In optics, aberration is a property of optical systems such as lenses that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements. An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration. Aberration can be analyzed with the techniques of geometrical optics.
在光学中，像差是光学系统(如透镜)的一种特性，它使光扩散到空间的某个区域而不是聚焦到一点。像差导致由透镜形成的图像模糊或扭曲，其畸变的性质取决于像差的类型。像差可以定义为光学系统所成的像与近轴光学所成像的偏差。在成像系统中，当物体的某一点的光通过系统后未会聚到(或不发散)某一点时，就会发生这种现象。像差的发生不是由于光学元件的缺陷所致，而是因为简单的近轴理论不是光学系统对光的一个完全准确的模型。具有像差的成像光学系统将产生不清晰的图像。光学仪器制造商需要校正光学系统以补偿像差。像差可以用几何光学技术进行分析。
With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane (or, more generally, the image surface). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called aberrations of the lens.Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.在理想的透镜中，来自物体上任何一点的光都将通过透镜，并汇聚在像平面(或者更一般地说，像表面)的一点上。然而，真正的镜片并不会将光精确地聚焦在一个点上，即使它们制作的很完美，这些偏离理想化镜片性能的偏差称为镜片像差。。像差分为两类: 单色像差和色差。单色像差是由透镜或反射镜的几何形状引起的，在光反射和折射时都会发生。它们甚至在使用单色光时也会出现，因此得名。。色差是由色散引起的，色散是透镜的折射率随波长的变化。由于色散，不同波长的光在不同的点聚集。使用单色光时，不会出现色差。
Reflection from a spherical mirror. Incident rays (red) away from the center of the mirror produce reflected rays (green) that miss the focal point, F. This is due to spherical aberration. 球面反射镜的反射。远离镜面中心的入射光线(红色)产生的反射光线(绿色)没通过焦点F，这是由于球差造成的。
Monochromatic aberrationsThe most common monochromatic aberrations are:1. Defocus In optics, defocus is the aberration in which an image is simply out of focus. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Optically, defocus refers to a translation of the focus along the optical axis away from the detection surface. In general, defocus reduces the sharpness and contrast of the image. What should be sharp, high-contrast edges in a scene become gradual transitions. Fine detail in the scene is blurred or even becomes invisible. Nearly all image-forming optical devices incorporate some form of focus adjustment to minimize defocus and maximize image quality.1. 离焦 在光学中，离焦是指图像完全失去焦点的像差。使用相机、摄像机、显微镜、望远镜或双筒望远镜的人都熟悉这种像差。在光学上，离焦是指焦点沿光轴的平移。通常，离焦会降低图像的清晰度和对比度。场景中应该是锐利的、高对比度的边缘变成渐变的过渡，场景中的细节会变得模糊甚至看不见。几乎所有的成像光学设备都采用某种形式的聚焦调节，以最大程度地减少离焦并提高图像质量。
A photograph of Christmas lights with significant defocus aberration. 离焦像差严重的圣诞灯照片。
2. Spherical aberration Spherical aberration is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non-spherical curved surfaces. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems.2. 球面像差 球面像差是使用球面元件光学系统中发现的一种像差。透镜和曲面镜的表面通常是球面，因为这种形状比非球形曲面更容易制作。偏离球面中心的光线比靠近球面中心的光线折射更多反射更少，这种偏差会降低光学系统产生的图像质量。
On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the focal point. The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point. The further the rays are from the optical axis, the closer to the lens they intersect the optical axis (positive spherical aberration). 上图是没有球差的完美镜头：所有入射光线都聚焦在焦点上。下图是一个具有球面的真实镜头，该球面会产生球差：不同的光线在一个焦点不相交。光线离光轴的距离越远，它们与光轴的相交越近（正球面像差）。
3. Coma In optics (especially telescopes), the coma, or comatic aberration, in an optical system refers to aberration inherent to certain optical designs or due to imperfection in the lens or other components that results in off-axis point sources such as stars appearing distorted, appearing to have a tail (coma) like a comet. Specifically, coma is defined as a variation in magnification over the entrance pupil. In refractive or diffractive optical systems, especially those imaging a wide spectral range, coma can be a function of wavelength, in which case it is a form of chromatic aberration. 3. 彗差 在光学系统（尤其是望远镜）中，光学系统中的彗差或彗形像差是指某些光学设计所固有的像差，或者是由于透镜或其他组件的不完美而导致的离轴， 诸如星星之类的点光源看起来扭曲、像彗星一样有尾巴（彗差）。具体地，彗差被定义为在入射光瞳上放大率的变化。在折射或衍射光学系统中，尤其是在宽光谱范围内成像的光学系统中，彗差可以是波长的函数，在这种情况下，它是色差的一种形式。
Coma of a single lens 单透镜彗差
4. Astigmatism An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. 4. 散光 有散光的光学系统是指在两个垂直面上传播的光线有不同的焦点。如果用散光的光学系统来形成一个十字像，则垂直和水平线将在两个不同的距离处形成清晰的焦点。（详细内容见本公众号文章-散光）
Graphic illustratic the astigmatism phenomenon.图示散光现象。
5. Field curvature Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis (or a non-flat object past the hyperfocal distance) cannot be brought properly into focus on a flat image plane. 5. 场曲 Petzval场曲率，以Joseph Petzval的名字命名，描述了垂直于光轴的平面物体(或超过超焦距离的非平面物体)不能在像平面上被正确聚焦的光学像差。
Field curvature: the image "plane" (the arc) deviates from a flat surface (the vertical line).场曲: 图像“平面”(弧)偏离像平面(垂直线)。
6. Image distortion In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration. 6. 图像畸变 理论场景中的直线在图像中应保持直线。但在几何光学中，对直线投影发生了偏差，这也是光学像差的一种形式“畸变”。
Wine glasses create non-uniform distortion of their background 酒杯造成了背景的不均匀变形
Although defocus is technically the lowest-order of the optical aberrations, it is usually not considered as a lens aberration, since it can be corrected by moving the lens (or the image plane) to bring the image plane to the optical focus of the lens.In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.虽然离焦在技术上是光学像差的最低阶，但它通常不被认为是透镜像差，因为它可以通过移动透镜(或像平面)使像平面到达透镜的光学焦点来校正。除了这些像差外，偏心和倾斜也可对焦点的位置造成影响。偏心和倾斜不是真正的光学像差，因为当一个原本完美的波前被偏心和倾斜改变时，它仍然会形成一个完美的、无像差的图像，只是移动到不同的位置。Chromatic aberration occurs when different wavelengths are not focussed to the same point. Types of chromatic aberration are:1. Axial (or "longitudinal) chromatic aberration Axial aberration occurs when different wavelengths of light are focused at different distances from the lens (focus shift). Longitudinal aberration is typical at long focal lengths.2. Lateral (or "transverse) chromatic aberration Transverse aberration occurs when different wavelengths are focused at different positions in the focal plane, because the magnification and/or distortion of the lens also varies with wavelength.当不同的波长没有聚焦到同一点时，就会发生色差。色差的种类有:1. 轴向（或“纵向”）色差 当不同波长的光聚焦在距镜头的不同距离处（焦点偏移）时，就会发生轴向色差。纵向色差在长焦距下很典型。2. 侧向（或“横向”）色差 当不同波长聚焦在焦平面上的不同位置时，会发生横向像差，这是因为透镜的放大率或畸变也随波长而变化。
Comparison of an ideal image of a ring (1) and ones with only axial (2) and only transverse (3) chromatic aberration 比较理想的环像(1)和只有轴向色差(2)和横向色差(3)像的比较
王曌，光学博士，爱博诺德（北京）医疗科技股份有限公司研发总监、教授级高工。 |
