基于双泽尼克多项式的多视场稀疏孔径成像

基于双泽尼克多项式推导稀疏孔径光学系统与视场相关的广义光瞳函数,以Golay3稀疏孔径成像系统为例,通过ZEMAX软件进行光学设计和数据拟合获得广义光瞳函数的双泽尼克多项式系数,根据傅里叶变换关系计算得到稀疏孔径光学系统的调制传递函数（MTF）,并针对不同视场稀疏孔径光学系统进行成像模拟和图像复原。结果表明,调制传递函数的理论计算结果与ZEMAX设计结果一致,利用双泽尼克多项式可以表示不同视场稀疏孔径光学系统的成像特性。构建与视场相关的维纳滤波器进行图像复原,可有效提高不同视场稀疏孔径光学系统的成像质量。     

基于分数阶微分的消除局部强反射的孔径测量方法

针对视觉测量硬盘圆孔直径易受到圆孔周围高反光面强反射的影响而导致测量精度不高的问题,提出了一种基于分数阶微分的图像去噪声的处理方法。通过分数阶微分算法对相机采集的带有强反射、高反光的硬盘圆孔孔径图像进行处理,消除圆孔周围强反射表面等不相关信息对圆孔边缘提取带来的影响,通过实验分别与Prewitt、Soble、Laplacian算子进行比较,证明分数阶微分可有效减少所要分析的图像信息量,更好地增强圆孔边缘轮廓信息,可达到更好的视觉效果。对分数阶微分算法处理后的圆孔图像进行Canny边缘检测,提取出有效的圆孔边缘,利用最小二乘法对孔径边缘进行直径测量。实验结果表明:该文算法与其他算法相比,在保证精确提取孔径边缘信息的基础上,对圆孔周围的强反射面进行了抑制,误差控制在0.05 mm左右,保证了测量精度。     

两种对称型稀疏孔径系统的成像研究

提出了复合三子镜稀疏孔径结构,它由九个子镜组成,每三个子镜组成一个次级光瞳,三个次级光瞳组成一个主光瞳,其结构是对称的冗余结构.研究了三臂和复合三子镜两种对称型结构稀疏孔径系统,比较复合三子镜和三臂结构的特点与调制传递函数,对不同填充因子的两种结构的稀疏孔径模拟成像和维纳滤波,并进行像质评价,同时和非冗余的Golay6结构进行比较.结果表明：复合三子镜稀疏孔径系统在结构分布、成像质量等方面优于三臂对称结构稀疏孔径系统,对称型稀疏孔径系统在结构排列上具有对称易装调的优点.     

基于三维分数阶微分增强的边缘曲面重构算法

提出一种基于三维分数阶微分增强的三维边缘曲面重构算法,可重构出更多的三维不规则目标的细节结构信息,克服了原边缘曲面重构算法重构细节信息不充分的缺点.根据分数阶微分傅里叶变换的可分离性原理,将二维分数阶微分算子推广至三维并推导出三维分数阶离散滤波模板,利用三维分数阶微分对图像具有非线性增强作用的特性,对三维切片数据场进行三维分数阶微分增强.与传统三维边缘曲面重构算法相比,经过三维分数阶微分增强且采用分数阶梯度追踪细节改进的重构算法,能够重构出更丰富的三维目标细节结构信息.算法运用于神经元细胞的共焦显微图像中三维不规则目标的边缘曲面重构,实验结果验证了该算法的正确性和高效性,可推广应用至生物医学领域的三维可视化研究.     

稀稀疏孔径等边六孔径结构研究

对光学稀疏孔径子孔径空间分布结构与系统成像特性的基本关系进行了讨论.提出了一种新的子孔径分布结构——等边六孔径结构并给出了该结构的具体分布形式和光瞳函数.对等边六孔径结构的成像特性进行分析,把它与MMT型和Golay6型六孔径结构的调制传递函数进行了仿真实验和比较.     

含分数阶微分的线性单自由度振子的动力学分析(Ⅱ)

研究了含两类分数阶微分项的线性单自由度振子, 通过平均法得到了系统的近似解析解. 在近似解中, 两类分数阶微分项的系数和阶次均以等效线性阻尼和等效线性刚度的形式影响着系统的动力学特性, 这一点和现有文献中大多数直接将分数阶微分项归类为阻尼进行处理是完全不同的. 对近似解析解和数值解进行了比较, 二者符合精度很高, 证明了该结果的准确性. 然后分析了两类分数阶微分项的系数和阶次对系统响应特性的影响, 发现两类分数阶微分项的系数和阶次都既可以影响系统的共振振幅, 又可以影响系统的共振频率. 最后研究了第二类分数阶微分项对共振频率的影响, 指出了在振动控制工程中如何通过选取合适的第二类分数阶微分项的系数达到满意的控制效果.     

含分数阶微分的线性单自由度振子的动力学分析

研究了一个含分数阶微分的线性单自由度振子, 通过平均法得到了系统的近似解析解. 在近似解中, 分数阶微分项的系数和阶次以等效线性阻尼和等效线性刚度的形式影响着系统的动力学特性, 这一点与现有文献中直接将分数阶微分项归类为阻尼进行处理的方法完全不同. 比较了近似解析解和数值解, 二者的符合精度很高, 证明了近似解析解的准确性. 分析了分数阶系数和分数阶阶次对系统响应特性的影响, 发现分数阶系数和分数阶阶次都既可以通过等效线性阻尼影响系统的共振振幅, 又可以通过等效线性刚度影响系统的共振频率.     

基于光学扫描全息密码术的多图像并行加密

对光学扫描全息术中的双光瞳做出改进,提出对多图像并行加密和任意层图像再现的新方法.将其中一个光瞳设置成环形光瞳,另一个光瞳处插入随机相位板,干涉形成环形随机相位板,实现对多层图像的快速扫描和并行加密,扫描信号通过计算机合成为加密全息图,在数字全息再现的过程中进行解密,实现对任意层图像的精准重建.该方法快捷高效、安全可靠,抗噪声能力强.利用相关系数评估了该方法的加密效果,并通过仿真实验验证了该方法的有效性和安全性.     

关联噪声驱动系统的一阶数值模拟算法

在某些条件下共同驱动随机系统的乘法噪声和加法噪声可以相互关联,相关噪声驱动的随机微分系统具有独特的性质,而数值模拟是研究这类系统一种强有力的方法。研究相关噪声驱动系统的数值模拟算法,分别就白噪声情形和色噪声情形作了讨论,得到了一种一阶数值模拟算法,并与已有文献的解析结果进行了对比。     

印制电路板缺陷图像边缘检测

为了提取含噪声印制电路板(PCB)光板缺陷图像边缘信息,提出了一种基于混合法的图像边缘检测方法.在分析类间最大距离法图像分割基本原理的基础上提出了一种改进的类间最大距离法(IMDBC);设计了结合中值滤波、IMDBC、改进的数学形态学边缘检测算子与LOG算子进行PCB光板缺陷图像边缘检测的混合方法.用CCD及显微镜成像系统获取4幅PCB光板缺陷图像,结果表明:用本文方法提取出的图像边缘信息清晰且较精确,噪声点较少,所得到的4幅图像优质系数是其它6种方法的1.0111~1.3586倍.     

Characteristic investigation of Golay9 multiple mirror telescope with a spherical primary mirror

The sparse aperture provides a novel solution to the manufacturing difficulties of modern super large telescopes. Golay configurations are optimal in the sparse aperture family. Characteristics of the Golay9 multiple mirror telescope having a spherical primary mirror are investigated. The arrangement of the nine sub-mirrors is discussed after the planar Golay9 configuration is analyzed. The characteristics of the entrance pupil are derived by analyzing the sub-aperture shapes with different relative apertures and sub-mirror sizes. Formulas about the fill factor and the overlay factor are deduced. Their maximal values are presented based on the derived tangency condition. Formulas for the point spread function (PSF) and the modulation transfer function (MTF) of the Golay9 MMT are also deduced. Two Golay9 MMT have been developed by Zemax simulation. Their PSF, MTF, fill factors, and overlay factors prove that our theoretical results are consistent with the practical simulation ones.     

Demonstration of the Golay3 multiple-mirror telescope with a spherical primary mirror

The sparse aperture system is a novel solution to design larger telescope of high angular resolution by utilizing several small sub-apertures to displace the full aperture. The system is of light weight and low cost. Multiple-mirror telescope (MMT) is one type of sparse aperture systems. We have analyzed the Golay3 MMT with a spherical primary mirror to obtain the relationships between the sub-mirrors on the primary mirror and the shapes of sub-apertures on the entrance pupil with different relative aperture by investigating the entrance pupil characteristics. The maximum fill factor and the maximal overlay factor were derived, and the tangency condition when sub-mirrors of the Golay3 MMT are tangency was also given out. The expressions of the point spread function (PSF) and the modulation transfer function (MTF) of the Golay3 MMT were deduced. The characteristics of both the PSF and the MTF were obtained based on the deduced formulas and Matlab simulating patterns. Two Cassegrain telescopes of a spherical primary mirror with the Golay3 configuration and with an aspherical secondary mirror were designed. Based on the relationships between the fill factor and the overlay factor, the optimal parameters of sub-mirrors on the primary mirror were selected. The PSFs and MTFs of Cassegrain telescopes with the Golay3 MMT were designed by Zemax simulation. The simulation results are consistent with the theoretical results.     

Laser confocal microscope with wavelet-profiled point spread function

We report a laser-scanning confocal reflectance microscope with a wavelet-profiled point spread function (PSF) for rapid multi-resolution extraction and analysis of microscopic object features. The PSF is generated via holography by encoding a π-phase shifting disk unto a collimated laser beam via a phase-only spatial light modulator (SLM) that is positioned at the pupil plane of the focusing objective lens. Scaling of the transverse PSF distribution is achieved by selecting a suitable ratio of the π-phase shifting disk radius and the pupil aperture radius. With one and the same objective lens and one SLM to control the phase profile of the pupil function, we produce amplitude PSF distributions that are accurate scaled representations of the circularly-symmetric Mexican hat mother wavelet.     

Super-resolution by pupil plane phase filtering

Resolution capability of any optical imaging system is limited by residual aberrations as well as diffraction effects. Overcoming this fundamental limit is called super-resolution. Several new paradigms for super-resolution in optical systems use ‘a posteriori’ digital image processing. In these ventures the three-dimensional point spread function (PSF) of the lens plays a key role in image acquisition. A straightforward tailoring of the PSF can be performed by appropriate pupil plane filtering. With a brief review of the state-of-art in this research area, this paper dwells upon the inverse problem of global optimization of the pupil function by phase filtering in accordance with the desired PSF.     

Reconstruction of the Point-Spread Function of the Human Eye Using a New Phase-Retrieval Algorithm

The double-pass method is thought to obtain the point spread function (PSF) in human eyes based on two techniques: the symmetric double-pass method using the same pupil size and the asymmetric double-pass method using a different pupil size. The symmetric double-pass method provides autocorrelation of the retinal PSF and, thus, the modulation transfer function. The asymmetric double-pass method provides low-frequency partial-phase information and the partial phase-retrieval algorithm is applied to obtain the complete-phase information, and to estimate the PSF. The partial phase-retrieval algorithm is based on the iteration method proposed by Fineup and Kowalczyk and requires a lengthy computation. In this study, we propose a new high-speed phase-retrieval algorithm based on the property that the real and imaginary parts of optical transfer functions (OTFs) continuously change in value.     

Phase-Space Analysis of Wavefront Coding Imaging Systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function （PSF） of an incoherent defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invariant to the defocus-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.     

基于实际空间截止频率的稀疏孔径双圆周阵列的优化

提出了一种新的稀疏孔径光瞳结构-两个圆周阵内外嵌套而成的双圆周结构,并研究了该结构的调制传递函数.该结构以实际空间截止频率作为约束条件,保证调制传递函数在最小截止频率以内无零频,以阵列的u-v覆盖点间距最大化及最小冗余度来设计目标函数,并采用这种优化方法对3-3、5-3以及6-3双圆周阵列进行了优化排列.将优化结果与相同子孔径数目的均匀圆周阵以及Golay结构进行仿真实验和比较.结果表明,优化后的双圆周阵列,具有最大的实际空间截止频率和实际等效口径.     

倾斜入射的波前编码系统的点扩散函数扩大效应分析

通过对坐标系统进行旋转，计算得到了三次型波前编码系统的倾斜入射的光瞳函数，并给出了近似表达式. 分析表明倾斜入射会产生三次相位扩大效应和离焦扩大效应，它们和入射角的正负无关，且随着入射角绝对值的增大而增大. 这表现在点扩散函数(point spread function, PSF)上会扩展PSF包络的两条直角边，表现在调制传递函数(modulation transfer function, MTF)上会降低MTF值. 子午面倾斜入射时，子午方向的三次相位扩大效应和离焦放大效应大于弧矢方向，从而导致子午方向