Modern Lens Design - Cooke Triplet

Modern Lens Design - Cooke Triplet -1- Modern Lens Design - Cooke Triplet K,K，K，K,dKK,dKK,dKK,dKK，ddKKK 12311211321322312123 已知 焦距、像高、F/#。 玻璃材料。 Power and spacing solution Power: 1K,(hK，hK，hK) (採平行光軸之入射邊緣光) 112233h1 Axial color KKKK2222i123C,h,h，h，h ,Li123VVVVi123 1',,,lCFCL2''nu Lateral color KKKKi123C,hh,hh，hh，hh ,Tii112233VVVVi123 1,T',CFCTn'u' Petzval sum: 191630845.doc -2- KKKKKKK222123123S,H,H，，,nu，，()(','')(),4nnnnnnn123123 KKK112123,zSnu' ,,,,(''')(，，)4p22nununnn2''2''123 KKK12123n,,(',')(，，)nnn2123 K,aK(1) Set , is a typical value from prior experience. a,1.231 K,aK,abK(2) Set K,bK, is an arbitrary value. . b,1.5311 Solve K from S: 24 KKK2123S,H，，()4nnn123 ddC(3) Set a value for about 1/5 to 1/10 of the focal length. Solve from . L12u,u,hKu (get ) 1o111 h,h，duh (get ) 21112 u,u,hKu (get ) 21222 KKK222123Chhhh,，， (get ) 3L123VVV123 h,h，dud (get ) 32222 h,0(4) Set the position of stop, which is usually placed at element 2. . 2 hhh(5) Trace a paraxial chief ray to find the values of , and . 312 KKK123C,hh，hh，hhFind . T112233VVV123 dC(6) Repeat form step 3 with a new choice of until is desired. T1 K(7) Determine . If not as desired, set a new value of in step 2 and repeat K1 from step 2. 191630845.doc -3- 單薄透鏡球差,彗差,像散,場曲及畸變公式 43hK22S,(MX,MXY，MY，M) 101234 22,HhKS,(MX,MY)2c452 SSES,，221C 22S,HK，2ES，ES 32c1 K122SHHK,,,4nn K2223S,E(3HK，H)，3ES，ES5,2c1n 23,E(3S，S)，3ES，ES3C42c1 MM至為折射率之函數 05 2n，241()n，nn32，,,MnMn(),(),M(n),, , Mn, (),,,01232nn(),1nn(),1n,1n,, n，1n21，Mn(),Mn(),45nn(),1n, Element Shape Solution SX(1) Assume a value for and calculate (1) for element 1. 31 2S(2),HKSince the stop is located at element 2, 32 XS(3)S,S(1),S(2)(2) Solve which gives =. 33333 May have two, one or no solutions XUsually there are two solutions of , choose the reasonable one. 3 191630845.doc -4- (3) Evaluate and . S(1)S(3)22 Solve X which gives S(2) =S,S(1),S(2). 22222 S(2),S(2)Since the stop is located at element 2, which is linear in . A X22C2 could always be found. unique value of X2 (4) Determine the total spherical aberration S. 1 X. (5) Repeat the procedure from step 1 with a new value of 1 Plot a graph of S against X( parabolic ). 11 Choose the X with desiredS. 11 May have two, one or no solutions S(6) If distortion is within acceptable limits, well and good; if not, a new power 5 a,K/KSand space solution must be made with a different value of . The value of 315 a,K/Kcan be plotted for several values of as an aid in effecting a solution. 31 May have two, one or no solutions Usually there is only one reasonable solution and occasionally there are two. Initial choice of desired aberration values. The initial desired 3td-order aberration sums of spherical, Petzval, and axial chromatic should be small and negative, since the higher-order aberrations are usually positive. Since the Cooke triplet is relatively symmetrical, the residuals of distortion, coma, and lateral color are small, and initial desired values of zero are appropriate. The desired Petzval Radius PR, =1/PTZ in Code V, should be definitely negative. PR,,2f~,3fFast lenses: PR ,,3f~,4fModerate-speed lenses (f/3.5): PR ,,5fSlow lenses: or longer The flatter the Petzval surface, the stronger the lens powers and the higher the 191630845.doc -5- 3S,Kresidual aberrations, especially zonal spherical ( ) 1 The value of Petzval target is important in determining whether or not there is a solution. 1z' SThe desired astigmatism is best set slightly positive, ,,ts32n' u' ,1, so that the inward curvature of the Petzval surface is offset by the z' ,0~z'tsP3 overcorrected astigmatism. Glass choice. A very important design factor for triplet STo reduce. 4 Positive elements with high index glasses. Negative element with low one. CTo reduce L Positive elements with high V. Negative element with low V. Ordinary crown glass or even plastics can not give good performance. Large difference between the V-values of the positive and negative elements would lead to long systems (i.e., d1 and d2 are large). A lens with a large vertex length will, at any given diameter, vignette at a smaller angle than will a short lens. (長系統比短系統更容易在小視角時就已產生漸暈) Further, it turns out that the longer the lens: (1) the smaller the spherical zonal (2) the smaller the field coverage (i.e., the higher-order astigmatism and coma are greater and limit the angle over which a good image can be obtained when the lens is long). 191630845.doc -6- Thus, long systems are appropriate for high-speed, small-angle systems; short systems for small-aperture, wide-angle applications. The length of the triplet can be controlled by the choice of the glasses used. To get a shorter system, use High V-value flint Low V-value crown To get a longer system, High V-value crown Low V-value flint A too long system will have no solution for the element shapes. The ray height on the negative element may be so low that its overcorrecting contribution to the spherical aberration is insufficient to offset the undercorrection of the positive elements simultaneously with the requirements for coma and astigmatism correction as well as chromatic and Petzval. 191630845.doc