1、6.8 The Illuminance Equation For Image Points Off The Axis:, is the image field angle of view,E is the marginal illuminance(邊緣光照度),E0 the axial illuminance(軸上光照度),K is the radio of clear aperture (通光孔徑)between the oblique(傾斜的) beam and the axial beam,Chapter 7 Image Quality Of Optical System,常見的像差,7

2、.1 Introduction(簡(jiǎn)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 (變形) 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 whi

4、ch is already produced(制造完成后). The second type of aberrations are suitable for the design stage(設(shè)計(jì)階段).,Resolution Measurement1,The so-called resolution power of an optical system is the smallest distance which can be resolved by the system 系統(tǒng)所能分辨的最小的間隔,所能分辯的最 小間隔，可以 代表系統(tǒng)成像 的清晰度,空間頻率,Fig. 7.1 Resolut

5、ion 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(倒數(shù))is also used to represent the resoluti

6、on power: The spatial frequency(空間頻率): =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. 根據(jù)彌散斑的大小和能量分布的情況，就可以評(píng)價(jià)系統(tǒng)像質(zhì)的優(yōu)劣。,Geometrical optics2,Geometrical aberration (幾何像差)，Wave front aberration(波像差)，Spot diagram(點(diǎn)列圖)，Geometry OTF（Optics Transfer Function）(幾何光學(xué)傳遞函數(shù)), etc.,單色光像差有五種： 球差Spherical aberration 彗差Coma,comatic aberration 像

8、散Astigmatism 場(chǎng)曲Curvature of field 畸變Distortion,復(fù)色光像差有兩種： 軸向色差The axial chromatic aberrations 垂軸色差The lateral chromatic aberrations,幾何像差:,Physics optics2,Point Spread Function(點(diǎn)擴(kuò)散函數(shù),點(diǎn)列圖)，Relative central luminous intensity(相對(duì)中心光強(qiáng))，Physical OTF(Optics Transfer Function)(物理光學(xué)傳遞函數(shù)), etc.,7.2 Color Dispe

9、rsion(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),

10、to represent the color dispersion, which is called mid-dispersion (中部色散).,Chromatic Aberrations(色差),蘭,綠,紅,lF,-lFC,lc,AF,Ac,軸向（位置）色差定義為：,The Axial Chromatic Shifts(軸向色差),較長(zhǎng);,較短,較大;,較小,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(軸向色差).,Usually, the distance along the axis between two image points of wavelengt

12、h F and wavelength C is called the axial chromatic aberration(軸向色差).,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).,稱為色差校正不足,稱為色差校正過(guò)渡,若AF和AC重合，則,稱為光學(xué)系統(tǒng)對(duì)F光(蘭)和C光(紅)消色差。,消色差系統(tǒng)是指對(duì)兩種色光消軸向（位置）色差的系統(tǒng)。,位置色差的性質(zhì)類似于球差。,光

13、學(xué)系統(tǒng)只能對(duì)一個(gè)孔徑的光線進(jìn)行校正色差。,一般情況下對(duì)0.7孔徑的光線校正位置色差。,隨著接收器的不同，應(yīng)取接近接收器有效波段邊緣的波長(zhǎng)進(jìn)行校色差,B,A,yzF,yzc,垂軸色差,The lateral color aberrations(垂軸色差),較高;,較低。,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(垂軸色差).,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(軸上點(diǎn)的單色像差) 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 at

16、(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 (用球差表示光線與光軸的交點(diǎn)沿光軸方向的離散程度).,2）球差的表達(dá)式：,The axial spherical aberration (軸向球差)of the image point is abbreviated L (用符號(hào)L表示) : L=L-l (7

17、.4),Where L denotes the image distance by tracing a trigonometric(寬孔徑的) ray and l denotes the distance by tracing a paraxial(近軸的)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 Spheri

18、cal Aberration（垂軸球差),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(最小彌散圓

19、).,4）球差的校正：,Spherical aberration is determined by tracing a paraxial ray and a trigonometric (寬孔徑的) ray from the same axial object point and determining their final intercept distance(間距).,By combining a positive and a negative lenses(組合正透鏡和負(fù)透鏡) we can correct the spherical aberration(校正球差). 這種組合光組稱

20、為“消球差光組”，如微分離型雙膠合透鏡組和緊貼型雙膠合透鏡組等。,注意：球差不可能完全消除，也沒有必要將所有的球差都設(shè)計(jì)為零。 (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 some

21、 spherical aberrations.),通常校正球差僅僅是讓邊緣光線和光軸的交點(diǎn)與近軸光線和光軸的交點(diǎn)重合而已，而其它口徑的邊緣光線和光軸的交點(diǎn)并不完全和軸光線和光軸的交點(diǎn)重合，此時(shí)仍有殘余球差存在。如果系統(tǒng)對(duì)球差的要求很高就需要繼續(xù)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 ab

22、erration is negative(負(fù)的), and this is called undercorrected spherical aberration(球差欠校正).,Overcorrected spherical aberration(球差過(guò)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 overco

23、rrected spherical aberration(球差欠校正).,Positive lens/converging lens: Contribute undercorrected spherical aberration. 正/會(huì)聚透鏡產(chǎn)生負(fù)球差(球差欠校正)。 Negative lens/Diverging lens: Contribute overcorrected spherical aberration. 負(fù)/發(fā)散透鏡產(chǎn)生正球差(球差過(guò)校正)。,A,-Umax,-U,hmax,h,A,L,L,y,l,若h/hmax=0.7，則稱為0.7孔徑或0.7帶光（帶光球差）, hmax稱

24、為全孔徑(邊光球差)。,加發(fā)散透鏡消除球差,最大孔徑處消球差,中央孔徑球差為0,最大剩余球差,7.4 Off-Axial Monochromatic Aberrations(離軸的單色像差),1)軸外無(wú)限遠(yuǎn)物點(diǎn)成像特點(diǎn)：只存在一個(gè)對(duì)稱平面。There will be only a symmetrical plane (對(duì)稱平面) BOZ, which is determined by the object point and the axis, as shown in Fig.7.6. 2) The Principal, Or Chief Ray(主光線): The oblique (傾斜的)

25、ray through the center of the aperture (孔徑) of a lens system is called the principal, or chief ray.,3)子午面和弧矢面的定義：,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 p

26、lane(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(子午線或切向線). Rays which do not lie in a meridional plane are called skew rays (斜線).,Ano

27、ther 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 (斜線) from the object which lie in sagittal plane are sagittal rays(弧矢線). 4)子午面和弧矢面的關(guān)系：相

28、互垂直。,7.4.1 Meridional Aberrations(子午像差):,1) 子午面的特點(diǎn)： 子午面既是光束的對(duì)稱面也是系統(tǒng)的對(duì)稱面。 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) 子午光線對(duì)：,In Fig.7.7, are called the couple of meridional rays(子午光

29、線對(duì)). The intersect point BT of rays will neither at the principal ray nor on the paraxial image plane,3）子午場(chǎng)曲：,The axial distance XT from the intersect BT of the rays to the paraxial image plane is called meridional field curvature(子午場(chǎng)曲).,子午場(chǎng)曲,子午彗差,細(xì)光束子午場(chǎng)曲,4）子午彗差：,The vertical distance(垂直距離)KT from t

30、he intersect point BT of the rays perpendicular to the principal ray (主光線) is called meridional coma(子午彗差).,5)細(xì)光束子午場(chǎng)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 prin

31、cipal ray. The distance from the point Bt to the paraxial image (近軸像)is called paraxial field curvature(細(xì)光束子午場(chǎng)曲)， represented by xt.,6) 軸外子午球差：,The differentce of meridional field curvature(子午場(chǎng)曲) XT and paraxial field curvature (細(xì)光束子午場(chǎng)曲) is called meridional spherical aberration(軸外子午球差), which repre

32、sents 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. Sim

33、ilar to the condition of meridional aberrations, the distance from the intersect point BS of the sagittal rays(弧矢線) to paraxial image is called sagittal curvature(弧矢場(chǎng)曲), represented by XT. The vertical distance(垂直距離) KS from the intersect point BS of the rays perpendicular to the principal ray is ca

34、lled 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(弧矢場(chǎng)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 represents the difference of intersect points of large aperture and small aperture rays, similar to the