximation for a nodal point if the node is not a point. Examples in the Appendix , including a model eye, illustrate the several possibilities.