Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

Incorporating lens distortion into the design of undistorted catadioptric omnidirectional cameras

An improved approach for design of the catadioptric omnidirectional camera with horizontal scene undistorted imaging is described. In the proposed approach, the influence of the lens distortion on the imaging quality of the omnidirectional camera is taken into account. We establish a radial distortion model for an image pickup lens and retain some opposite distortion in the mirror to correct the distortion existing in the image pickup lens. A horizontal scene undistorted catadioptric omnidirectional camera is designed with an off-the-shelf TV short focus lens using our approach; the numerical simulation shows that the distortion introduced by the imaging lens is eliminated effectively.     

Keystone aberration correction in overhead projectors

Keystone distortion that occurs in overhead projectors when the projecting lens head is tilted upward to a high screen is commonly observed. Here we suggest a modification of the typical overhead projector to eliminate this distortion of the image.     

A method for correcting radial distortion based on verifying the planarity of specimens

Image distortion is inevitable when an image is captured through a lens. While the digital image measurement technique is getting popular, image distortion problem can result in significant error. A new distortion correction method is proposed in this study. The proposed method is based on the fact that a flat surface should keep flat when it is measured using three-dimensional (3D) digital image measurement technique. The 3D digital image measurement technique adopted in this research is the simplified 3D digital image correlation (DIC) method. Because radial distortion has a more noticeable influence than other types of distortions, this method deals only with radial distortion. A few experiments are carried out in this study to verify the correctness of this method and its accuracy. Both simulated data and actual image data are adopted in these experiments. The results show that this method can achieve a good accuracy. The standard deviations caused by random errors are about the same order as the random errors. It also shows that this method is suitable for both large and small distortion conditions.     

光点位置测量系统摄像镜头设计

针对使用线阵列电荷耦合器件(CCD)的二维位置定位系统中的光学系统的特殊要求,本文提出一种以球面镜作为前组柱面镜作为后组,前组像面作为后组物面的二级成像结构作为线阵CCD的摄像镜头.该镜头使具有相同一维坐标值的点成像为同一条直线,并且具有广角视场,畸变小,成像质量优良等性能特点.对其设计思想、像差特点进行了分析,并给出了f'=.20 mm,2ω=74,畸变小于1.6%的柱面镜摄像镜头实例及其像差和传递函数计算曲线.     

Effect of lens distortion in optical step-and-scan lithography

A model is presented with which the effect of lens distortion on the optical transfer function is calculated for a step-and-scan lithographic system. The spatially varying lateral image shift and the relative loss in modulation depth are derived from the exposure pattern that is built up during the image scanning. Other important phenomena such as lens aberrations, the effect of finite image aperture, and polarization are deliberately left out of the model; from the simplified model, analytic expressions can be obtained that relate the distortion coefficients of the projection system to the local shift and the relative loss in modulation depth of the exposed pattern that is built up during scanning. As a scanning aperture, we have taken either part of an annulus or a rectangular section in the image field.     

广角镜头桶形畸变的样条函数修正方法

为了修正广角镜头的桶形畸变,本文提出了一种基于样条函数的修正方法.依据镜头桶形畸变产生的物理机制,本文首先制作了一个同心圆标定模板并用该模板对广角镜头进行标定.然后利用样条函数的光滑性和桶形畸变的径向连续性,采用三次样条函数拟合桶形畸变规律.最后,用该样条函数拟合的桶形畸变规律对同一个视觉系统拍摄的变形图像进行恢复.在实验中,该方法能够对畸变图像进行快速恢复并表现出良好的效果.因此对于固定焦距视觉系统,在不考虑视觉系统具体参数的情况下,新的方法能够快速有效地对广角镜头桶形畸变进行修正.     

Optical compensation of hologram distortion avoiding interpage crosstalk on reconstructed image in angle-multiplexed holograms

We are studying a form of holographic data storage with phase conjugation, and we compensated for hologram distortion due to shrinkage of photopolymer materials in the holographic medium by controlling the wavefront of the reference beam. When a high NA lens and narrow angle interval of angle multiplexing are employed to obtain a high data recording density, some wavefronts cause interpage crosstalk on the reconstructed image. We tried to determine the moving range of actuators in a deformable mirror for controlling the wavefront. As a result, we found that the distortion in the hologram could be compensated while avoiding interpage crosstalk and that the bit error rates of the reproduced data could be decreased. We also found that the optimized wavefront could compensate for distortions in several neighboring data pages. This method can ensure a high data recording density in holographic data storage.     

三维重构视觉系统的标定

文章基于改进两步法的标定思想,在三维重构中提出了一种新的视觉系统参数标定与镜头畸变修正方法.该方法根据图像中心附近点畸变量较小的性质,利用中心附近点和全场视点对CCD相机和DLP投影仪的内外部参数标定和镜头畸变修正进行分离.在标定过程中,所设计的带标准圆阵列的靶标和伪随机连续方形编码可以实现特征点的自动识别和匹配.实验表明,该方法能快速、方便地对视觉系统参数进行标定和镜头畸变修正.     

Content- and disparity-adaptive stereoscopic image retargeting

The paper proposes a content- and disparity-adaptive stereoscopic image retargeting. To simultaneously avoid the saliency content and disparity distortion, firstly, we calculate the image saliency region distortion difference, and conclude the factors causing visual distortion. Then, the proposed method via a convex quadratic programming can simultaneously avoid the distortion of the salient region and adjust disparity to a target area, by considering the relationship of the scaling factor of salient region and the disparity scaling factor. The experimental results show that the proposed method is able to successfully adapt the image disparity to the target display screen, while the salient objects remain undistorted in the retargeted stereoscopic image.     

应用经纬映射的鱼眼图像校正设计方法

为了消除鱼眼镜头带来的形变,该文提出了一种应用经纬映射的鱼眼图像校正设计方法,推导了消除变形的数学依据,总结出一种不需要任何标定数据,快速的纠正等角鱼眼变形的算法。使用经纬映射图像的校正方法,可以把扭曲的半球鱼眼图像投射为普通照片的四方形状,也即通过投射降低图像的扭曲程度,在视觉上基本达到实用要求。     

Scalable high-resolution integral videography autostereoscopic display with a seamless multiprojection system

We propose a scalable high-resolution autostereoscopic display that uses integral videography (IV) and a seamless multiprojection system. IV is an animated extension of integral photography (IP). Although IP and IV are ideal ways to display three-dimensional images, their spatial viewing resolution needs improvement; the pixel pitch of the display and the lens pitch are the main factors affecting IV image quality. We improved the quality by increasing the number and density of the pixels. Using multiple projectors, we create a scalable high-resolution image and project it onto a small screen using long-focal-length projection optics. To generate seamless IV images, we developed an image calibration method for geometric correction and color modulation. We also fabricated a lens array especially for the display device. Experiments were conducted with nine XGA projectors and nine PCs for parallel image rendering and displaying. A total of 2868 x 2150 pixels were displayed on a 241 mm x 181 mm (302.4 dots/in.) rear-projection screen. The lens pitch was 1.016 mm, corresponding to 12 pixels of the projected image. Measurement of the geometric accuracy of the reproduced IV images demonstrated that the spatial resolution of the display system matched that of the theoretical analysis.     

现场勘察中广角镜头相机快速标定算法及实现

基于摄影资料的图像测距技术已广泛应用于交通事故、考古等不可复原的现场勘察工作中,利用普通相机进行摄影测量也日趋成熟。但是普通相机没有广角镜头相机的取景优势,现场分析也比较局限,因此广角镜头相机逐渐取代普通相机。而广角镜头相机容易产生图像畸变效应。为此,本文基于相机成像原理,通过精确网格模板标定图像,利用相机参数间物理关系计算出相机内参和畸变参数,提出了一种广角镜头相机的快速标定算法,结合拍摄现场图像,精确定位参考模板标志牌在照片中的成像结果,计算出广角镜头相机的外参,建立广角镜头相机摄影测量系统。现场实验应用表明,本算法标定快速、简单、测量精度高,可以应用于交通事故现场勘测。     

Improving fast aspheric convex surface tests with dynamic null screens using LCDs

A method for testing fast aspheric convex surfaces with dynamic null screens using LCDs is shown. A flat null screen is designed and displayed on an LCD monitor with drop-shaped spots in such a way that the image, which is formed by reflection on the test surface, becomes an exactly square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. Here the whole surface is tested at once. The position of the spots on the LCD can be changed in a dynamic way, to perform point-shifting of the image spots. The proposed procedure improves the dynamic point-shifting method. As has been shown previously, this process reduces the numerical error during the integration procedure, thereby improving the sensitivity of the test. The positioning accuracy for the screen spots is related to the LCD's spatial resolution. Results of the evaluation of a parabolic convex surface with f/#=0.22 are shown.     

Modulation transfer function of a lens measured with a random target method

We measured the modulation transfer function (MTF) of a lens in the visible region using a random test target generated on a computer screen. This is a simple method to determine the entire MTF curve in one measurement. The lens was obscured by several masks so that the measurements could be compared with the theoretically calculated MTF. Excellent agreement was obtained. Measurement noise was reduced by use of a large number of targets generated on the screen.     

成像距离对图像畸变系数的影响研究

基于共线特征点求解图像畸变系数的方法,研究了拍摄物体平面与镜头平面间的不同距离参数对图像畸变系数的影响,并结合实验结果探寻了畸变系数的变化规律。在此基础上,指出镜头的畸变系数不仅与焦距有关,成像距离也是重要的影响因素,不可忽略。进行了不同距离参数下的畸变系数对相同标准量块图像校正的实验研究,比较了不同畸变系数下校正量块图像的不同高度位置的宽度曲线。实验结果表明,不同距离参数下的畸变参数对量块图像进行校正的结果是不同的,且当选用的畸变参数的距离与实际的成像距离相同时,其校正结果的精度最高,量块图像宽度测量的精度最高。     

背投影显示系统及双重功能屏幕设计与研究

为了实现背投影显示系统的超薄化,介绍一种新的背投影显示系统和双重功能屏幕的设计方案,利用屏幕对不同入射角的入射光线进行选择,采用高折射率的有机材料构成三棱柱屏幕微结构,设计出厚度为20cm的40寸背投影显示系统的结构.并对所设计的系统在ASAP中进行了模拟,得出了屏幕图像畸变、均匀性和像面光照度分布等性能指标,得到令人满意的结果.最后提出了改进方向.     

Object surface for applying a modified hartmann test to measure corneal topography

A modified Hartmann test is proposed for measuring corneal topography. The plane screen with holes used in the typical Hartmann test is replaced with a curved object surface. This object surface yields a plane image for a spherical mirror surface. We show that the object surface is an oval of revolution that can be modeled by an ellipsoid. The plane image will be formed by a square array of circular spots, all with the same diameter. To obtain the square array in the image, we calculated the spatial distribution of the spots on the object surface.     

Zoom projection lens design for small throw ratio and large field of view

In order to meet the requirements of large screen projection displays, we propose an ultra-thin zoom projection lens with a small throw ratio (TR), ultra-short throw distance and large field-of-view (FOV) using a digital micromirror device as a spatial modulator. A refractive–reflective system is developed to correct the distortion and shorten the projection distance. The image size (diagonal, 16:9 aspect ratio) of the projector is 80–120 in. (2.032–3.048 m) with a TR of 0.22, TV distortion < 0.6%, root mean square (RMS) spot size < 1.1 mm, relative illumination > 85% and modulation transfer function > 0.4 at 0.55 lp/mm for all fields and zoom conditions. When the tolerance error is considered, the RMS value is less than 1.3 mm for all fields and zoom conditions. Finally, the projection lens is fabricated and tested according to the designed model.     

Estimating three-dimensional vehicle motion in an outdoor scene using stereo image sequences

We propose a motion estimation system that uses stereo image pairs as the input data. To perform experimental work, we also obtain a sequence of outdoor stereo images taken by two metric cameras. The system consists of four main stages, which are (1) determination of point correspondences on the stereo images, (2) correction of distortions in image coordinates, (3) derivation of 3D point coordinates from 2D correspondences, and (4) estimation of motion parameters based on 3D point correspondences. For the first stage of the system, we use a four-way matching algorithm to obtain matched point on two stereo image pairs at two consecutive time instants (t_i and t_{i + 1}). Since the input data are stereo images taken by cameras, it has two types of distortions, which are (i) film distortion and (ii) lens distortion. These two distortions must be corrected before any process can be applied on the matched points. To accomplish this goal, we use (i) bilinear transform for film distortion correction and (ii) lens formulas for lens distortion correction. After correcting the distortions, the results are 2D coordinates of each matched point that can be used to derive 3D coordinates. However, due to data noise, the calculated 3D coordinates to not usually represent a consistent rigid structure that is suitable for motion estimation; therefore, we suggest a procedure to select good 3D point sets as the input for motion estimation. The procedure exploits two constraints, rigidity between different time instants and uniform point distribution across the object on the image. For the last stage, we use an algorithm to estimate the motion parameters. We also wish to know what is the effect of quantization error on the estimated results; therefore an error analysis based on quantization error is performed on the estimated motion parameters. In order to test our system, eight sets of stereo image pairs are extracted from an outdoor stereo image sequence and used as the input data. The experimental results indicate that the proposed system does provide reasonable estimated motion parameters.