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1、幻灯片 1 Chapter 5 Wave-Optics Analysis of Coherent Optical Systems Weimin SunCollege of ScienceHarbin Engineering University幻灯片 2 A thin lens as a phase transformationLet the maximum thickness of the lens (on its axis) be 0, and let the thickness at coordinate (x,y) be (x,y).Then the total phase delay
2、 suffered by the wave at coordinate (x,y) in passing through the lens may be writtenwhere n is the refractive index of the lens material, kn(x,y) is the phase delay introduced by the lens, and k0 -(x,y) is the phase delay introduced by the remaining region of free space between the two planes .(x,y
3、)0yx),(),(),( 0 yxkyxknyx +=fSuffer： 遭受 ， 经历 幻灯片 3 n Equivalently, the lens may be represented by a multiplicative phase transformation of the formn The complex field Ul(x,y) across a plane immediately behind the lens is then related to the complex field Ul(x,y) incident on a plane immediately in fr
4、ont of the lens byn The problem remains to find the mathematical form of the thickness function (x,y) in order that the effects of the lens may be understood.),()1(exp)exp(),( 0 yxnjkjkyxtl =),(),(),( yxUyxtyxU lll =Equivalently： 等效地 幻灯片 4 The thickness functionn In order to specify the forms of the
5、 phase transformation introduced by a variety of different types of lenses, we first adopt a sign convention:n As rays travel from left to right,n each convex surface encountered is taken to have a positive radius of curvature;n each concave surface is taken to have a negative radius of curvature.n
6、R10 and R20n Negative lens or diverging lens: f0幻灯片 11 Fourier transforming properties of lensesn One of the most remarkable and useful properties of a converging lens is its inherent ability to perform two-dimensional Fourier transforms.n The complicated analog operation can be performed with extre
7、me simplicity in a coherent optical system, taking advantage of the basic laws of propagation and diffraction of light.n The input of a system is a spatial light modulator, which is called as transparencies or object.inherent ability： 固有的能力 extreme simplicity： 极其简单 Coherent： 相干的 ， 一致的 ， 连贯的 spatial
8、light modulator： 空间光调 制器 Transparency： 透明片 幻灯片 12 Three arrangements n The illumination is collimated plane wave which is incident either on the input transparency or on the lens.Collimate： 准直 ， 校准 幻灯片 13 Input placed against the lensn Let a planar input transparency with amplitude transmittance tA(
9、x,y) be placed immediately in front of a converging lens of focal length f.n The input is assumed to be uniformly illuminated by a normally incident, monochromatic plane wave of amplitude A, in which case the disturbance incident on the lens is),(),( yxAtyxU Al =Planar： 平面的 ， 平坦的 Transmittance： 透射系数
10、 幻灯片 14 n The finite extent of the lens can be accounted for by associating with the lens a pupil function P(x,y) defined byn Thus the amplitude distribution behind the lens becomes=otherwise0aperture lens theinside1),( yxP)(2exp),(),(),( 22 yxfkjyxPyxUyxU ll +=account for： 导致 ， 提出理由 ， 做出解释 Pupil： 瞳
11、孔 ， 光阑 ， 小学生 幻灯片 15 n Putting z=f, the distribution Uf(u,v) in the back focal plane of the lens isn where a constant phase factor ejkf has been dropped. +=-)()(222 dd),()(exp),( 2222 yxeeyxUfjvujvuU yvxujyxjlfkfffklpl幻灯片 16 +=-)()(222 dd),()(exp),( 2222 yxeeyxUfjvujvuU yvxujyxjlfkfffklpl)(2exp),(),(
12、),( 22 yxfkjyxPyxUyxU ll += +=-)(222 dd),(),()(exp),( 2 yxeyxPyxUfjvujvuU yvxujlfkfflpl幻灯片 17 n When the physical extent of the input is smaller than the lens aperture, the factor P(x,y) may be neglected, yieldingn The complex amplitude distribution of the field in the focal plane of the lens is the
13、 Fraunhofer diffraction pattern of the field incident on the lens, even the distance to the observationplane is equal to the focal length of the lens, rather than satisfying the usual distance criterion for observing Fraunhofer diffraction.fX=u/lf, fY=v/lf +=-)(222 dd),()(exp),( 2 yxeyxUfjvujvuU yvx
14、ujlfkfflplNeglected： 被忽视的 Yielding： 柔顺的 ， 获利 ， 产生 Criterion： 判据 幻灯片 18 n In most case it is the intensity across the focal plane is of real interest. n This phase term is important if the ultimate goal is to calculate another field distribution after further propagation and possibly passage through
15、additional lenses, in which case the complete complex field is needed.n In most cases, the intensity distribution in the focal plane will be measured, and the phase distribution is of no consequence.n Measurement of the intensity distribution yields knowledge of the power spectrum (or energy spectru
16、m) of the input 2-)(222|dd),(|),( 2 += yxeyxtfAvuI yvxujAfflplultimate goal： 最终目标 Consequence： 重要地位 ， 结果 ， 推论 ，因果关系 幻灯片 19 Input placed in front of the lensn The input, located a distance d in front of the lens, is illuminated by a normally incident plane wave of amplitude A.n The amplitude transmittance of the input is again represented by tA.n Let Fo(fX,fY) represent the Fou
