空间相干光通信外差效率及天线像差的影响

空间相干光通信中接收天线像差会使光外差效率下降.对本振光为高斯分布,信号光为爱里斑分布的光外差效率进行了研究,给出了无像差时外差效率的解析表达式.当焦平面上爱里斑半径与本振高斯光束光腰半径之比为1.71时,有最大外差效率81.45%.然后以本振光为理想的高斯光束,信号光受像差的影响,研究了倾斜、离焦、球差、彗差、像散等像差引起的光外差效率损失,给出了存在像差时外差效率的一维积分表达式.研究表明即使在采用离焦校正后,一个波长的球差引起的附加外差效率损失仍可达0.9 dB.因此对于爱里斑位于光轴上的接收天线,在设计时需仔细处理球差的影响.     

Compact description of substrate-related aberrations in high numerical-aperture optical disk readout

Optical disks are read out by focusing a beam of high numerical aperture (NA) through the substrate. Deviations of the thickness from the nominal value result in spherical aberration; tilting the substrate results in coma. Exact analytical expressions for the rms aberration per micrometer thickness mismatch (for spherical aberration) and per degree tilt (for coma) are derived. The paraxial estimates for these sensitivities proportional to NA4 (spherical aberration) and NA3 (coma) underestimate the exact values by a factor of approximately 2 for the value NA = 0.85, corresponding to the new Blu-ray disk format. Expansion of the aberration function in Zernike aberrations shows that the exact aberration functions are well described by the lowest-order Zernike spherical aberration (A40) and coma (A31) term for all but the very highest NA values.     

Application of nonperiodic phase structures in optical systems

Wide, nonperiodic stepped phase structures are studied to correct various parameter-dependent wave-front aberrations in optical systems. The wide nature of these phase structures makes them easy to manufacture with sufficient compensation of the wave-front aberrations. Wave-front aberration correction for both continuous and discrete parameter variations are studied. An analytical method is derived for the discrete parameter variations to find the optimal phase structure. Both theoretical and experimental results show that these nonperiodic phase structures can be used to make (1) lenses athermal (defocus and spherical aberration compensated), (2) lenses achromatic, (3) lenses with a large field of view, (4) lenses with a reduced field curvature, and (5) digital versatile disk objective lenses for optical recording that are compatible with compact disk readout.     

TMC系统主镜的平板补偿自准检验方法

针对TMC(三镜卡塞格林)光学系统凹椭球面主镜的检验,本文提出了一种平板补偿的自准检验方法.该方法克服了OFFENER零位补偿器本身性能难以检验,只能靠加工和装调保证精度的问题.针对TMC主镜面形与抛物面接近的特点,对平板补偿的自准检验方案进行了理论分析,利用二次非球面的法线像差性质推导了检验光路中球差的表达式,并利用最小剩余球差进行补偿平板参数的确定.对某TMC系统顶点曲率1 589mm,二次系数-0.983,口径φ500 mm的主镜检验,设计了尺寸仅为φ34.2 min×9.126 5 mm的补偿平板.在ZEMAX中计算的结果表明,经平板补偿后的检验光路波像差RMS值为0.003λ,可满足TMC主镜的高精度检验要求.对补偿平板的检验方法,以及加工和使用中应当采取的措施也进行了考虑.与常用检验方法相比,本文方法具有容易对平板性能进行检验,成本低、研制周期短等优点.     

Axial irradiance of a focused beam

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.     

Normalized parameter relating the spherical aberration of a thin lens to the diffraction limit and fiber coupling efficiency

In this paper, we calculate the transverse spherical aberration TA of a thin lens and defines a normalized aberration Y equal to TA divided by the theoretical resolution limit. As a rule of thumb, (a) a thin lens that suffers only from spherical aberration may be considered effectively diffraction-limited as long as Y < 1.6. Similarly, (b) the coupling efficiency of a Gaussian beam to a single-mode fiber may be high even when Y > 1.6, and, specifically, (c) the lens need be diffraction-limited only over a radius approximately equal to the radius (to the 1/e-point) of the Gaussian beam.     

Properties of caustics produced by a positive lens: meridional rays

We study the formation of the caustic surfaces formed in both convex-plane and plano-convex spherical lenses by considering a plane wave incident on the lens along the optical axis. Using the caustic formulas and a paraxial approximation we derive analytical expressions to evaluate the spherical aberration to third order. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens.     

Analysis of reentrant two-mirror nonplanar ring laser cavity

A rigorous analysis is performed on the reentrant nonplanar ring laser cavity constructed by a Herriott-type multipass cell. Since the cavity is highly nonplanar, the angle between the incident planes at each reflection becomes different from that of the image rotation angles. The beam rotation, astigmatism, and spherical aberration are considered to obtain a self-consistent solution of the Gaussian beam. It turns out that spherical aberration is an important issue for this nonplanar resonator. Without taking into account the spherical aberration, a stable resonator would be difficult to realize. Using a self-consistent Gaussian beam propagation method, the laser beam characteristics are solved analytically. The results are compared with that of the 2 x 2 ABCD method.     

Caustics in a meridional plane produced by plano-convex conic lenses

We study the formation of caustic surfaces formed in both convex-plano and plano-convex conic lenses by considering a plane wave incident on the lens along the optical axis. By using the caustic formulas and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens as a function of all parameters involved in the process of refraction through the conic lenses.     

Design of fast aplanatic IR objectives using high refractive-index materials

A method for correcting spherical aberration and coma in fast two-element objectives using high-index materials is discussed. It involves use of an aplanatic lens with a single lens having a minimum spherical aberration and no coma. The method deals only with monochromatic designs. It can be effective in designing high-aperture aplanatic IR objectives. Optical data and performance characteristics of germanium and silicon two-lens systems designed by the proposed method are given.     

引入声汇的相位共轭方法进行声场识别

在时间反转方法中引入声汇概念的基础上,提出两种方法计算引入的声汇幅值：第一种方法是直接推导出相位共轭阵列在声源聚焦处的幅值,将其作为声汇的幅值;第二种方法是在近场引入一个测量球面计算声汇的幅值,并讨论引入测量球面半径对声场重建结果的影响。数值计算结果表明：引入声汇之后,在一定的测量距离上,采用两种计算方法都能突破声波的衍射极限;通过引入的测量球面方法,采用封闭的球形阵列在远场也能突破声波的衍射极限,得到结果更精确,与点声源理论解吻合较好;根据倏逝波传播性质,引入的测量球面半径需小于一个波长。     

Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration

Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by a power series in the aberration coefficients. An accurate approximation (in elementary functions) to the OTF is obtained for a defocused optical system with a circular pupil. We experimentally demonstrate the validity of the OTF approximations in sharp-focus image restoration from two defocused images. A digital focusing method is presented.     

The design of a triplet with a shape-dependent third-order aberration optimization technique

Abstract

We have derived a series of shape-dependent third-order aberration equations involving lens thickness. These equations are used in a simple and direct method to correct real aberrations and to find the minimum aberration for triple design that has been proposed. These calculated third-order aberrations can exactly meet the target values for each stage by means of the damped least-squares method. The shape of the three elements permits the control of three third-order aberrations: spherical aberration, coma and astigmatism. The spherical aberration is targeted first. The minimal value of the real on-axis aberration is obtained. Similarly, the coma and astigmatism target values are adjusted so as to force the full field angle real off-axis aberrations down to a minimum. Finally, the manual adjustment of the lens thickness and air spacing is used to attain the minimum aberration at the 0.7 field angle. To verify the method, two triplet design examples are presented.     

Blue/DVD/CD compatible optical head

Compatibility with Digital Versatile Disc and Compact Disc has been demonstrated for two options of high-density optical disk systems using a blue laser diode. Option 1 (HD DVD) employs a 0.65 numerical aperture objective lens and a 0.6 mm thick protective layer disk, while Option 2 (Blu-ray Disc) employs a 0.85 numerical aperture objective lens and a 0.1 mm thick protective layer disk. An optical head has three laser diodes whose wavelengths are 405 nm, 660 nm, and 785 nm. A spherical aberration caused by the difference in the protective layer thickness of the disk is corrected by an objective lens magnification change, while the numerical aperture of the objective lens is controlled by a wavelength-selective aperture. Experimental results have shown that Option 1 is more preferable, but Option 2 is also acceptable from the viewpoint of the compatibility.     

Dual-wavelength optical head with a wavelength-selective filter for 0.6- and 1.2-mm-thick-substrate optical disks

A dual-wavelength optical head, believed to be new in design, for 0.6- and 1.2-mm-thick-substrate optical disks was developed by use of 650- and 780-nm-wavelength light and a wavelength-selective filter, which reduces the spherical aberration that is due to the difference in substrate thicknesses and restricts the numerical aperture for 780-nm-wavelength light. According to this configuration, both high light power efficiency and wide image field characteristics are obtained, which are suitable not only for read-only but also for recordable or rewritable optical disk systems. A reading operation for a digital video disc and for a compact disc and a recording operation for a phase change optical disk were successfully demonstrated.     

Analysis of Seidel aberration by use of the discrete wavelet transform

Seidel aberration coefficients can be expressed by Zernike coefficients. The least-squares matrix-inversion method of determining Zernike coefficients from a sampled wave front with measurement noise has been found to be numerically unstable. We present a method of estimating the Seidel aberration coefficients by using a two-dimensional discrete wavelet transform. This method is applied to analyze the wave front of an optical system, and we obtain not only more-accurate Seidel aberration coefficients, but we also speed the computation. Three simulated wave fronts are fitted, and simulation results are shown for spherical aberration, coma, astigmatism, and defocus.     

Optical aberrations of the human cornea as a function of age

We investigated how the optical aberrations associated with the anterior surface of the human cornea change with age in a normal population. Aberrations were computed for a central part of the cornea (4, 5, and 6 mm in diameter) from the elevation data provided by a videokeratographic system. Measurements were obtained in 59 normal healthy, near-emmetropic [spherical equivalent lower than 2 diopters (D)] subjects of three age ranges: younger (20-30 years old), middle-aged (40-50 years old), and older (60-70 years old). The average corneal radius decreased with age and the cornea became more spherical. As a consequence, spherical aberration was significantly larger in the middle-aged and older corneas. Coma and other higher-order aberrations also were correlated with age. The root mean square of the wave aberration exhibited a linear positive correlation (P < 0.003) with age for the three ranges of pupil diameter. Despite a large intersubject variability, the average amount of aberration in the human cornea tends to increase moderately with age. However, this increase alone is not enough to explain the substantial reduction previously found in retinal image quality with age. The change in the aberrations of the lens with age and the possible loss of part of the balance between corneal and lenticular aberrations in youth may be the main factors responsible for the reduction of retinal image quality through the life span.     

机床直线轴重复定位精度三维评价方法研究

重复定位精度是机床的一个重要性能指标，会直接影响加工产品的质量一致性。现有以直线轴运动方向的位置偏差作为评价指标的一维评价方法已经不适用于精密机床重复定位精度的评价。为了更全面地评价机床直线轴重复定位精度，提出了机床直线轴重复定位精度的三维评价方法，以球概率误差半径作为评价指标，将一维定位评价扩展到三维空间评价。首先，以卧式加工机床为例，通过齐次坐标变换建立了运动件单轴和机床的重复定位精度的数学模型，对现有一维评价方法的局限性进行分析。其次，基于卡方分布的性质，对球概率误差半径的计算过程进行简化。最后，通过简化的球概率误差半径计算方法对机床直线轴重复定位精度进行评价。以精密卧式机床的工作台为研究对象，通过实验对一维评价方法和三维评价方法进行了对比，结果表明，以球概率误差半径为评价指标的三维评价结果与定位点空间分布的离散程度基本一致。采用三维评价方法可以使机床重复定位精度的评价更加全面，可为机床整体性能的提升提供更可靠的理论指导。     

Spherical aberration correction using a liquid-crystal spatial-light modulator in off-axis electron holography

One can correct spherical aberration in a transmission electron microscope by using a newly developed aberration-correction method involving off-axis electron holography. In this method, a liquid-crystal spatial-light modulator (LC SLM) is employed during the holographic reconstruction step to compensate for spherical aberration. Application of this method to high-resolution off-axis electron holograms of fine gold particles is presented. The phase distribution of the corrected object wave is visualized by the Zernike phase-contrast method carried out with the same LC SLM.