基于插值数浮动的MTF精确测量方法

采用刀口法测量成像系统调制传递函数(MTF)时,刀口装置与探测器矩阵夹角的准确测量是难点和关键点之一.针对这一问题,首先模拟刀口图像倾角对应的理论基准插值,研究了加载噪声情况下插值数浮动与线扩散函数(LSF)波动性变化以及MTF曲线衰减特性的定量关系;接着对实际X射线数字化成像系统获得的特定倾角下的刀口边缘图像进行了基于插值浮动的MTF测量,并将由其获得的MTF值与线对卡结果进行比较,证明了该方法用于成像系统MTF测量的有效性.结果表明:角度测量误差造成实际插值数偏离理想基准插值,导致LSF曲线光滑性变差,MTF衰减程度高于实际衰减.通过插值浮动方法,能够有效地避免角度测量误差引起的MTF测量的误差,降低角度测量的高精密性要求.     

Influence of the type of illumination on the measurement of the modulation transfer function in the living human eye: A theoretical study

Abstract

Applications such as refractive surgery demand an objective appraisal of the retinal image quality. The modulation transfer function (MTF) provides that information when measured directly. Moreover, the MTF obtained using a simple and objective method such as that described in this paper allows the neural contrast sensitivity function (CSF) to be obtained from the global CSF and the MTF. When calculating the MTF it must be borne in mind whether the applicable theory is coherent or incoherent. In the literature, the developed theory presents some approximations and incongruities. Also, it is interesting to note that the method of recording the MTF (short or long time of integration, sum of images, etc.) and the source used (laser or others) can essentially change the nature of the problem. This theory is not directly applicable to any experiment. This work comprises a thorough theoretical study of the possible cases according to the experimental method and therefore as a function of the coherence degree. Two different solutions are found: the MTF calculated as the square root of the Fourier Transform (FT) of the recorded intensity for any light source or the MTF calculated as the FT square root of the image.     

Criteria for the Evaluation of Photographic Lenses

Simplified test conditions for the evaluation of lenses based on MTF measurements are described, and criteria for interchangeable lenses for 35 mm cameras are proposed. Measurements are to be made for white light, at the infinite conjugate plane, on axis and at 0·7 field (15 mm off axis) positions, at full aperture and ?/5·6. The focus is to be adjusted at each aperture so as to give the best MTF response at 30 lines/mm on axis. The MTF responses at 15 and 30 lines/mm are to be examined for the evaluation of the lenses. Simple criteria based on the experimental data for about 100 different types of interchangeable lenses are proposed.     

Modal analysis of transport processes in SPRITE detectors

Carrier transport in signal-processing-in-the-element (SPRITE) detectors is an important phenomenon because it determines properties such as the responsivity and the modulation transfer function (MTF). The previous literature has presented approximate solutions to the transport problem that neglect boundary effects, which have long been thought to play a major role in SPRITE behavior. We present a new solution to the problem through the use of modal analysis. This method intrinsically includes boundary conditions and thus is more complete than the previous analysis. Furthermore we use this solution to derive expressions for the MTF. The effects of the boundary conditions on the MTF are studied to determine their optimum values.     

Modulation transfer function evaluation of linear solid-state x-ray-sensitive detectors using edge techniques

The exact determination of the modulation transfer function (MTF) of a physical system is a persistent problem. We present a practical method of measuring numerically the MTF of linear solid-state x-ray-sensitive detectors. The method is based on the use of edge techniques and allows us to obtain the MTF of a linear detector from its edge-spread function (ESF). ESF measurement techniques are discussed in detail, and calculation of the corresponding MTF's are shown.     

Modulation transfer function measurement of an infrared focal plane array by use of the self-imaging property of a canted periodic target

We present a new technique for measuring the modulation transfer function (MTF) of a focal plane array (FPA). The main idea is to project a periodic pattern of thin lines that are canted with respect to the sensor's columns. Practically, one aims the projection by using the self-imaging property of a periodic target. The technique, called the canted periodic target test, has been validated experimentally on a specific infrared FPA, leading to MTF evaluation to as great as five times the Nyquist frequency.     

Surface electromigration of sputtered copper patterned using ion milling or chemical mechanical polishing

Electromigration characteristics of sputtered copper patterned both by ion milling and, more recently, by chemical mechanical polishing (CMP) have been studied. Comparison was made with the electromigration characteristics of sputtered aluminum. Standard unpassivated copper lines, patterned by ion milling, and stressed at 300 °C and 2MAcm^-2 in a N₂ ambient, exhibited a mean-time-to-failure (MTF) of 90 h, compared with only 20 h for aluminum lines of similar dimensions. CMP of the electromigration test structures proved quite challenging because of the large contact pads. Benzotriazole (BTA), used as a passivating agent in the polish process, is effective in preventing copper corrosion. However, the MTF obtained for copper lines patterned by CMP is only approximately 60 h. This is attributed to a reduction in surface diffusion caused by scratches from the alumina abrasive particles. Copper grain size plays an important role in electromigration. The longest electromigration resistance test period was achieved on copper composed of small grains. A decrease in lifetime was also found to be caused by oxidation of the samples. However, a passivating layer of spin-on-glass (SOG) further increased the MTF to greater than 100 h.     

Calculation of the modulation transfer function for object brightness distribution function oriented along any direction in axis-symmetrical optical systems

The literature deals with the modulation transfer function (MTF) only for object brightness distribution functions (OBDFs) oriented along the meridional and sagittal directions. This paper addresses computation of the geometrical MTF for an off-axis source point when the OBDF is oriented along any arbitrarily defined direction. This study finds that the MTF is not a monotonic increasing or decreasing function when the direction of the OBDF is changing. Consequently, the extreme MTF values may occur when the OBDF is aligned at any direction between the meridional and sagittal directions. Four theorems are provided for the MTF and the phase shift variations that take place when the OBDF is translated or rotated. It is found that the MTF and the phase shift are symmetrical or antisymmetrical about certain directions. Thus, to observe all possible changes in the MTF and the phase shift, it is sufficient to rotate the OBDF through a range of just 90°. The presented method is based on a recent irradiance method for MTF computation that does not rely on counting the number of ray hits on a mesh, making the method immune to effects of grid size and thus improving traditional accuracy.     

The Optimal Sight Angle Problem

We introduce the following problem in this paper. There are n points on the plane that are to be observed from some point on a circle of given radius that encloses all of the points. We wish to find the observation point that has the best possible view of the n points in the sense that if we draw lines of sight from the observation point to the given points, the smallest angle between the lines is maximized. Applications could include the planning of photographs or displays. This is a “maximin problem” in which the function to be maximized has many local optima. We present two methods for solving the problem, one more efficient in computer time, and the other in storage. We also present a simplified procedure for the case where the observation point is “infinitely” distant from the given points.     

Estimation of point-spread functions and modulation-transfer functions of optical devices by statistical properties of randomly distributed surfaces

The point-spread function a(PSF) and the modulation-transfer function (MTF) are important tools to characterize the information transfer through optical devices. They give useful information about the resolution. Several methods have already been achieved to calculate the PSF and the MTF from theoretical aspects of wave propagation or from experimental results. I present a novel way of estimating these two functions. It deals with statistical considerations for a randomly distributed surface involving a statistical determination of the PSF and the MTF. Indeed, in this case the theoretical shape of the autocorrelation function of such surface profiles is known. It is a decaying exponential function α[exp(-β|x|)]. Comparingthe theoretical autocorrelation-function profile with the experimental one and deconvolving in Fourier space leads to an estimation of the MTF of the imaging device. Applying the inverse Fourier transform to the MTF involves the computation of the PSF, assuming that the latter has no imaginary part and is symmetrical. The two-dimensional images are regarded as an iteration of one-dimensional ones according to the orthogonal direction. The MTF's and PSF's are therefore one-dimensional. Different results are presented. The first result proceeds from investigation with scanning near-field microscopy and illustrates the method step by step. The tunneling effect is detected assuming that the information transfer is linear. The last result concerns an optical profilometer, and the influence of the microscope objective is studied.     

圆孔阵列对“猫眼”目标成像质量的影响分析

利用圆孔阵列光强调制作用可以有效减弱光学窗口的“猫眼”效应,同时也会对“猫眼”目标成像质量产生一定不利影响.考虑到利用调制传递函数(MTF)可对光电仪器成像质量进行综合评价,分别给出了测试望远系统和微光夜视系统MTF的数学模型,利用自行研制的光学仪器MTF数字化检测系统,实现了这两种典型“猫眼”目标MTF的数字化检测.结果表明,圆孔阵列在全空间频率上均使“猫眼”目标的MTF有所下降,且孔径较小、孔阵较密的圆孔阵列对“猫眼”目标MTF的影响较小,这为合理设计圆孔阵列结构以减小对“猫眼”目标成像质量的影响提供了可靠的实验数据.     

CMOS APS图像传感器的像质分析

使用标准CMOS制作工艺生产的有源像素传感器（APS）引起了广泛关注。为了确定CMOS APS成像系统设计的主要参数选择的正确性,以及能否满足要求或指标,需要对相机系统的像质进行分析。考虑到CMOS APS图像传感器与CCD的不同,在分析时计算了CMOS APS成像系统中的镜头、滤光片和焦平面的调制传递函数（MTF）,系统MTF曲线为各个部分MTF值之积。在系统截止频率范围内,利用MTF曲线所围面积的大小来评价系统的成像质量。在系统制造之前,用调制传递函数作为像质的评价方法,看其是否符合使用要求,是十分有价值的工作。     

Modulation transfer function measurement of sparse-array sensors using a self-calibrating fringe pattern

A simple method for the measurement of the pixel modulation transfer function (MTF) of sparse-array (extended MTF) sensors has been developed. We use a phase-shifting Twyman-Green interferometer to generate a series of single spatial-frequency fringe patterns incident on the sensor The resulting signal modulation is measured. We achieve self-calibration by restricting the measured spatial frequencies to multiples of the Nyquist frequency. The aliased patterns at these frequencies are unique and easily identifiable. Spatial frequencies of 480 cycles/mm are generated and measured. This frequency value is more than ten times that of the sensor sampling frequency. The expected MTF shape is obtained at multiples of the sampling frequency. At odd multiples of the Nyquist frequency, the MTF's are affected by the electronic bandwidth and cross talk in the charge-injection device sensor.     

Analytical optimal solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Reduced-complexity approximate representation of the modulation transfer function

In this paper we derive an approximate analytical representation for the modulation transfer function (MTF) of an imaging system possessing a defocused cubic-phase pupil function. This expression is based on an approximation using the Arctan function and significantly reduces the computational time required to calculate the resulting MTF. We derive rigorous bounds on the minimum and average accuracy of our approximation. Using this approximate representation of the MTF, the analytical solution of the problem of calculating the extension of the depth of field for a circular aperture with a cubic phase mask becomes possible. We also comment on how one can modify our method to construct a lower-bound or an upper-bound approximate analytical expression for the MTF.     

基于改进Hough变换的直线图形快速提取算法

为能够有效解决实时直线图形提取问题,提出了一种基于多约束Hough变换(HT)的直线提取算法.该算法首先分析了数字图像中直线边缘的三种结构特征,提出采用基元结构表示目标边缘点,并在约束条件下计算基元结构的基元倾角.在此基础上,结合传统的HT的思想对基元结构进行极角约束HT,以获得最终的直线参数.实验结果表明,对合成图像和自然图像,该算法比梯度HT的运算速度分别提高约190倍和22倍.     

An Afocal-system OTF Test Standard

Several standard test lenses for evaluating the accuracy of OTF measuring equipment have been described in the literature. However, these are not generally suitable for evaluating the equipment and test procedures used for afocal systems which differ from those used with normal lenses in several significant ways. A special afocal system in the form of a straight-through telescope has been designed and built for this purpose. The paper describes the design and construction of this telescope and compares the calculated and experimentally measured values for the MTF of the system. A particular feature of the MTF calculations is that they have been carried out, not only for the usual radial and tangential azimuths, but also for several intermediate azimuths. Thus it has been possible to determine the value of a range of different MTF-based criteria which relate to measuring equipment where the MTF is measured at a single spatial frequency in all azimuths.     

Aberrated Optical Systems with Optimum Apodizers for the Strehl Ratio: Axial and Extra-axial Point-spread Function and Modulation-transfer Function

Abstract

The amplitude distribution at the aperture of an optical system for off-axis object points due to the introduction of a non-uniform transmission filter depends on the transmission function and on the longitudinal filter position. The effects of several filters on the axial and extra-axial point-spread function (PSF) and modulation-transfer function (MTF) of an optical system for different filter positions are studied. The filter transmission function and the filter position are obtained by the optimization of the axial and extra-axial Strehl ratios. The axial and extra-axial effects of the filters on the PSF and on the MTF are analogous. There are some positions of the filter for which the overall performance is significantly improved. The optimum longitudinal positioning of the apodizing filter is achieved in a process which is analogous to the stop shift effect in conventional optical design. The lack of radial symmetry in the off-axis wavefront aberration function at any particular field angle is convolved with the apodizing function and this leads to the anticipated improvement.     

具有离散参数齐次随机场的线性预测（XV）

本文进一步研究了预测问题9（N，M）及17（N，M），在频域上及时域上都求得了齐次随机场{x（m，n）}在任意点上的预测值及预测误差，从而改进了徐业基已往的结果。     

具有离散参数齐次随机场的线性预测(ⅩⅤ)

本文进一步研究了预测问题9(N,M)及17(N,M),在频域上及时域上都求得了齐次随机场{x(m,n)}在任意点上的预测值及预测误差,从而改进了徐业基已往的结果。     

两种排列方式光纤传像束的像质评价

根据调制传递函数对比度定义,推导了线列光纤传像束调制传递函数(MTF)的数理关系,建立了光纤直径有随机误差的线列光纤传像束MTF仿真模型,对MTF进行数值分析。通过考虑在光纤传像束中输入信号与光纤的位相匹配对MTF的影响,分析了V型槽排列和紧密排列两种不同方式的光纤传像束的平均MTF。结果显示,有随机误差的光纤束的平均MTF值分别分布于理想传像束平均MTF曲线附近,表明了光纤自身的误差对传像束的平均MTF影响不大;V型槽排列的线列光纤束的像质优于紧密排列方式的线列光纤束。