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1、*1第八章第八章 光学系统成像质量光学系统成像质量 评价评价*2实际光学系统都有一定大小的相对孔径实际光学系统都有一定大小的相对孔径 合视场，远远超出近轴区所限定的范围。合视场，远远超出近轴区所限定的范围。8-1 8-1 概概 述述与近轴区成像比较必然在成像位置和像与近轴区成像比较必然在成像位置和像 的大小方面存在一定的差异，被称为的大小方面存在一定的差异，被称为像差像差指在光学系统中由透镜材料的特性或折指在光学系统中由透镜材料的特性或折 射（或反射）表面的几何形状引起实际像与射（或反射）表面的几何形状引起实际像与 理想像的偏差。理想像的偏差。*3The gaussian formulas d
2、eveloped and used in the preceding chapters give, therefore, only an idealized account of the images produced with lenses of wide aperture.When ray tracing is applied to object points farther and farther off the axis, the observed image defects become more and more pronounced. *4Expansion Of The Sin
3、e. First-Order Theory In order to formulate a satisfactory theory of lens aberrations, its convenient to start with the correct and precise ray-tracing formulas and to expand the sines of each angle into a power seriesMaclaurins theorem*5For small angles this is a rapidly converging series. For para
4、xial rays, we may , to a first approximation, neglect all terms beyond the first When is small ,the other angles , and are also small, provided the ray lies close to the axis. so*6All angles can be eliminated. The final equation obtained by these substitutions is none other than the gaussian formula
5、The equation and others developed from it form the basis of what is usually called first-order theory*7The justification for writing ,etc, for all small angles*8*9If a lens were to be free of all defects in is ability to form images, all five of these sums would have to equal zero.No optical system
6、can be made to satisfy all these conditions at once.It is customary to treat each sum separately, and the vanishing of certain ones corresponds to the absence of certain aberrations*10If for a given axial object point the Seidel sum ,there is no spherical aberrations at the corresponding image point
7、. If both and ,the system will also be free of coma(彗差). If in addition to and ,the sums and as well, the images will be free of astigmatism（象散） and curvature of field（象场 弯曲）. If finally could be made to vanish, there would be no distortion（畸变） of the image.These aberrations are also known as the fi
8、ve monochromatic aberrations because they exist for any specified color and refractive index.*11像差的大小反映了光学系统质量的优劣像差的大小反映了光学系统质量的优劣几何像差主要有七种：几何像差主要有七种： 单色光像差有五种： 球差 彗差(正弦差) 像散 场曲 畸变 复色光像差有两种： 轴向像差(位置色差) 垂轴像差(倍率色差)*12在实际光学系统中，各种像在实际光学系统中，各种像 差是同时存在的。差是同时存在的。这些像差影响光学系统成像的清晰这些像差影响光学系统成像的清晰 度、相似性和色彩逼真度等，
9、降低度、相似性和色彩逼真度等，降低 了成像质量。了成像质量。 1、球差：球面像差的简称*13Spherical Aberration of a Single SurfaceA blurring of the image that occurs upon refraction by spherical surfaces*14The distance is a measure of the longitudinal spherical aberrationA measure of the deviations from first-order theoryIts magnitude varies
10、with the position of the object point and for any fixed point is approximately proportional to ,the square of the radius of the zone on the refracting surface through which the rays pass*15If the object point is at infinity so that the incident rays are parallel to the axis*16Again the magnitude of
11、the aberration is proportional to ,the square of the height of the ray above the axis*17Spherical Aberration of a Thin Lens The existence of spherical aberration for a single spherical surface indicates that it may also occur in combinations of such surfaces ,e.g., in a thin lensIt is usual for comp
12、arison purposes to determine the spherical aberration for parallel incident lightThe paraxial focal point*18Illustrates the difference between longitudinal spherical aberration , abbreviated Long. SA, and lateral spherical aberration, abbreviated Lat. SA*19A graph showing this variation of focal len
13、gth with zone radius For small h , the curve approximates a parabolaSince the marginal rays intersect the axis to the left of the paraxial focal point, the spherical aberration is said to be positive*20A similar curve, drawn for a typical double concave lens of nearly the same dimensionsBending to t
14、he right, this lens is said to have negative spherical aberration*21A series of positive lenses of the same diameter and paraxial focal length but of different shape*22The alteration of shape represented in this series is known as bending the lens.Each lens is labeled by a number q called its shape
15、factor配曲调整*23e.g. if the two radii of a converging meniscus lens are and it has a shaper factor*哈工大光电测控技术与装备研究所24The usual reason for considering the bending of a lens is to find that shape for which the spherical aberration is a minimumThe least spherical aberration*25The amount of this aberration for the ray having h=1.0cm is shown for the same series of lenses by the curves of FigureOver the range from about q=+0.4cm to q=+1.0cm the spherical aberration is close to a minimum, but it goes to zero at no point *26We see th
