基于夏克‐哈特曼波前检测的无透镜屈光测量系统
China currently has the highest myopia rate among youth in the world, with myopia in children and adolescents becoming the leading cause of visual impairment in the country. Myopia is a progressive condition, but early detection and treatment during the pre-myopia stage can help restore vision. Currently, most children and adolescents rely on traditional computerized optometry in hospitals and ophthalmology institutions for vision screening. However, the monitoring density is insufficient to keep up with the rapid progression of myopia, and if parents notice abnormal vision in their children, they may have missed the optimal intervention period. The objective of this study is to address the issues of bulky and expensive existing computerized optometry and vision-screening instruments. We aim to provide an experimental reference for the miniaturization and instrumentation of refractive measurement systems, enabling their application in scenarios that require portability and miniaturization.
In this paper, we first provide a detailed introduction to the measurement principles of Shack-Hartmann wavefront sensing technology, followed by the derivation of the wavefront reconstruction algorithm principles. Human eyes with different diopters were modeled using Zemax software, and a Shack-Hartmann wavefront sensor was used to simulate the diffuse reflection phenomenon of a laser spot used as a point light source at the fovea centralis of the human eye, which is located at the center of the retina. The human eye and Shack-Hartmann wavefront sensor were placed at different distances, capturing the outgoing wavefront of the human eye at the corresponding location and imaging it on the detector. This simulated the image acquisition optical path in the refractive measurement system. The collected refractive power images were fed into the algorithm to calculate and then analyze the relationship between the actual measured refractive power and true refractive power at different distances between the human eye and Shack-Hartmann wavefront sensor. Finally, we designed the optical-mechanical structure of an experimental prototype and constructed the system. Model eyes with different diopters were placed at different distances (55, 60, and 65 mm) from the Shack-Hartmann wavefront sensor and measurements were repeated ten times. The actual measurement values were compared with the true values of the model eye to validate the accuracy of the measurements, and the coefficient of variation was used to assess the repeatability of the measurement results.
Measurements on model eyes with different diopters show that the stability of the measurement results is better for myopic eyes than for hyperopic eyes. Additionally, the maximum deviation between the measurement results of myopic eyes and the true values of the model eye is generally smaller than that of hyperopic eyes. This is because the wavefront of hyperopic eyes expands outward after exiting the eyeball, leading to fragmentation of the spot formed on the CMOS sensor by the received wavefront in the Shack-Hartmann wavefront sensor, thereby affecting the centroid-localization accuracy in the diopter calculation algorithm. A certain amount of astigmatism is observed in the measurement results for the diopter of cylinder on model eyes without astigmatism. This is due to the inability to strictly align the main optical axes of the human eye, Shack-Hartmann wavefront sensor, and central area of the CMOS during the device adjustment process, which subsequently affects the calculation of astigmatism values. However, overall, the coefficient of variation for repeated measurements of the diopter of sphere in the diopter measurement results remains below 3%, with a maximum error of 0.2 D. The coefficient of variation for repeated measurements of the diopter of cylinder is below 9%, with a maximum error not exceeding 0.25 D. The measurement accuracy meets the requirements of the “Verification Procedures for Ophthalmic Instruments” (JJG892—2022) of the People’s Republic of China, which stipulates a maximum allowable error for the diopter of sphere within a range of -10 to +10 D with error of ±0.25D, and a maximum allowable error for the diopter of cylinder within a range of 0 to 6 D with error of ±0.25 D.
In this study, we design a compact diopter measurement system based on Shack-Hartmann wavefront sensing technology. The system is calibrated using a model eye provided by the National Institute of Metrology of China to observe the diopter measurement results. An analysis of the results shows that the system’s measurement results are highly consistent with the true values of the model eye, with no significant differences and good repeatability. The system is capable of effectively measuring the diopter within a range of -10‒+10 D, even at non-fixed distances along the z-axis. Furthermore, the system has a simple structure and low cost. It is expected that the size of the device can be further reduced with the future customization of key components, making it more suitable for scenarios requiring miniaturized instruments. Therefore, this system has broad prospects for applications.
1 引言
我国青少年近视率已经高居世界第一。国家卫健委发布的《中国眼健康白皮书》显示,目前我国近视患者人数多达6亿,几乎占到我国总人口数量的50%。2020年,我国儿童青少年总体近视率高达52.7%[1]。近视发病年龄越小,进展时间越长,成年后发生高度近视的风险越大[2],增加了视网膜疾病、青光眼和白内障等相关眼部病变导致失明的风险[3-4]。近视是一个渐变的过程,如果在近视前期发现视力异常并及早治疗,视力是可以恢复正常的[5]。目前,大多数儿童青少年仍依赖医院、眼科机构的传统电脑验光仪进行视力定点检查,监控密度难以应对近视的快速进展,家长在发觉孩子视力异常时很可能已经错过了最佳干预期。
近年来,有许多学者对验光仪的小型化进行了不懈探索。亚利桑那大学的法哈德·阿克洪迪等开发了一款便携式自动验光仪[6],该系统采用定制的夏克-哈特曼波前传感器,可以在8 s内以±0.25 D的误差完成测量。他们还设计了三个液体透镜,可以实时矫正视力。阿米尔索莱马尼研制了一款小型验光仪[7],该系统基于三个可调焦液体透镜和薄膜全息光学元件实现屈光度的自动测量。兰德尔·马克斯研制了一种由可调散光和离焦的透镜组成的小型光学验光仪[8],透镜通过流体控制,可以在不机械移动透镜的情况下纠正任意的屈光误差。图宾根埃伯哈德卡尔斯大学的莱纳斯·艾默里奇开发了一款双通道成像的紧凑型自动验光仪[9],该验光仪依靠双通道成像以及点扩散函数和数字图像处理的物理特性,可以完成-15~+15 D范围内的球镜度测量及-3 D的柱镜度测量。上海理工大学的王成等[10]结合干涉、波像差和图像分析等技术建立了眼屈光度与生物参数一体化测量系统,该系统主要测量眼轴长度、角膜曲率、前房深度和屈光度等参数。中国科学院长春光学精密机械与物理研究所的刘春华等[11]设计了一套基于偏心摄影成像的光学系统,该系统具有简单、紧凑、成像质量良好等特点,可以满足偏心摄影验光设备的成像要求。
目前,市面上的屈光测量装置主要有电脑验光仪和视力筛查仪两类。电脑验光仪的原理主要以环厚法和基于夏克-哈特曼波前检测的方法为主。夏克-哈特曼波前检测法是自适应光学中波前探测的常用方法,具有客观准确、测量速度快、可重复性强等特点,在大气扰动监测、人眼像差测量、激光光束质量测量、光学元件测试、光学系统准直等领域具有重要应用[12]。为了获取瞳孔处的波前信息,基于夏克-哈特曼波前检测原理的电脑验光仪的图像采集光路中往往需要一组中继透镜(即4f望远系统),以便使瞳孔面共轭出来[13],同时需要将夏克-哈特曼波前传感器(SHWS)放置在瞳孔共轭面处。这就导致整个光学系统体积变大。由于镜片数目增多,镜片的装调难度增大,因此还会引入系统像差。并且,在测量时需要将仪器的z轴调整到使人眼瞳孔与夏克-哈特曼波前传感器所在位置共轭的一个固定面上,即限制了一个固定的工作距离,对被测者的配合度要求较高。青少年正处于频繁近距离用眼阶段,调节痉挛现象较为常见,传统闭窗电脑验光仪模拟性看远看近搭配雾化机制的手段难以使被测者眼睛充分放松,从而产生了更多的仪器性近视漂移[14]。视力筛查仪的工作原理主要以偏心检影法和夏克-哈特曼波前检测法为主。基于偏心检影法的视力筛查仪虽然有着易于操作、配合度要求低的优点,但其精度较低;而基于夏克-哈特曼波前检测的视力筛查仪较少且价格昂贵。故而,研制一款准确度高、成本低的小型化屈光测量装置具有重要的理论研究意义和实际应用价值。
笔者提出的基于夏克-哈特曼波前检测的屈光测量系统,可以在距离人眼50 mm内任意对中位置有效测量-10~+10 D范围内的屈光度,最大误差不超过0.25 D。视标光路采用敞开视窗型设计,使人眼看到的是真实世界中的物体,以便达到充分放松人眼、得到客观屈光数据的目的。由于不引入中继透镜,大大缩小了系统的体积,节约了成本,减小了系统误差。同时,测量时z轴无须限定在一个固定的共轭距离上,为屈光测量系统的小型化与仪器化提供了实验参考。
2 屈光度测量原理
2.1 哈特曼波前检测技术
自1994年Liang等[15]用哈特曼波前传感器首次成功测量人眼像差后,哈特曼波前检测技术便被广泛应用于临床。夏克-哈特曼波前传感器由上百个各项参数都相同的微透镜有序紧密排列组成。如
式中:
2.2 波前重构
Zernike多项式是圆形光瞳上常用的正交归一化多项式,其在圆形光瞳上具有良好的数学性能,并且其前几项的值与光学系统的初级像差相对应,故而被美国光学学会(OSA)和美国国家标准协会(ANSI)采纳为人眼像差表示的标准[17-18]。
本文所选夏克-哈特曼波前传感器中的微透镜阵列是按方形排列的,故统一在直角坐标系中进行推理。待测波前可以用不同项Zernike多项式的加权叠加和表示,具体公式为
式中:
夏克-哈特曼波前传感器探测到的是子孔径内的平均斜率,第
式中:
当夏克-哈特曼波前传感器有
上式表示成矩阵形式为
式中:
利用第二阶和第四阶Zernike多项式系数计算屈光度,
式中:
3 测量系统的模拟与分析
通过Zemax软件实现对哈特曼图像采集光路的模拟。如
表 1. 眼模型参数
Table 1. Parameters of the eye model
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包含人眼波前像差的光波前被置于人眼前方的夏克-哈特曼波前传感器接收后,在探测面上形成一幅光斑图。
为了探究夏克-哈特曼波前传感器在距离人眼不同位置时所测屈光度的变化情况,建立了不同屈光状态下的人眼模型,通过调节夏克-哈特曼波前传感器与眼模型的距离,采集不同距离对应的光斑图并将其输入程序中进行屈光度计算。如
图 5. 实测屈光度与夏克-哈特曼波前传感器到人眼距离的关系
Fig. 5. Actual measured diopter as a function of distance between Schack-Hartmann sensor and human eye
可以看到,随着夏克-哈特曼波前传感器与人眼的距离增大,远视眼、近视眼的实测屈光度相对于真实屈光度的绝对值分别呈下降和上升趋势。这是由于近视眼和远视眼成像焦点分别位于视网膜的前面和后面,导致其出射光分别以会聚和发散的球面波形式出射人眼。对于单纯的近视眼和远视眼而言,其出射波前的等相位面是一系列同心球面结构。当夏克-哈特曼波前传感器位于系统光轴不同位置时,所探测到的波前曲率是不同的。
这里借用人眼远点的概念来解释这一现象。在眼科医学上,用人眼远点距离lr(mm)的倒数来表示屈光不正的程度,其单位为屈光度(D)。对于正视眼,人眼远点在无限远处,因此,无论夏克-哈特曼波前传感器在什么位置,所探测到的波前均为平面波,即在不同位置处测得的屈光度数值均为0 D。
如
图 6. 近视眼波前随传播距离变化示意图
Fig. 6. Schematic illustration of the variation of wavefront with propagation distance in myopic eyes
同样,对于远视眼,有
在仿真实验中,由于夏克-哈特曼波前传感器与人眼的距离是可控的,即
4 屈光度测量系统的搭建
屈光度测量系统主要由哈特曼图像采集光路、瞳孔对中光路、视标光路构成。图像采集光路采用准直的激光光源作为波前探测光源,准直激光经偏振分光棱镜(PBS)反射后途经二色镜(BS1)进入人眼,经眼底反射后依次经过玻璃体、晶状体、瞳孔、前房、眼角膜出射人眼。这部分携带人眼波前信息的光波前依次经过BS1、PBS后进入夏克-哈特曼波前传感器,由放置在传感器微透镜焦距处的哈特曼相机接收。如
4.1 激光光源的选取
在哈特曼图像采集光路中,为减小激光光源对人眼的刺激,得到客观的屈光信息,采用850 nm激光准直器发射直径为1 mm的激光束照射人眼眼底,利用眼底反射光进行人眼屈光度测量。
国际电工委员会(IEC)制定的有关激光产品安全的国际标准IEC60825-1(A2:2001)中规定激光产品最大允许曝光量[21]为0.78 mW。使用光功率计对入射人眼的实际光强进行测量,测得入射人眼的光功率为0.07 mW,远低于人眼安全标准。
4.2 夏克‐哈特曼波前传感器的选取
为了保证夏克-哈特曼波前传感器有足够的探测灵敏度和动态测量范围,需要对微透镜的焦距和尺寸等参数进行限制。假设CMOS的像元尺寸为
假设微透镜单元的尺寸为
由
对于球面波前,最大波前斜率在其最边缘处。为了使仪器能达到-10~+10 D的动态测量范围,夏克-哈特曼波前传感器所能探测的最大波前斜率应该大于±10 D边缘处的波前斜率。而球面波前的波前斜率为
式中:
综上所述,本文选取的夏克-哈特曼波前传感器参数为:微透镜单元尺寸0.4 mm,焦距4.1 mm,单元数17×17。可探测的最大波前倾斜角度为2.79°,大于1.43°。
本系统的实验样机实物如
5 测量实验与结果分析
为了保证测量结果的准确性,采用中国计量科学研究院校准且溯源的标准模拟眼进行屈光度测量。分别对不同屈光状态下(0 D、±2.5 D、±5 D、±10 D)的7组模拟眼(无散光)进行了测量,每组测量10次。在实验过程中,采用机械限位的方式将模拟眼分别放置在距离夏克-哈特曼波前传感器55、60、65 mm的对中位置上进行测量,以达到获取
由
分析柱镜度的测量结果可以发现,标准模拟眼(无散光)的测量结果中均出现了一定的散光数值。这是因为在屈光度计算过程中,为了保证散光结果计算准确,需要寻找模拟眼严格对中时波面顶点与CMOS靶面对应的位置,即光斑图的光斑中心(相对于正视眼光斑图光斑没有发生偏移)位置。而在器件装调过程中,没有一套完整的装调基准,无法使人眼、夏克-哈特曼波前传感器、CMOS靶面中心这三者的主光轴严格对齐,即靶面中心不一定与光斑中心对应,进而影响到了散光数值的计算。
表 2. 测量结果
Table 2. Measurement results
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由
6 结论
针对现有电脑验光仪和视力筛查仪体积庞大、价格昂贵的问题,开发了基于夏克-哈特曼波前检测原理的小型屈光测量系统。与传统的基于夏克-哈特曼波前检测原理的电脑验光仪相比,该系统不使用中继透镜,直接获取人眼出射波前。视标光路采用敞开视窗型设计,可以得到更加客观真实的测量结果。球镜度重复测量变异系数均低于3%,误差最高不超过0.2 D;柱镜度重复测量变异系数均低于9%,误差最高不超过0.25 D。该系统可以在z轴非固定距离下有效地对-10~10 D范围内的屈光度进行测量,并且该系统结构简单、成本低廉,未来对关键器件进行定制后有望进一步缩小该装置的体积。
由于在不同距离下测量人眼屈光度信息时,需要实时测量夏克-哈特曼波前传感器与人眼的距离
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Article Outline
耿康杰, 张贺童, 丁上上, 张洋, 刘敏, 付威威. 基于夏克‐哈特曼波前检测的无透镜屈光测量系统[J]. 中国激光, 2024, 51(3): 0307401. Kangjie Geng, Hetong Zhang, Shangshang Ding, Yang Zhang, Min Liu, Weiwei Fu. Lensless Refractive Measurement System Based on Shack‐Hartmann Wavefront Detection[J]. Chinese Journal of Lasers, 2024, 51(3): 0307401.