编码孔径成像系统中的点扩散函数

在X光编码孔径成像系统中，系统的点扩散函数决定成像系统的成像质量。由于系统的点扩散函数可用来求解系统的传递函数，并可由此制作实现图像重构的滤波器，因此点扩散函数的精确程度直接影响重构过程中图像的质量。本文以标量衍射理论为基础，从理论上推导出了衍射效应条件下编码孔径中圆环的点扩散函数，并将它用于制作光学系统的滤波器。最后利用Wiener滤波函数对编码重叠像的频谱分布进行滤波处理，再经过逆傅里叶变换得到了重构图像。     

Hybrid pupil filter design using Bessel series

We propose a simple method of designing pupil filters for transverse super-resolution. For this end we represent the amplitude Point Spread Function (PSF) as a series expansion, constructed from the Fourier transform of a basis of Bessel functions. With this representation we optimize the intensity PSF according to certain desired characteristics, such as a smaller disk diameter than the corresponding, clear aperture, Airy disk. It is proved that by using few basis functions, it is possible to design pupils with similar or better PSF characteristics than previously reported.     

Differential confocal technology based on radial birefringent pupil filtering principle

In order to improve the spatial resolution of a confocal system, a radial birefringent pupil filter (RBPF) is introduced into a differential confocal system. RBPF consists of two polarizers with a birefringent element between them, and its pupil function is deduced from Jones matrix. The thickness and curvature radius of RBPF are optimized independently, using the first zero coordinate ratio. The pupil function is modulated by RBPF to enhance the half-width of the response function, and lateral resolution is improved when response curve is changed with the position of RBPF as well as the polarization; then axial super-resolution of the system can be guaranteed using differential confocal detection mechanism. In comparison with conventional pupil filtering technology, RBPF features high lateral resolution and can be easily produced; moreover, it also has a simple structure. Together with its low cost, RBPF provides a new way for the improvement of super-resolution of confocal system. It is indicated from theoretical analysis and preliminary experiments that the lateral resolution can be significantly improved and the measurement error is reduced by 76 nm when measuring a standard grating of period 3 μm; the axial resolution up to 3 nm has been achieved using the optimized pupil filter. In addition to its application for measurement of a small irregular surface in a limited space, the whole differential confocal system proposed can be fitted onto a coordinate measuring machine for non-contact measurement of dimensions and surface roughness.     

High resolution optical image restoration for ground-based large telescope using phase diversity speckle

Phase diversity speckle (PDS) is an image restoration technique which is based on the idea of phase diversity (PD). It uses multi-frame short-exposure image sequence to calculate their corresponding wave-front information. Each image pair consists of two images collected by two cameras at the same time with one in focus and the other with known defocus value. Multi-frame processing can significantly improve the target signal to noise ratio, and decrease noise influence. In this paper, based on the principle of pupil Fourier imaging, by adjusting the pupil size, we get different scales of the optical point spread function (PSF). Also, we analysis different camera noise distribution channels, location differences and other factors to optimize the objective evaluation function, and this can reduce the computational complexity and improve the processing speed of image restoration. In the indoor environment, we build optical platform, and use multi-frame phase diversity speckle to make experiment under different turbulence conditions. The experimental results show that the image restoration effect of the proposed method is close to the diffraction limit.     

A hybrid optical-digital processor for image deblurring

A hybrid optical-digital image processing system is developed for deblurring out-of-focus pictures. The optical part is a dual-channel non-coherent processor which implements the Wiener filter for deblurring through appropriate pupil functions. The methods of implementing the bipolar PSF in a non-coherent processor are described, as are the methods of determining the pupil functions from the given PSFs. The digital part of the processor subtracts or demodulates the outputs from the dual-channel optical processor to give the final deblurred picture. The pupil functions are experimentally realized and the deblurred outputs are presented.     

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.     

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     

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 关键词： 倾斜入射 波前编码 三次相位扩大效应 离焦扩大效应     

A lateral super-resolution differential confocal technology with phase-only pupil filter

In order to achieve a higher lateral resolution required for ultraprecision measurement of microstructural workpieces, phase-only pupil filtering differential confocal microscopy (PFDCM), a new approach is proposed based on the differential confocal microscopy (DCM), which uses a three-zone phase-only pupil filter with lateral super-resolution capability obtained through optimized design to change the distribution of DCM three-dimensional point spread function, so that the DCM lateral resolution is therefore significantly improved while its axial resolution is slightly improved. Preliminary experimental comparison and analyses indicate that, the lateral and axial resolutions of PFDCM are better than 0.2 μm and 2 nm, respectively, when wavelength of incidence laser beam , numerical aperture of measuring lens NA=0.85, and lateral spot size with a three-zone phase-only pupil filter G_T=0.65. It is therefore concluded that PFDCM is a new approach to further improvement of lateral resolution in laser probe measurement systems.     

基于PIV评价的光瞳超分辨理论与技术

随着成像探测技术的发展，对光学系统的分辨能力提出了更高的要求，用传统的光学理论需增大光学系统口径才能满足要求，在对尺寸，重量和价格有限制的实际系统中往往很难实现。基于瑞利判据作为ＰＩＶ指标的光瞳超分辨技术，可以在不增加光学系统口径的条件下提高系统分辨率，由于本技术可以用光瞳滤波器的形式以硬件实现，成像探测过程不必增加额外的工作时间，在理论分析的基础上，设计了实际的超分辨光瞳，并给出了计算机模拟和实     

Effect of fabrication errors on axial super-resolution property of a three-zone pupil filter

Two models have been established using the basic definitions of super-resolution characteristic parameters for normalized spot size G_A and Strehl ratio S_A, of a three-zone axial super-resolution pupil filter with fabrication errors, to quantitatively analyze the effect of these fabrication errors on the axial super-resolution property. These new models established to describe the analytic relationship of G_Ae and S_Ae of a pupil filter with its fabrication errors and its transmission function A(ρ), phase function φ(ρ) and structural parameters, directly relate the super-resolution parameters of a three-zone axial super-resolution pupil filter to its fabrication errors to make the quantitative analyses of the effect of fabrication errors easier, thereby providing a theoretical basis for the analysis, design and fabrication of a three-zone axial super-resolution pupil filter. The models established for G_Ae and S_Ae have been used to analyze the effect of the fabrication errors of a pupil filter on its super-resolution property, with a three-zone phase-only pupil filters as example.     

衍射受限光学合成孔径成像系统像质评价

简述了光学合成孔径成像系统的原理,合成孔径成像系统在获得高截止频率的同时,降低了系统的中频性能,在空域表现为点扩展函数次峰增加。然后运用两点分辨率和光学传递函数对衍射受限光学合成孔径成像系统的像质评价问题进行了分析,指出了瑞利判据、斯派罗准则和“门限”判据的不足,认为当点扩展函数次峰大于主峰的0．5倍时,合成孔径系统与单孔径系统相比将失去优势。以光学传递函数为标准。分析三孔径合成系统子孔径尺寸、相互间距与等效系统孔径尺寸之间的关系。当子孔径直径不变时,随着其所在圆半径的增大,实际截止频率先增大,然后减小。     

一种基于减法运算的图象解卷积算法

分析了光学成象系统中点扩展函数的作用,采用减法运算从图象中消除了点扩展函数对图象造成的影响,从而实现了图象恢复.文章给出了该算法的流程及实例.     

Golay6结构复杂光瞳成像研究

Golay6为非冗余的复杂光瞳结构,导出Golay6结构复杂光瞳的光瞳函数解析式和点扩散函数的解析式,在此基上用Matlab软件模拟了调制传递函数图像,并对目标图像进行模拟成像。针对所成像对比度下降问题,在不含噪声和含噪声情况下分别进行了讨论,利用分数阶微分算子对模拟所得图像进行图像增强,结果表明经分数阶微分算子空域增...     

基于Poisson-Markov分布最大后验概率的多通道超分辨率盲复原算法

在Poisson和Markov随机场分布假设基础上,改进了存在噪声时多通道互限制原则,提出了一种基于最大后验概率判据的多通道图像盲复原算法,可在无需已知通道内离散点扩散函数性质、类型和具体分布等先验知识的情况下,在图像幅度限制约束空间和离散点扩散函数能量恒定约束空间内,通过对图像和离散点扩散函数的交替迭代,使两者收敛到全局最优解,最终复原出超分辨率图像.对计算机模拟和实际存在微平移、微离焦情况的图像处理表明：算法在不同信噪比水平和非命中PSF尺寸下具有良好的图像复原效果和稳定性. 关键词： 泊松-马尔科夫分布 最大后验概率 多通道 盲复原     

基于改进维纳逆滤波的衍射成像光谱仪数据误差分析与重构

衍射成像光谱仪探测到的高光谱数据需要进行计算与反演才可以得到成像光谱数据,本文对衍射成像光谱仪的成像过程及数据误差产生的原理从空间维和光谱维两方面进行了分析,并针对其光谱重构过程中系统点扩散函数标准差较大时重构结果清晰度较低、存在振铃等问题,提出了基于改进维纳逆滤波的光谱数据重构算法,该方法在分析衍射成像光谱仪数据特点与误差的基础上,将每一次维纳逆滤波的重构结果视为新的模糊图像,利用成像过程及维纳逆滤波的基本原理确定新的模糊图像对应的点扩散函数,反复进行维纳逆滤波达到提高图像清晰度的效果,再根据图像自身的空间和光谱特征分布,进行自适应性的噪声去除.利用模拟的衍射成像光谱数据进行验证,在系统点扩散函数的标准差为2.5的情况下,能得到无振铃的重构结果,且与传统维纳逆滤波法的重构结果进行比较,清晰度、细节能力等指标均有所提高,满足了衍射成像光谱数据应用需求.     

Effect of fabrication errors on lateral super-resolution property of a three-zone pupil filter

Two models have been established using the basic definitions of super-resolution characteristic parameters for normalized spot size G_T and Strehl ratio S_T of a three-zone lateral super-resolution pupil filter with fabrication errors to quantitatively analyze the effect of these fabrication errors on the lateral super-resolution property. These new models established to describe the analytic relationship of G_Te and S_Te of a pupil filter with its fabrication errors and its transmission function A(ρ), phase function φ(ρ) and structural parameters directly relate the super-resolution parameters of a three-zone lateral super-resolution pupil filter to its fabrication errors to make the quantitative analyses of the effect of fabrication errors easier, thereby providing a theoretical basis for the analysis, design and fabrication of a three-zone lateral super-resolution pupil filter. The models established for G_Te and S_Te have been used to analyze the effect of the fabrication errors of a pupil filter on its super-resolution property with a three-zone phase-only pupil filter as an example.     

空间变化PSF非盲去卷积图像复原法综述

传统的图像复原一般认为点扩散函数(PSF)是空间不变的,实际光学系统由于受到像差等因素的影响,并非严格的线性空间不变系统,基于空间变化PSF的非盲去卷积图像复原法逐渐体现其优越性。空间变化PSF的非盲去卷积图像复原法先准确估计图像空间变化的PSF,再利用非盲去卷积算法对图像进行复原,有利于恢复出高质量图像。本文从算法的角度综述了近几年提出的基于空间变化PSF的非盲去卷积图像复原方法,并对比了基于强边缘预测估计PSF的非盲去卷积法、基于模糊噪声图像对PSF估计非盲去卷积法等算法的优缺点,各算法分别在PSF估计精确度、振铃效应抑制效果、适用范围等方面体现出各自的优劣。空间变化PSF的非盲去卷积图像复原法的研究,有利于推进图像复原技术向更高水平发展,使光学系统往轻小型化方向发展,从而在多个科学领域发挥其重要作用。     

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.