激光原位角膜磨镶手术后不良症状的光学分析

测量了准分子激光原位角膜磨镶(LASIK)手术后人眼的单色像差。并根据术后症状,将所有数据分类为视物星芒状组、单眼复视组、视物雾状组和参考组。视物星芒状组和视物雾状组的三阶和四阶泽尼克(Zernike)像差的均方根(RMS)值明显大于无症状的参考组。术后有不良症状各组的人眼的调制传递函数(MTF)明显低于参考组的调制传递函数。在明视觉条件下,四阶像差特别是对称性的泽尼克球差,对调制传递函数的影响大;而在暗视觉条件下,三阶像差特别是非对称性的泽尼克彗差对调制传递函数的影响大。四阶以上的高阶像差对各有症状组的调制传递函数曲线有影响,而这些高阶像差对参考组的调制传递函数已无明显影响。像差的均方根值和调制传递函数曲线是研究术后不良症状的较有效光学手段。     

The aberration and the modulation transfer function in LASEK and LASIK: Pupil size dependence

The wave-front aberrations on the postoperative eyes with two different type of excimer laser surgery have been measured by a Hartmann-Shack wave-front sensor. We have calculated the aberrations for both 3 and 6 mm pupils, and with which to acquire the MTF of the eye. There are no significant differences in wave-front aberrations postoperatively (P>0.05) for 3 mm pupil size, but with 6 mm pupil, LASIK-treated eyes exhibit significant higher aberrations than LASEK-treated eyes for 4th and 5th-order aberrations. For individual Zernike terms, there are significant difference in , and . The MTF for 6 mm pupil is much lower than those for 3 mm pupil across all spatial frequencies. The LASEK curve shows higher than that with LASIK at spatial frequencies less than 60 c/d, which means that the optical quality in LASEK-treated eyes showed better than in LASIK-treated eyes.     

投影式头盔物镜设计在视空间的性能评价

对一款折衍混合投影式头盔(Head-mounted projective displays,HMPDs)物镜进行了精确的视空间评价,并给出了详细的评价步骤和评价结果。在对调制传递函数(MTF)进行评价时,充分考虑了人眼的焦距和瞳孔对评价结果的影响,给出了调节和像散所造成的分辨力损失的计算公式。评价结果显示:对于3 mm瞳孔,该系统中心视场调制传递函数在0.5 cycles/(′)达到了0.55,达到了人眼的最小分辨角(1′)。当眼睛注视投影像面中心时,轴外点最大需要0.35D的调节量,由此造成的分辨力损失最大为3.5′。由于像散造成的分辨力损失最大只有1.1′。横向色差和二级光谱最大值分别只有0.57′和0.17′,均小于人眼的最小分辨角。这些结果证明此设计满足投影式头盔物镜的使用需要。该方法适用于所有的头盔系统在视空间的性能评价。     

Effects of interactions among wave aberrations on optical image quality after refractive surgery

Research on wave aberrations indicates that interactions and balances among aberrations can provide better visual quality for normal eyes. In this paper, we investigate the aberration compensatory mechanism for eyes after LASIK surgery. Data of Zernike coefficients of wave-front aberrations are collected from 60 post-operative eyes through a Hartmann-Shack wave-front sensor, and then a series of Monte Carlo simulations are performed by manipulating the value of each Zernike coefficient (second order through seventh order). The modulation transfer function (MTF) ratio as a function of spatial frequency is used to evaluate the aberrations’ characteristic of independence. Finally, in a control condition, “synthetic” model eyes are produced through Monte Carlo arithmetic and the aberration independence of the synthetic eyes is analyzed. The results suggest that, for 6 and 3 mm pupil size, aberrations of the eyes after LASIK surgery are still not independent and the adaptive mechanism still exists. However, the adaptive mechanism does not hold for the “synthetic” eyes.     

基于三片曲面反射镜的离轴投影成像系统

采用调制传递函数和波前像差分析方法,设计了基于偶次非球面反射镜和Zernike自由曲面反射镜构成的放大倍数为80,相对孔径为2.8的三个离轴投影成像系统.其中第一片反射镜M1表面为凹面用于减小第二片反射镜的尺寸及获得高的对比度,而第二片反射镜M2和第三片反射镜M3表面为凸面用于校正系统像差及获得更短的投影距离.经软件设计与分析,三系统中基于三片Zernike自由曲面反射镜的成像系统光学性能最好,调制传递函数实现60lp/mm时60%以上,畸变小于2.0%.与其它文献相比,基于三片Zernike自由曲面反射镜系统可以更好地消除像差,缩短系统厚度,增大系统的可视角与相对孔径.     

Monte Carlo simulations on corneal and total aberrations before and after LASIK

Previous Monte Carlo simulations which manipulate each Zernike coefficient of total aberrations of human eyes indicate that interactions among wave-front aberrations can provide better visual quality for both pre-LASIK eyes and post-LASIK eyes. In this paper, we go a step further for Monte Carlo simulations which are not only on total aberrations but also on corneal aberrations, before and after LASIK, for a set of eyes. The corneal aberrations after LASIK are acquired through a new reliable method. Then a series of Monte Carlo simulations (including sign simulation, value simulation and meridional simulation) are performed by manipulating each Zernike coefficient (second through sixth-order) of total aberrations as well as corneal aberrations. The results are evaluated by modulation transfer function (MTF) ratio. Total aberrations for post-LASIK eyes still show MTF advantage over randomized aberrations, with slightly change as compared to that for pre-LASIK eyes. However, true corneal aberrations before and after LASIK have no MTF advantage over random aberrations. From this research, we draw conclusions: there is apparent advantage for the complete eye's true aberrations over random aberrations, whether pre-LASIK or post-LASIK, which does not exist for any biological optical surfaces in isolation, and the ability of adaptive mechanism of human eyes, increases after LASIK.     

用于头盔显示器的折/衍混合目镜设计

设计了一个用于头盔显示器的40°目镜,由两片镜组成,其中含有一个二元衍射面和一个非球面.该折/衍目镜具有10 mm的出瞳直径和25 mm的出瞳距离,结构紧凑,总重量仅为16.6 g.像差特性优于传统的折射目镜,轴上视场传递函数良好,适用于SXGA分辨率的显示.     

基于三片曲面反射镜的离轴投影成像系统

采用调制传递函数和波前像差分析方法,设计了基于偶次非球面反射镜和Zernike自由曲面反射镜构成的放大倍数为80,相对孔径为2.8的三个离轴投影成像系统.其中第一片反射镜M₁表面为凹面用于减小第二片反射镜的尺寸及获得高的对比度,而第二片反射镜M₂和第三片反射镜M₃表面为凸面用于校正系统像差及获得更短的投影距离.经软件设计与分析,三系统中基于三片Zernike自由曲面反射镜的成像系统光学性能最好,调制传递函数实现60 lp/mm 时60%以上,畸变小于2.0%.与其它文献相比,基于三片Zernike自由曲面反射镜系统可以更好地消除像差,缩短系统厚度,增大系统的可视角与相对孔径.     

光学系统的波面不均匀性与MTF理论值的计算精度

在计算光学系统的ＭＴＦ值时，无论采用什么方法，一般都假设光能在光学系统的出射波面上的分布是均匀的，即假设瞳函数的振幅为常数，但由于实际光学系统存在光阑像差，出射波面上的光能分布是非均匀的，故上述假设给ＭＴＦ的计算带来了误差。本文在计算ＭＴＦ值时，推导出了出射波面的相对能量公式，并通过典型光学系统的实际比较计算，分析了出射波面光能分布的不均匀程度的大小与ＭＴＦ值计算精度的关系。最后得出结论：光学系统的波面不均匀性对ＭＴＦ理论值的计算精度的影响是可观的，当光学系统的ＭＴＦ值计算精度要求较高时，不能近似处理。     

人眼视觉的传递特性及模型

介绍了国内外对人眼视觉特性及其调制传递函数的研究 ,对几种典型的人眼视觉模型进行了分析。较之以往采用的具有低通特性的指数型和高斯型 ,及具有带通特性的Barten模型和复合模型更符合人眼视觉传递特性。在此基础上将两种带通模型和国内外一些典型的试验数据进行了比较研究 ,得出 :Barten模型参数简单 ,计算方便 ,但实用的范围较复合模型小。复合模型综合考虑了人眼瞳孔、显示器亮度、视场角、量子效率、积分时间等因素的影响 ,是一种更全面的反映人眼传递特性的视觉模型     

基于近红外远心镜头的双目瞳孔检测仪光学系统设计

为了降低双目瞳孔检测系统放大率对瞳孔位置的敏感性,设计了一款基于近红外远心镜头的双目瞳孔检测仪。阐述了系统中的核心部件——近红外远心镜头光学参数的计算过程,分前后组进行设计,并运用Zemax完成光学系统优化,以全视场MTF、全视场最大畸变和物方远心度为指标对系统进行公差分析,利用标准圆对仪器进行标定,拟合出像素数和瞳孔大小的对应关系。结果表明,对于55 mm~75 mm的瞳距,瞳孔的直径测量精度可达0.05 mm,满足使用要求。     

用于检测设备标定的标准头盔瞄准具设计

为标定和校准头盔瞄准具检测设备,提出一种新的光学结构,并设计了一款标准头盔显示系统（HMD）。该系统采用球面共轴设计,在有限体积的限制下满足了低畸变、高清晰的光学指标要求。利用对称性光学设计原则分步设计,设计的标准HMD系统出瞳清晰,可保证系统各种光学像差的综合校正。针对1．27cm（1／2in）微显示器设计了视场为30°、出瞳距离为75mm的标准HMD光学系统,各视场在分辨率30lp／mm处的MTF值均大于0．3,系统畸变小于0．9％。设计的标准HMD光学系统形式简单、结构紧凑,光学性能优良,可作为头盔瞄准具检测设备标准件。     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Analysis of pupil and corneal wave aberration data supplied by the SN CT 1000 topography system

Ocular aberrations depend on pupil size and centring and the retinal image quality under natural conditions differs from that corresponding to laboratory ones. In the present article, pupil and wave aberration data supplied by the Shin Nippon CT 1000 (SN CT 1000) topography system are analysed. Two groups of eyes under natural viewing conditions are considered ((260±20) lux at the eye under study). The first group consists of 10 normal eyes (−1.25 to 3 D sphere; 0 to −1.75 D cylinder) of five young subjects (age between 18 and 33 years). For this group, five determinations per eye are performed and the repeatability of results is analysed. Pupil centre is displaced from corneal vertex towards the temporal region, the largest displacement being (0.5±0.1) mm. The variation of pupil diameter in each eye is less than 21% while the inter-subject variability is large since diameters are between (3±0.3) and (5.3±0.6) mm. Aberrations are evaluated for two different pupil sizes, the natural one and a fictitious one of 6 mm. The corneal higher-order root-mean square wavefront error (RMS_HO) for a 6 mm pupil centred in the corneal vertex, averaged across all eyes, is (0.37±0.06) μm while, considering the natural pupil diameter, the average in each eye is significantly lower, up to eight times smaller. The fourth-order spherical aberration is an important aberration in the considered eyes, its maximum value for a 6 mm pupil being (0.38±0.02) μm. The second group consists of 24 eyes of 12 subjects (age between 25 and 68 years) such that four eyes are of normal adults (1.25 to +6 D sphere; 0 to −0.5 D cylinder), eight have astigmatisms (−5.5 to +3.25 D sphere; −1.5 to −4.5 D cylinder), six have post-refractive surgery (+0.5 to +3.5 D sphere; −0.5 to −4 D cylinder) and six have keratoconus (−9.5 to +1 D sphere; −1 to −4.5 D cylinder). For this group only one determination per eye is performed. Pupil centre is displaced from corneal vertex towards the temporal region except in cases of keratoconus, where there can be a dominant upwards displacement. Pupil diameters are between 2.7 and 5.6 mm. The corneal higher order root mean square wavefront error for a 6 mm pupil ranges between 0.3 (normal eye) and 5.3 μm (keratoconus).     

Measurements of AIM for Visible Wavelength Based on Individual Eye Model

We measure and calculate the aerial image modulation （AIM） of human retina for visible wavelengths based on the individual eye model. By employing the optical design software ZEMAX, we obtain the modulation transfer function （MTF） of human eye in visible wavelengths. Using CSV-1000 and VAF-1000, the contrast sensitivity function （CSF） and the visual acuity （VA） for the same eye are measured. Then the AIM of human retina could be acquired by the relations between MTF and CSF and between MTF and VA. The AIM of human retina is independent of MTF, and the values of AIM for normal eyes （without retina disease） are similar, so the assembly average for large numbers of normal eyes can be a standard AIM curve, which is helpful for the diagnosis of diseases in the retina system.     

Orthonormal polynomials in analysis of single-mode fiber coupling

Zernike polynomials have been widely used for wave-front analysis because of their orthogonality over a uniform circular pupil. However, the pupil is not uniform but weighted by the backpropagated fiber mode in analyzing fiber coupling efficiency. Zernike polynomials are not appropriate for a weighted pupil due to their lack of orthogonality over such pupil. We emphasize the advantages of using orthonormal polynomials in fiber coupling systems. The orthonormal polynomials over weighted pupil are derived by matrix approach. The effects of primary aberrations are investigated based on the orthonormal polynomials. The accuracy of the Strehl ratio approximation for primary aberrations is evaluated.     

人眼的高级像差对视功能的影响

准确测量和分析人眼的高级像差有助于更好地改善视觉,具有重要的实验和临床意义。测量了实际人眼的波前像差,分析了高级像差对人眼视功能的影响。像差数据由哈特曼-夏克（Hartmann-Shack）波前传感器分别对不同瞳孔的人眼进行测量而获得,视功能的评价方法采用了调制传递函数（MTF）、对比敏感度函数（CSF）、斯特雷尔（Strehl）比率。由人眼的波前像差数据和视网膜空间像调制度（AIM）曲线直接给出了视锐度值与对比敏感度值。矫正了离焦与像散后．被测者的平均视锐度值达到了1．0,对比敏感度在低频（20c／mm）处约为52,高频（80c／mm）处约为1;矫正了前4阶像差后,平均视锐度值可提高到1．2,对比敏感度在低频（20c／mm）处提高到96,高频（80c／mm）处提高到7。实际人眼各不相同,达到理想成像需矫正高级像差的阶数也不同。矫正了前九阶像差后,均可达到理想成像,斯特雷尔比率值大于0．8。     

折反式微光夜视物镜的光学设计

介绍一种长焦距、大相对孔径微光夜视物镜的光学设计。设计参数为焦距100 mm,相对孔径1/1.4,视场10。为增大视距,减小物镜尺寸和质量,并且满足在宽光谱范围消色差的要求,选择均为球面的折反式物镜结构,在相同焦距和相对孔径的条件下折反式系统比折射系统尺寸更小,质量更轻。在设计过程中引入曼金反射镜,增加设计自由度。经优化设计达到较好的成像质量,空间频率在50 lp/mm时,轴上传递函数大于0.4,轴外传递函数大于0.2,与像增强器极限分辨率相匹配,全视场畸变小于2 %,物镜总长达到67 mm。     

Closed-loop adaptive optics in the human eye

We have developed a prototype apparatus for real-time closed-loop measurement and correction of aberrations in the human eye. The apparatus uses infrared light to measure the wave-front aberration at 25 Hz with a Hartmann-Shack sensor. Defocus is removed by a motorized optometer, and higher-order aberrations are corrected by a membrane deformable mirror. The device was first tested with an artificial eye. Correction of static aberrations takes approximately five iterations, making the system capable of following aberration changes at 5 Hz. This capability allows one to track most of the aberration dynamics in the eye. Results in living eyes showed effective closed-loop correction of aberrations, with a residual uncorrected wave front of 0.1microm for a 4.3-mm pupil diameter. Retinal images of a point source in different subjects with and without adaptive correction of aberrations were estimated in real time. The results demonstrate real-time closed-loop correction of aberration in the living eye. An application of this device is as electro-optic "spectacles" to improve vision.     

一种新型稀疏孔径结构的研究

提出了一种由九个孔径组成的稀疏孔径结构。给出了该孔径结构的光瞳函数,并分析了其孔径结构的特点。具体对不同填充因子时的新结构进行了仿真,得出了新型稀疏孔径结构的调制传递函数的分布特点,以及系统的等效直径和调制传递函数的变化情况。对新型稀疏孔径结构与三臂结构进行了比较和分析,新结构的传递函数分布比较均匀,对频域有较大的覆盖面积,系统的等效直径较大。新结构在等效直径和调制传递函数的均匀性方面优于所比较的三臂稀疏孔径结构,新结构在成像性能方面具有一定的优势。