汉英对照:
Chinese-English Translation:
色差（色像差）是指光学上透镜无法将各种波长的色光都聚焦在同一点上的现象。它的产生是因为透镜对不同波长的色光有不同的折射率。对于波长较长的色光，透镜的折射率较低
Chromatic aberration (chromatic aberration) refers to the phenomenon that the lens cannot focus the colored light of various wavelengths on the same point. It is produced because the lens has different refractive index to the color light of different wavelengths. For long wavelength colored light, the refractive index of lens is lower
用白光进行成像时，除了每种单色光仍会产生五种单色像差外，还会因不同色光有不同折射率造成的色散，而使不同的色光有不同的传播光路，从而呈现出因不同色光的光路差别而引起的像差，称之为色像差（简称色差）。色像差因性质不同而分为位置色差和倍率色差两种。
When white light is used for imaging, in addition to five monochromatic aberrations of each monochromatic light, different chromatic lights will have different propagation paths due to dispersion caused by different refractive indices of different colored lights. Therefore, the aberration caused by the difference of optical paths of different colored lights is presented, which is called chromatic aberration (hereinafter referred to as chromatic aberration). Chromatic aberration can be divided into position aberration and magnification aberration.
色差是指光学上透镜无法将各种波长的色光都聚焦在同一点上的现象。它的产生是因为透镜对不同波长的色光有不同的折射率。对于波长较长的色光，透镜的折射率较低。在成像上，色差表现为高光区与低光区交界上呈现出带有颜色的“边缘”，这是由于透镜的焦距与折射率有关，从而光谱上的每一种颜色无法聚焦在光轴上的同一点。
Chromatic aberration refers to the phenomenon that the lens can not focus the colored light of various wavelengths on the same point. It is produced because the lens has different refractive index to the color light of different wavelengths. For long wavelength colored light, the refractive index of lens is lower. In imaging, the color difference shows that there is a “edge” with color at the junction of the high light area and the low light area. This is because the focal length of the lens is related to the refractive index, so each color in the spectrum cannot be focused on the same point on the optical axis.
像差概念的来源
The origin of the concept of aberration
实际光学系统中，存在着远轴区产生的实际像与近轴区产生的理想像之间的偏离。此时，从物体上任一点发出的光束通过光学系统后不能会聚为一点，而形成一弥散斑，使像不能严格地表现出原物体形状，这就是像差。
In the actual optical system, there is a deviation between the real image generated in the far axis region and the ideal image generated in the near axis region. At this time, the light beam from any point of the object can not converge into a point after passing through the optical system, thus forming a diffuse spot, which makes the image unable to strictly show the shape of the original object, which is called aberration.
简介
brief introduction
用白光进行成像时，除了每种单色光仍会产生五种单色像差外，还会因不同色光有不同折射率造成的色散，而使不同的色光有不同的传播光路，从而呈现出因不同色光的光路差别而引起的像差，称之为色像差（简称色差）。色像差因性质不同而分为位置色差和倍率色差两种。
When white light is used for imaging, in addition to five monochromatic aberrations of each monochromatic light, different chromatic lights will have different propagation paths due to dispersion caused by different refractive indices of different colored lights. Therefore, the aberration caused by the difference of optical paths of different colored lights is presented, which is called chromatic aberration (hereinafter referred to as chromatic aberration). Chromatic aberration can be divided into position aberration and magnification aberration.
位置色差
Position color difference
定义
definition
位置色差是描述 2 种色光对轴上物点成像位置差异的色差。
Position chromatic aberration is the color difference that describes the imaging position difference of two kinds of color light on the object point on the axis.
色差严重影响光学系统成像性质，一般光学系统都必须校正色差。可以用正负透镜适当组合来校正位置色差。
Chromatic aberration seriously affects the imaging properties of optical systems, which must be corrected in general optical systems. The position chromatic aberration can be corrected by proper combination of positive and negative lenses.
影响位置色差的主要因素
The main factors affecting the position color difference
（1）随孔径角的增大而增大；
(1) It increases with the increase of aperture angle;
（2）与光学材料的折射率和色散率有关；
(2) It is related to the refractive index and dispersion index of optical materials;
（3）与透镜的焦距有关。
(3) It is related to the focal length of the lens.
倍率色差
Magnification chromatic aberration
定义
definition
倍率色差是一种因不同色光成像的高度（也即倍率）不同而造成的像大小差异的色差。
Magnification chromatic aberration is a kind of color difference caused by different imaging heights (i.e. magnification) of different color lights.
它是以两种色光（此即 F 光和 C 光）的主光线在高斯像面上的交点高度之差来度量，以符号
It is measured by the difference in the height of the intersection of the main rays of the two colored lights (i.e. f light and C light) on the Gaussian image plane
倍率色差随视场的增大而增大，由于倍率色差的存在，使物体边缘呈现彩色，从而，造成白光所成的像呈现彩色斑。
The magnification chromatic aberration increases with the increase of the field of view. Due to the existence of the magnification chromatic aberration, the edge of the object appears color, thus resulting in the image formed by white light showing color spots.
对于一般光学系统来说，球差、慧差和位置色差这三种对对成像性质影响较大，所以首先考虑消除，因人眼具有自动校正色差功能，故影响成像质量主要是球差和慧差。
For general optical systems, spherical aberration, coma aberration and positional chromatic aberration have great influence on imaging properties. Therefore, elimination should be considered first. Since the human eye has the function of automatically correcting chromatic aberration, spherical aberration and coma are the main factors affecting the imaging quality.
影响倍率色差的主要因素
The main factors affecting the chromatic aberration of magnification
（1）随视场的增大而增大；
(1) It increases with the increase of field of view;
（2）与光阑位置有关；
(2) It is related to the position of diaphragm;
（3）与光学材料的折射率和色散率有关
(3) It is related to the refractive index and dispersion index of optical materials
单色像差
Monochromatic aberration
分类
classification
球差——轴上点宽光束像差；
Spherical aberration the aberration of a wide beam on the axis;
彗差——轴外点宽光束像差；
Coma — off axis point wide beam aberration;
像散——轴外点细光束像差；
Astigmatism aberration of off-axis point thin beam;
像面弯曲（简称场曲）；
The image plane is curved;
畸变；
Distortion;
1.球差：
1. Spherical aberration:
轴上物点以宽光束成像时产生的像差。
The aberration caused by the wide beam imaging of the object on the axis.
不同孔径角的光线所成的像点相对于理想像点的位置偏离。
The position of the image point formed by the light with different aperture angle deviates from the ideal image point.
由于此球差是沿光轴方向度量的，也称为轴向球差。
Because the spherical aberration is measured along the optical axis, it is also called axial spherical aberration.
球差的存在，使像面上形成一个弥散斑，其半径称为垂轴球差。
The existence of spherical aberration makes a diffuse spot on the image plane, whose radius is called vertical spherical aberration.
影响球差的主要因素：
The main factors that affect the spherical aberration are as follows
（1）随物方孔径角的增大而增大 ；
(1) It increases with the increase of aperture angle;
（2）与透镜形状有关 ；
(2) It is related to the shape of lens;
（3）与焦距有关，焦距越长，球差越小。
(3) The longer the focal length, the smaller the spherical aberration.
轴外像差
Off axis aberrations
彗差——轴外点宽光束像差；
Coma — off axis point wide beam aberration;
像散——轴外点细光束像差；
Astigmatism aberration of off-axis point thin beam;
像面弯曲（简称场曲）；
The image plane is curved;
畸变 。
Distortion.
1.慧差：
1
子午面：由轴外物点 B 和光轴组成的对称面。
Meridian plane: the plane of symmetry composed of point B and optical axis.
弧矢面：通过主光线和子午面垂直的面。
Sagittal plane: the plane perpendicular to the meridian plane through the main ray.
主光线：由轴外物点 B 发出并通过入瞳中心的光线。
Main light: the light emitted by the off axis point B and passing through the center of the pupil.
（1）子午彗差：子午面上、下光线的交点 BT′到主光线在垂直光轴方向的偏离，称为子午彗差，用符号 KT′表示。
(1) Meridional coma: the deviation from the intersection point BT ‘of the upper and lower rays in the meridian plane to the main light axis in the direction perpendicular to the optical axis is called the meridional coma, which is represented by the symbol KT’.
（2）弧矢彗差：弧矢面上前、后光线的交点 BS′到主光线在垂直光轴方向的偏离，称为弧矢彗差，用符号 KS′表示。
(2) Sagittal coma: the deviation from the intersection point BS’ of the front and back light lines on the sagittal plane to the main ray in the direction perpendicular to the optical axis is called sagittal coma, which is represented by the symbol KS’.
畸变的产生
Generation of distortion
对于一般实际光学系统来说，只有在近轴区垂轴放大率才是常数。当视场增大时，像的垂轴放大率便会随视场变化而异，这将会使像相对于原物失去相似性。这种使像变形的成像缺陷就称为畸变。
For general practical optical systems, the vertical magnification is constant only in the paraxial region. When the field of view increases, the vertical magnification of the image will vary with the change of the field of view, which will make the image lose the similarity with the original object. This image distortion is called distortion.
如光学系统存在正畸变即实际像高大于理想像高，所成的像为枕形，负畸变则成桶形。
If there are orthodontic changes in the optical system, that is, the actual image height is greater than the ideal image height, the resulting image is pillow shaped, and the negative distortion is barrel shaped.
畸变只引起变形，不影响像的清晰度
Distortion only causes distortion and does not affect the clarity of the image
光学系统对共轭面上不同高度的物体垂轴放大率不同产生畸变。
The optical system distorts the objects with different heights on the conjugate surface with different vertical magnification.
像失真，但不影响像的清晰度（是由于垂轴放大率不同）。
Image distortion, but does not affect the image clarity (due to different vertical magnification).
光学设计的意义
The significance of optical design
尽管光学系统有一系列像差，而且一般总不能将其完全校正和消除。但由于人眼和所有其它光能接收器也有一定的敏感缺陷，只要使得各种像差的数值小于一个容许的限度，人眼和其它光接收器还是觉察或反映不出其成像的不完善性。这样的光学系统从实用意义来说，可认为是理想的。
Although the optical system has a series of aberrations, it can not be completely corrected and eliminated. However, the human eye and all other light energy receivers also have certain sensitivity defects, so long as the values of various aberrations are less than a allowable limit, the human eyes and other light receivers can not detect or reflect the imperfection of their imaging. Such an optical system can be regarded as ideal in practical sense.
