1、6.8 The Illuminance Equation For Image Points Off The Axis:, is the image field angle of view,E is the marginal illuminance(边缘光照度),E0 the axial illuminance(轴上光照度),K is the radio of clear aperture (通光孔径)betweenthe oblique(倾斜的) beam and the axial beam,Chapter 7 Image Quality Of Optical System,常见的像差,7.
2、1 Introduction(简介),1) Two requirements for the imaging properties (成像性能)of the system: The first requirement includes the effective focal length(有效焦距)，the object and image distance(物距和像距), the magnification(放大率), the entrance pupil (入瞳)position and distance, etc.,The second requirement includes the
3、image quality of the optical system. The image formed by the system should be similar to the object, and should be clear (清晰) enough and distort (变形) as small as possible.,2) Two type of the aberrations(像差):,The first type of aberrations are suitable for the measurement of an optical instrument whic
4、h is already produced(制造完成后). The second type of aberrations are suitable for the design stage(设计阶段).,Resolution Measurement1,The so-called resolution power of an optical system is the smallest distance which can be resolved by the system 系统所能分辨的最小的间隔,所能分辩的最 小间隔，可以 代表系统成像 的清晰度,空间频率,Fig. 7.1 Resoluti
5、on test plate,In the actual measurement, a resolution test plate(分辨率板) is used to be the object. Then the smallest distance(mm)on the image plane which can be resolved by the system will be the resolution power (分辨能力) of the system.,Sometimes the reciprocal(倒数)is also used to represent the resolutio
6、n power: The spatial frequency(空间频率): =1/ (7.1)，the unit of is lp/mm.,modulation transfer function (MTF),Star Test1,If the image is not ideal or is a blur(one object point can not be imaged as a perfect image point according to wave optics), the size and the energy distribution (分布) of the blur (光斑)
7、 can be used to estimate the image quality of the system. 根据弥散斑的大小和能量分布的情况，就可以评价系统像质的优劣。,Geometrical optics2,Geometrical aberration (几何像差)，Wave front aberration(波像差)，Spot diagram(点列图)，Geometry OTF（Optics Transfer Function）(几何光学传递函数), etc.,单色光像差有五种： 球差Spherical aberration 彗差Coma,comatic aberration 像散
8、Astigmatism 场曲Curvature of field 畸变Distortion,复色光像差有两种： 轴向色差The axial chromatic aberrations 垂轴色差The lateral chromatic aberrations,几何像差:,Physics optics2,Point Spread Function(点扩散函数,点列图)，Relative central luminous intensity(相对中心光强)，Physical OTF(Optics Transfer Function)(物理光学传递函数), etc.,7.2 Color Disper
9、sion(色散) And Chromatic Aberrations(色差),1) The Define Of Color Dispersion(色散) For a certain medium the difference ( ) of two index of the indexes for two different wavelengths, is called the color dispersion(色散).,We select the difference ( ) of two indexes of two special wavelengths, (C光) and (F光), t
10、o represent the color dispersion, which is called mid-dispersion (中部色散).,Chromatic Aberrations(色差),兰,绿,红,lF,-lFC,lc,AF,Ac,轴向（位置）色差定义为：,The Axial Chromatic Shifts (轴向色差),较长;,较短,较大;,较小,Because of the fact that the index of refraction varies as a function of the wavelength of light, the focal length al
11、so varies with wavelength. The image points of different wavelengths locate along the axis in turn, and the distance along the axis between the image points of different wavelengths represent the axial chromatic shifts(轴向色差).,Usually, the distance along the axis between two image points of wavelengt
12、h F and wavelength C is called the axial chromatic aberration(轴向色差).,We use and to represent the paraxial image distances of wavelengths F and C, then the axial chromatic aberration can be defined as (7.2).,称为色差校正不足,称为色差校正过渡,若AF和AC重合，则,称为光学系统对F光(兰)和C光(红)消色差。,消色差系统是指对两种色光消轴向（位置）色差的系统。,位置色差的性质类似于球差。,光
13、学系统只能对一个孔径的光线进行校正色差。,一般情况下对0.7孔径的光线校正位置色差。,随着接收器的不同，应取接近接收器有效波段边缘的波长进行校色差,B,A,yzF,yzc,垂轴色差,The lateral color aberrations (垂轴色差),较高;,较低。,From the equation we can see that since the effective focal length of the lens varies with the wavelength the image height y will also vary with the wavelength. The
14、 differences of the image heights of different wavelength lights are the so-called lateral color aberrations(垂轴色差).,Usually, the lateral color aberration is defined on the paraxial image surface of D light, and it is just the distance vertical to the axis between two image points of wavelength C and
15、 F. We use and to represent the image heights of wavelengths F and C, then the lateral chromatic aberration can be defined as(7.3).,7.3 The Axial Monochromatic Aberration(轴上点的单色像差) Spherical Aberration(球差),Fig.7.4,In Fig.7.4 we can see that the rays emitted from one object point will not intersect a
16、t(相交于) one point after refraction, or the system forms a blur(模糊的) image. Usually, we use spherical aberration to denote the spread of the rays intersection along the axis (用球差表示光线与光轴的交点沿光轴方向的离散程度).,2）球差的表达式：,The axial spherical aberration (轴向球差)of the image point is abbreviated L (用符号L表示) : L=L-l (
17、7.4),Where L denotes the image distance by tracing a trigonometric(宽孔径的) ray and l denotes the distance by tracing a paraxial(近轴的)ray from the same axial object point, as shown in Fig.7.4. If the spherical aberrations are large the image quality will be poor.,3) The Diagram Of The Longitudinal Spher
18、ical Aberration（垂轴球差),If there are spherical aberrations the spot diagram of different image planes will be different, as shown in Fig.7.4. There will be no clear image point at any places. The spot will be the smallest and the image quality be the best only at the circle of the least confusion(最小弥散
19、圆).,4）球差的校正：,Spherical aberration is determined by tracing a paraxial ray and a trigonometric (宽孔径的) ray from the same axial object point and determining their final intercept distance(间距).,By combining a positive and a negative lenses(组合正透镜和负透镜) we can correct the spherical aberration(校正球差). 这种组合光组
20、称为“消球差光组”，如微分离型双胶合透镜组和紧贴型双胶合透镜组等。,注意：球差不可能完全消除，也没有必要将所有的球差都设计为零。 (On this condition, the intersection point of the marginal rays coincides with that of the paraxial rays. However, at other ray heights the intersection points do not coincides with that of the paraxial rays, or there will still be som
21、e spherical aberrations.),通常校正球差仅仅是让边缘光线和光轴的交点与近轴光线和光轴的交点重合而已，而其它口径的边缘光线和光轴的交点并不完全和轴光线和光轴的交点重合，此时仍有残余球差存在。如果系统对球差的要求很高就需要继续校正球差，即“二次校正球差” .,Undercorrected spherical aberration (球差欠校正),If the intersection point of the marginal rays locates at the left hand of the paraxial image point, the spherical a
22、berration is negative(负的), and this is called undercorrected spherical aberration(球差欠校正).,Overcorrected spherical aberration(球差过校正),If the intersection point of the marginal rays locates at the right hand of the paraxial image point, the spherical aberration is positive(正的), and this is called overc
23、orrected spherical aberration(球差欠校正).,Positive lens/converging lens: Contribute undercorrected spherical aberration. 正/会聚透镜产生负球差(球差欠校正)。 Negative lens/Diverging lens: Contribute overcorrected spherical aberration. 负/发散透镜产生正球差(球差过校正)。,A,-Umax,-U,hmax,h,A,L,L,y,l,若h/hmax=0.7，则称为0.7孔径或0.7带光（带光球差）, hmax
24、称为全孔径(边光球差)。,加发散透镜消除球差,最大孔径处消球差,中央孔径球差为0,最大剩余球差,7.4 Off-Axial Monochromatic Aberrations(离轴的单色像差),1)轴外无限远物点成像特点：只存在一个对称平面。There will be only a symmetrical plane (对称平面) BOZ, which is determined by the object point and the axis, as shown in Fig.7.6. 2) The Principal, Or Chief Ray(主光线): The oblique (倾斜的
25、)ray through the center of the aperture (孔径) of a lens system is called the principal, or chief ray.,3)子午面和弧矢面的定义：,In order to simplify the study we use two planes, which are vertical to (相互垂直的)each other, to denote the structure of the rays.,One of the two planes is called meridional or tangential
26、plane(子午面或切向面), BM+M- plane as shown in Fig.7.6, which is determined by the principal ray, or chief ray, BZ as shown in Fig.7.6, and the axis. Rays lie in the meridional or tangential plane are called tangential rays(子午线或切向线). Rays which do not lie in a meridional plane are called skew rays (斜线).,An
27、other plane is called sagittal plane(弧矢面), BM+M- plane as shown in Fig.7.6，which passes through the chief ray，BZ as shown in Fig.7.6，and is perpendicular to(垂直于) the meridional plane(子午面). Similarly, the skew rays (斜线) from the object which lie in sagittal plane are sagittal rays(弧矢线). 4)子午面和弧矢面的关系：
28、相互垂直。,7.4.1 Meridional Aberrations(子午像差):,1) 子午面的特点： 子午面既是光束的对称面也是系统的对称面。 Since the meridional plane is the symmertrical plane of the system, the rays lying in the plane will also lie in the same plane after passing through the sysem.,2) 子午光线对：,In Fig.7.7, are called the couple of meridional rays(子午
29、光线对). The intersect point BT of rays will neither at the principal ray nor on the paraxial image plane,3）子午场曲：,The axial distance XT from the intersect BT of the rays to the paraxial image plane is called meridional field curvature(子午场曲).,子午场曲,子午彗差,细光束子午场曲,4）子午彗差：,The vertical distance(垂直距离)KT from
30、the intersect point BT of the rays perpendicular to the principal ray (主光线) is called meridional coma(子午彗差).,5)细光束子午场曲：,When the couple of rays go near to the principal ray, the width of the couple ot rays will go gradually to zero and the intersect point BT will go to point Bt , which is on the pri
31、ncipal ray. The distance from the point Bt to the paraxial image (近轴像)is called paraxial field curvature(细光束子午场曲)， represented by xt.,6) 轴外子午球差：,The differentce of meridional field curvature(子午场曲) XT and paraxial field curvature (细光束子午场曲) is called meridional spherical aberration(轴外子午球差), which repr
32、esents the difference of intersect points of large aperture and small aperture rays, similar to the spherical aberration(球差)of axial image point. Meridional spherical aberration can be expressed by the following equation:,7) 弧矢像差：,The hatched part is the sagittal plane(弧矢像差), as shown in Fig.7.8. Si
33、milar to the condition of meridional aberrations, the distance from the intersect point BS of the sagittal rays(弧矢线) to paraxial image is called sagittal curvature(弧矢场曲), represented by XT. The vertical distance(垂直距离) KS from the intersect point BS of the rays perpendicular to the principal ray is c
34、alled sagittla coma(弧矢彗差).,8) 弧矢球差:,The distance from the point BS to the paraxial image plane is called the paraxial sagittal field curvature(弧矢场曲), represented by xs . The difference of sagittal field curvature XT and paraxial field curvature xt is called sagittal spherical aberration(弧矢球差), which
35、 represents the difference of intersect points of large aperture and small aperture rays, similar to the spherical aberration (球差)of axial image point.,Sagittal spherical aberration(弧矢球差) can be expressed by the following equation:,9) 正弦差：,We use the tatio of coma(彗差)to the image height to denote th
36、e coma aberration. This ratio is called sine aberration(正弦差), represented by SC:,10) 像散:,For the systems whose apertures are small, the image quality is mainly determined by paraxial meridional and sgittal field curvatures xt (近轴子午场曲)and xs(近轴弧矢场曲). The difference of xt (近轴子午场曲)and xs(近轴弧矢场曲)denotes
37、 the difference of the principal ray and the oblique (倾斜的)rays, and we call this difference astigmatism(像散), represented by xts:,11) 畸变：,The difference of the real image height and the paraxial image height is called distortion(畸变), represented by,If the images are displaced outward from the correct
38、 position, the distortion is called overcorrected, or pincushion distortion(桶形畸变). And if the distortion is of the opposite type and the corners of the square are pulled inward more than the sides, the distortion is called barrel distortion (鞍形畸变).,桶形畸变,鞍形畸变,彗差图：As shown in Fig.7.11. 像散图：As shown in Fig.7.12 and Fig.7.13. 场曲图：As shown in Fig.7.9.,
