内调焦准距式望远系统光学设计

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内调焦准距式望远系统光学设计1、技术参数选择;放大率:r 24x分辨率:p 4视场角:2w2m 筒 长: LT=170mm2、外形尺寸计算;这里取厂=-24,取不同的筒长L和缩短系数Q,根据上述公式(15)计算的结果列表2-1。表 2-1r = -24xL=150mmQf 12f 1d0f 2f 3l f(12)I20.55272.73121.2098.16-41.4711.3651.8423.045.060.60250.00123.9798.36-50.8010.4251.6525.614.080.65230.77126.8398.56-62.769.6251.4428.273.310.70214.28129.8098.77-78.718.9351.2231.032.720.75200.00132.8798.97-101.008.3351.0333.092.250.80187.50136.0599.17-134.407.8150.8336.881.90L=160Qf 12f 1d0f 2f 3l f(12)l2%0.55290.91129.28104.71-44.2212.1255.2924.575.060.60266.67132.23104.92-54.1711.1155.0827.314.080.65246.15135.29105.14-66.9410.2654.8630.153.310.70228.57138.45105.35-83.959.5254.6433.102.720.75213.33141.73105.57-107.748.8954.4336.162.250.80200.00145.12105.78-143.378.3354.2239.341.90L=170Qf 12f 1d0f 2f 3l F(l 2)l2%0.55309.09137.36111.25-46.9912.8858.7526.115.060.60283.33140.50111.48-57.5711.8058.5629.024.080.65261.54143.74111.71-71.1110.9058.2832.033.310.70242.86147.11111.94-89.2010.1258.0635.172.720.75226.67150.59112.17-114.479.4457.8338.422.250.80212.50154.20112.40-152.368.8557.6041.801.90L=180Qf 12f 1d0f 2f 3l F(l 2)l2%0.55327.27145.44117.80-49.7513.6462.2027.645.060.60300.00148.76118.04-60.9412.5061.9530.724.080.65276.92152.20118.26-75.3111.5461.7233.923.310.70257.14155.76118.52-94.4610.7161.4827.242.720.75240.00159.45118.76-121.2410.0061.2440.692.250.80225.00163.26119.01-161.269.37560.9844.251.90上述计算表明:1、为了使仪器结构紧凑,必须缩短仪器筒长。缩短筒长L,儿、f彳、f 3减小,导致各 透镜组的相对孔径 D/f 将增大。透镜组相对孔径的增大,将使 像差校正困难,或使结构复 杂,成本增加。因此,仪器筒长L不宜术小。2、当筒长L 一定时,希望一定筒长所能获得的组合焦距几2越大越好,即缩短系数Q 越小越好。Q越小,几、f 2就越小,从而DJf和D2/f2增大,且勺增大,主物镜的剩余像 差经调焦镜后将被放大勺倍,于像差校正是不利的。另一方面,Q越大,f 12和f 3就越小, 但目镜的焦距不能太小,否则,目镜的镜目距小,影响观察。综上所述,应该取适当的L和Q。作为例子,我们取:r =-24x ,L =170,Q = 0.65f 12= 261.54,d0= 111.71f 1 = 143.74,f 2=-71.11,f 3= 10.90由于计算误差和取舍误差,亦或计算错误,使得加常数c工0。因此,必须检验加常数是否 为 0。检验公式为:(2-4)将所确定的参数代入,得:c = 0.00254由此可见,系统满足准距条件,其所引起的测量误差可以忽略不计。为了满足分辨率的要求得:即g 4,由D = 140 n140=35mm方面,由厂=D可知,厂一定时,出瞳D随D的增大而增大。D的增大,即物镜通光孔径增大,使仪器外形增大。当f 1 一定时,物镜的相对孔径D/ f 1也随之增大,物镜的高 级像差增大,像差校正困难。通常,用于大地测量仪器的望远镜系统,为了提高测量精度 出瞳直径 D = 1.31.5mm,一般取 D = 1.5m m,则:D = -r D 24 x 1.5 =36mm因此,取入瞳直径,即物镜的通光孔径D1=36mm,对应的出瞳直径D=1.5mm。二、调焦镜的通光孔径如图2-5所示,调焦镜的通光孔径D2由 轴外物点的上光线的入射高度确定。由图中 三角关系,有:D / 2 -yD / 2 -D / 211 二一12f d10而:y 1 =f 1tgw则得调焦镜的通光孔径:图2-5调焦镜的通光孔径D2= D1- d0(D1/f1- 2tgw)=36-111.71x(36/143.74-2xtg0.8。) = 11.14mm三、分划板直径及视距丝间隔由于场阑与分划板重合,所以分划板的通光孔径即为场阑直径,即dp= D 场=2尸/gw=2x261.54xtg0.8=7.30mm根据乘常数的定义:k = f12b得视距丝间隔f261.54b = 12 = 2.615mmk 100四、像方视场角、出瞳距和目镜孔径1、像方视场角由r=-型,得:tgwtgw = -r tgw = 24xtg0.8o = 0.33512499所以像方视场角2w,=37.05。2、出瞳距 出瞳距的确定可由入瞳逐面用成像公式 计算而得:因 lz1 = 0,所以 l z1 = 0,lz2 =l z1-d0 = -111.71l - flf =亠 # = -43.45z2l + fz2l = l -d = l -L-d + f )= -112.64z3z2 2z203于是得出瞳距为:wDF3y 27D3图2-6目镜的成像光路l = lz z3l-z33lz 3 + 广= 12.07mm3、目镜的通光孔径由图2-6可得,目镜的通光孔径为:D = D + 2l - tgww3z=1.5 + 2 x 12.07 x 24 x tg 0.8。= 9.594、目镜的视度调节为了适应不同视力的人眼观察的需要,目镜应具备视度调节功能。目镜的视度调节范围 一般取5个折光度,它是通过目镜相对于分划板前后移动一定和距离来实现的。因此,视 度调节时,目镜的最大移动范围为:x = 53=51:9i qo.61000 1000五、调焦镜的调焦移动量在调焦过程中,调焦镜沿光轴前后移动,其移动量必须保证对无穷远至有限远最短视距范围内的物体能调焦清晰。一般情况下,调焦镜的初始位置对应无穷远物体,因此,只须计 算出物体在有限远最短视距处调焦镜的位置,就可以确定出调焦镜的移动量。-2000m m,由物像关系的高斯公式,计算得1; = 154.87。由公式(1-6)计算得:d = 11r+ L- Gi-L)0-L + 4广)1 128.77mm2 1 1 1 2于是得调焦镜的调焦量:Ad = d - d0 = 128.77 - 111.71 = 17.06mm3、结构选型;在本设计中,主物镜的相对孔径约1:4,调焦镜的相对孔径 1:5.6,因此,主物镜和调 焦镜均可选用最简单的双胶合物镜。图2-9折射式望远物镜的常用结构型式4、初始结构参数求解;146.25mm。2、求解初始结构参数2.1 确定基本像差参量根据像差校正的要求,令血=0、SC =0及从仁=0,即码=亦广巧=0。即:YS = h 4 3 P = 0i ES = h 3 h 3 P + Jh 2 2 W = 0IIz_EC =h 2 C =0I ii得:p=W=CI=0这只是物体在有限远时的像差参量,还必须将其规化到无穷远。已知:NA = qsinq = 0.1, 因 n1 = 1,所以,取 u1 = sinU1 = -0.1。又:h = l1u1 = -48.75x(01) = 4.875mm,规化孔径 角:u1i-h-0.14.875 x 1/36.5625=-0.75于是,由公式(3-18)可求得规化后的基本像差参量如下:P = P + u 1(4W + 1) + u 2(5 + 2 卩)=0 - 0.75(4 x 0 +1) + (-0.75)2 x (5 + 2 x 0.65) = 2.79375W = W + u 1(2 + 卩)=0 + (-0.75) x (2 + 0.65) = -1.98753、选择玻璃组合玻璃组合选择的依据是P。和CI,同时,还必须注意:当Ws是较小的正值(0 Ws 1) 时,应尽可能取冕牌玻璃在前;当Ws是较大的负数(-3.5 Ws -2.5)时,则尽量取火石玻璃在前。这样可使双胶合透镜胶合面曲率半径较大,减小高级球差,有利于像差校正。这 里,我们取火石玻璃在前。根据公式(3-35)计算P0如下:P0 = 2.793750.85x(-1.9875+0.1)2 = 0.078根据P0和CI,查“光学设计手册”中“双胶合物镜P0表”选取玻璃组合。如果C/与表中 所给数值不符,可用插值法求出不同玻璃对的P0;如果所选玻璃对的P0与要求的值(本设 计实例为0.078)相差不大(如6100.60.810180.81.21.01.518301.21.81.52.230501.82.42.23.550802.43.03.55.0801203.04.05.08.01201504.06.08.012.0表3-2透镜中心及边缘最小厚度Pr= 1.117357614p2= 2.850973917P3 = 1.26004013则焦距f = 36.5625mm时对应的曲率半径为口 = f/p1 = 32.722mmr2 = f /P2 = 12.824mmr3 = f /p3 = 29.017mm2.5薄透镜加厚 以上所求的是厚度为0的所谓薄透镜组,这种薄透 镜对应理论分析与求解是有重要作用的,但无任何实际图3-3透镜边缘厚度与中心厚度的关系应用意义,也就是说,任何实际透镜都有厚度。因此,必须将上述薄透镜加厚。 透镜的厚度不仅与球面半径和透镜直径有关,还涉及透镜的装夹方式、质量要 求和加工难易程度等因素。透镜厚度的确定大致可分为如下三步:2.5.1确定透镜的全直径e透镜的全直径0与其通光孔径D的关系如下:= D + A式中是透镜安装时的装夹余量,视装夹方式而定。透镜的装夹方式有两种:压圈法和滚边法,其装夹余量见表 2-2(参见光学设计手册)所示。本例中,因为D = 2h = 2x4.875 = 9.75mm,采用压圈法固定,查表得A =1.0mm,故该显微物镜的外径0 = 10.8mm。2.5.2 确定透镜的中心厚度透镜中心厚度的确定除了与球面曲面半径和透镜外径有关外,还要考虑透 镜焦距、精度及加工情况。一般有两种方法确定:作图法和计算法。作图法是根据光学设计手册中有关光学零件中心和边缘厚度的规定(GB1205-75标准,见表3-2),按实际口 径作图确定。计算法主要考虑透镜在加工、装夹过程中不易变形,根据中心厚度D、边缘厚 度t和外径D之间满足一定经验公式来确定,这种经验公式参见光学设计手册。由图10-3得,透镜中心厚度、边缘厚度与两球面矢高的关系为:d = t x2 + x1(3-47)式中xx2为球面矢高:x = r Jr2 (D/2)2i = 1, 2(3-48)iii本例中,我们采用查表法确定透镜厚度。由表10-3,应有d1 1.0, t2 0.&计算得:x1 =0.45, x2 = 1.19,x3 = 0.51。则 t1 1.74,d2 2.5。于是,我们取 d1 = 1.2mm,d2 = 2.8mm。计算出中心厚度和边缘厚度后,可按实际尺寸(或按比例)作图验证。2. 5.3 确定厚透镜的曲率半径由公式(3-3)可知,当每个球面的u和u,不变时,P、W保持不变,放大率0 = nu/nu 亦不变。另一方面,当透镜由薄变厚时,第一近轴光线在主面上入射高度不变,则系统的光 焦度也不变。根据这两个原则,透镜由薄变厚时,一般需把由薄透镜确定的曲率半径值,变 换为相应的厚透镜的曲率半径值。当相对孔径不大时, D、 r 和 d 都较大,可不作厚度变换。这样引入的像差、放大率、 焦距和共轭距离变化都较小,可在后续的像差校正中予以修正。这样,我们就确定了本设计的初始结构参数如下:ird玻璃nDnFnC132.722mm1.2ZF11.64751.661191.64207212.824mm2.8K91.51631.521951.51389329.017mm经过像差计算,得该初始结构所对应的像差为h/h: 1.0m0.850.7070.50.250.0bL: 2.51071.25150.58920.15450.02590.0000SC : 0.00150.00090.00050.00020.00010.0000L)c: 1.28580.80520.46750.1270-0.0734-0.18105、像差校正;1. 透镜结构参数,视场、孔径等光学特性参数GENERAL LENS DATA:SurfacesStop:8:1系统光圈 : 入瞳直径 = 25Glass CatalogsRay Aiming: SCHOTT: Off变迹 : 均衡,统一的, 因子 = 0.00000E+000有效的焦点长度 :152.27 (系统温度和压力在空气中)有效的焦点长度 :152.27 (在像空间)Back Focal Length 统计轨迹 图像空间 F/# 离轴工作面 F/# : 工作面 F/#Image Space NA 物空间 NA 光阑半径离轴像高 : 近轴放大率 : 33.39723 :197.7966:6.0908016.090801: 6.066698: 0.0818158: 1.25e-009: 12.516.004220入瞳直径 :25入瞳区域 :0入瞳直径 入瞳直径区域 Field Type 最大视场 主光波长 镜头单位 角度放大率25.01441-151.8234: Angle in degrees60.5875618: 毫米0.999424#X-ValueY-ValueWeight10.0000000.0000001.00000020.0000002.0000001.00000030.0000006.0000001.000000Fields : 3Field Type: Angle in degrees#VDXVDYVCXVCYVAN10.0000000.0000000.0000000.0000000.00000020.0000000.0000000.0000000.0000000.00000030.0000000.0000000.0000000.0000000.000000Vignetting FactorsUnits: 祄# ValueWeight1 0.4861331.0000002 0.5875621.0000003 0.6562731.000000Wavelengths : 3SurfTypeCommentRadiusGlassDiameterConicOBJSTANDARD无限远00STOSTANDARD85.67779BAK125.1957602STANDARD-68.97856F225.314810SURFACE DATA SUMMARY:3 STANDARD -1073.516 25.45459 04 STANDARD无限 远BK7 26.70713 05 STANDARD无限 远30.02877 0Thickness无限远7330.82544124.108332.862836 STANDARD31.0 07 STANDARD31.0 0IMA STANDARD31.0 0无 限 远0无 限 远0无限远EDGE THICKNESS DATA:SurfEdgeSTO4.8975112 4.0957983 30.9008934 124.1083135 32.8628306 0.0000007 0.000000IMA0.000000INDEX OF REFRACTION DATA:SurfGlassTempPres0.4861330.5875620.656273020.001.001.000000001.000000001.000000001BAK120.001.001.579434571.572500121.569486582F220.001.001.632081461.620040141.61503169320.001.001.000000001.000000001.000000004BK720.001.001.522376291.516800031.51432235520.001.001.000000001.000000001.00000000620.001.001.000000001.000000001.00000000720.001.001.000000001.000000001.00000000820.001.001.000000001.000000001.00000000THERMAL COEFFICIENT OF EXPANSION DATA:SurfGlassTCE *10E-600.000000001BAK17.600000002F28.2000000030.000000004BK77.1000000050.0000000060.0000000070.0000000080.00000000F/# DATA:F/# calculations consider vignetting factors and ignore surface apertures.Wavelength:0.4861330.5875620.656273#FieldTanSagTanSagTanSag10.0000 deg:6.05036.05036.06676.06676.07676.076722.0000 deg:6.04406.04796.06046.06426.07036.074136.0000 deg:5.99386.02796.01016.04426.01996.0542CARDINAL POINTS:Object space positions are measured with respect to surface 1.Image space positions are measured with respect to the image surface. The index in both the object space and image space is considered.Object SpaceImage SpaceW = 0.486133Focal LengthFocal PlanesPrincipal PlanesAnti-Principal Planes : Nodal Planes Anti-Nodal Planes-151.809105-151.7616130.047492-303.5707180.047492-303.570718151.8091050.367289 -151.441816 152.176394-151.441816152.176394W = 0.587562 (Primary)Focal LengthFocal PlanesPrincipal Planes : Anti-Principal Planes : Nodal Planes Anti-Nodal PlanesW = 0.656273Focal LengthFocal PlanesPrincipal PlanesAnti-Principal Planes :Nodal Planes-152.270019-152.1823170.087702-304.4523370.087702-304.452337-152.539647-152.4362720.103375-304.9759180.103375152.2700190.534402 -151.735617 152.804422-151.735617152.804422152.5396470.671116 -151.868531 153.210762-151.868531Anti-Nodal Planes-304.975918153.2107622.像差指标数据:5 L1 m = 0.23mm,SC m=K/ S/y/ =-0.003208/16-004224=-0.00199996AL FC=0.5007230.240723=0.26mm,实际值目标值150mm0.23mm-0.0020.26mmf=150mm,5 L=0.23mm,mSC=000199996,mA L FC = 0.26mm,3. 像差公差数据:球差公差:5L mW4X0.00058三(0.5X1 三6)2=0.33429mm 正弦公差:SC m 0.0025轴向色差公差:ALfc三0.00058三(0.5X1 三6)2=0.08357mm望远镜物镜 2:设计要求:焦距:f=103mm相对孔径D/f= 1/2.0视场角:23=5象差要求:象差校正到 0,入瞳与物镜重合,像方顶焦距 60 mm1. 透镜结构参数,视场、孔径等光学特性参数:4-I II ILH i CiiJT口 /X注二.Z.l I.CTi| IFIQURRT工口M 1. rip 1疋:口 TUI I 2E- 20DE:TDTHL LEI IGTH :1OE.-E.口T二口GENERAL LENS DATA:SurfacesStop 系统光圈Glass CatalogsRay Aiming 变迹 有效的焦点长度 : 有效的焦点长度 : Back Focal Length 统计轨迹: 入瞳直径 = 51.5: SCHOTT CHENGDU: Off: 均衡, 统一的, 因子 = 0.00000E+000103 (系统温度和压力在空气中)103 (在像空间):88.31633105.5973图像空间 F/# 离轴工作面 F/# 工作面 F/# Image Space NA 物空间 NA 光阑半径 离轴像高 : 近轴放大率 : 入瞳直径 : 入瞳区域 : 入瞳直径 : 入瞳直径区域 Field Type 最大视场 主光波长 镜头单位 角度放大率 :22: 2.004945: 0.2425356 2.575e-009: 25.754.497077051.5049.34105-98.91958: Angle in degrees2.5: 0.5875618: 毫米1.043756Fields : 3Field Type: Angle in degrees#X-ValueY-ValueWeight10.0000000.0000001.00000020.0000001.0000001.00000030.0000002.5000001.000000Vignetting Factors# VDX VDYVCXVCY VAN1 0.0000002 0.0000003 0.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000Wavelengths : 3 Units: 祄#ValueWeight1 0.4861331.0000002 0.5875621.0000003 0.6562731.000000SURFACE DATA SUMMARY:SurfTypeCommentRadiusThicknessGlassDiameterConicOBJ STANDARD无限远无限远STO STANDARD81.898285.766996BK751.8680302 STANDARD-303.94220.174944851.7929803 STANDARD57.708237.942913BK749.4138504 STANDARD-145.25843.158622ZF249.2600305 STANDARD95.5453688.5538245.618330IMA STANDARD无限远9.2312870EDGE THICKNESS DATA:SurfEdgeSTO0.44717726.83662430.28309848.024489585.791309IMA0.000000INDEX OF REFRACTION DATA:SurfGlassTempPres0.4861330.5875620.656273020.001.001.000000001.000000001.000000001BK720.001.001.522376291.516800031.51432235220.001.001.000000001.000000001.000000003BK720.001.001.522376291.516800031.514322354ZF220.001.001.687517651.672701221.66660894520.001.001.000000001.000000001.00000000620.001.001.000000001.000000001.00000000THERMAL COEFFICIENT OF EXPANSION DATA:SurfGlassTCE *10E-600.000000001BK77.1000000020.000000003BK77.100000004ZF28.8000000050.000000000.00000000F/# DATA:F/# calculations consider vignetting factors and ignore surface apertures.Wavelength: 0.486133 0.587562 0.656273#FieldTanSagTanSagTanSag10.0000 deg:2.00952.00952.00492.00492.00462.004621.0000 deg:2.00882.00922.00422.00472.00392.004332.5000 deg:2.00512.00792.00062.00332.00022.0030GLOBAL VERTEX COORDINATES, ORIENTATIONS, AND ROTATION/OFFSET MATRICES:CARDINAL POINTS:Object space positions are measured with respect to surface 1.Image space positions are measured with respect to the image surface.The index in both the object space and image space is considered.Object SpaceImage SpaceW = 0.486133Focal Length :-103.050989103.050989Focal Planes :-107.719901-0.272399Principal Planes :-4.668912-103.323388Anti-Principal Planes :-210.770889102.778589Nodal Planes :-4.668912-103.323388Anti-Nodal Planes :-210.770889102.778589W = 0.587562 (Primary)Focal Length :-103.000000103.000000Focal Planes :-107.506834-0.237484Principal Planes :-4.506834-103.237484Anti-Principal Planes :-210.506834102.762516Nodal Planes :-4.506834-103.237484Anti-Nodal Planes :-210.506834102.762516W = 0.656273Focal Length :-103.056152103.056152Focal Planes :-107.502499-0.152734Principal Planes :-4.446347-103.208886Anti-Principal Planes :-210.558651102.903418Nodal Planes :-4.446347-103.208886Anti-Nodal Planes :-210.558651102.9034182. 像差指标数据目标值 实际值f = 103103lF=57.767488 L = 1.54376E 110mSC =6.175865E0130mALfc = 1.45546E0120象差校正到 0,入瞳与物镜重合3. 像差公差数据:球差公差:8L mW4X0.00058三(0.5X1 三2)2=0.0035mm 正弦公差:SC m 0.0025轴向色差公差:ALfc三0.00058三(0.5X1 4-2)2=0.000875mm6、绘制光学系统图与光学零件图;图3-6内调焦准距式望远镜光学系统图草图
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