RAA2016ol.16No.1,7(8pp)doi:10.1088/1674452716W1/007Research inhttp://www.raa-journalorg http://iopscience.iop.org/raaAstronomy andAstrophysicsAutomatic generation of optical initial configuration based on Delano diagram1 National Astronomical Observatories/Nanjing Institute of Astronomical Optics Technology,Nanjing 210042,China;xyyuan@niaot.ac.cn2 Key Laboratory of Astronomical Optics&Technology,Nanjing Institute of Astronomical Optics&Technology,Chinese Academy of Sciences,Nanjing 210042,China3 University of Chinese Academy of Sciences,Beijing 100049,ChinaReceived 2015 March9;accepted 2015 May 21Abstract This paper presents a method to automatically initialize an optical system based on the Delanodiagram.The process to generate the optical initial configuration is constrained by the control points,whichare deduced from parameters related to basic design requirements.We present the theory and method togenerate the optical initial configuration automatically when the basic design requirements are known.Twooptical systems are taken as examples to demonstrate the proposed method.Key words:telescopes-methods:analytical1 INTRODUCTIONused to deduce the control points in Section 3;in Section 3,the theoretical relationship between the control points andThe design of an optical system is convenient with thethe parameters of the design requirements is demonstratedaid of optical optimization software,provided that a rea-for systems with a finite object distance and an infinite ob-sonable initial configuration has been obtained.There areject distance;in Section 4,the automatic process to gen-many references(Fischer etal.2008;Kingslake Johnsonerate the initial configuration under the constraints of the2010;Geary 2002)regarding how to optimize and improvecontrol points is introduced,and in Section 5,two opticalthe performance of an initial configuration.systems designed by the proposed method are presented.There has been,however,no general method about2 BASIC PROPERTIES OF THE DELANOhow to calculate initial values of an optical system.In thisDIAGRAMpaper,we present a method to automatically generate anoptical initial configuration when the basic design require-The Delano diagram,(,is used to illustrate the heightsments are known.This method is based on the Delanoof the principal ray and the marginal ray propagatingdiagram,which was proposed by Erwin Delano in 1963through an optical system (Fig.1).When the Lagrange(Delano 1963).The Delano diagram is an excellent toolinvariant of the system is known,all of the other first-to illustrate the first-order parameters for a given system,order parameters can be obtained from the Delano dia-and has been utilized in optical designs since then(Shackgram.For the optical system,Lagrange invariant Q is de-1974;Bauman 2003;Pegis et al.1967;Kessler Shackfined in Equation(1)(Delano 1963)1992;Zhuang et al.1982).However,there is no generalmethod or process described in previous research about theDelano diagram.The general method in this paper is con-strained by control points in the Delano diagram,whichIf Equation(1)is changed to the form given in Equation(2)are deduced directly from the parameters of the design re-quirements and can thus ensure that the configuration ob-y=+tained can fulfill the design requirements.The theoreticalnurelationship between the control points and the parametersthen it is clear that the Delano diagram is the diagram il-of the design requirements is deduced and demonstrated inlustrating the Lagrange invariant in different positions ofthis paper.Based on the relationship between the controlthe optical system,and the slope of the line in the diagrampoints and the design goal of a given optical system,werepresents the ratio of the angle of the marginal ray to thehave written the program OMAX (one key to generate theangle of principal ray.optical initial configuration in Zemax)that acts as an in-Figure I is a Delano diagram,which represents anterface between Matlab and Zemax.In Section 2,the basicoptical system containing three optical components.Theproperties of the Delano diagram are introduced,which arecomponents labeled J and M are the object and image?1994-2016 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.netK.-Y.Zhang et al.plane in the Delano diagram,and A,B and C are threeoptical components.JA is the line that connects the objectplane and the first component,and CM is the line that con-nects the last component and the image plane.The compo-nent P is the intersection point of the line JA and CM,and it represents the principal plane of the system.The lineOF can be constructed to be parallel to line JA and to in-tersect line CM at the point F.Then F represents the0image focal plane of the system.The focal length of thesystem can be obtained by the cross product of vectors asfollows (Delano 1963)OF'xOPFig,2 Control points of a system with a finite object distance areshown in the Delano diagram.JA intersects the y axis at point S',which represents thepoints and design goal parameters are necessary and suffi-position of the entrance pupil of the system.CM intersectscient conditions to undertake this process.From the designthe y axis at point S",which represents the position of thegoal,we can obtain accurate values of control points,andexit pupil.The distance between two successive compo-we can achieve the design goal by making the system fulfillnents is (Delano 1963)the constraint conditions by using the control points.3.1 Control Points of a System with a Finite ObjectQ(4)DistanceLine OF can be constructed to be parallel to line BC,and to intersect the line CM at point Fe.F represents theFor an optical system with a finite object distance,we es-image focal plane of the component C,and the focal lengthtablish the basic design requirements as follows:of the component C is given below (Delano 1963)The object height:h.The image height:hM.(5)-The object numerical aperture:NA.QThe focal length:f.The entrance pupil diameter:D.个yFigure 2 shows the control points J,P and M of theoptical system with a finite object distance.J in Figure 2represents the object plane,P represents the principalplane and M represents the image plane.From the basicdesign goal of the object height and image height,the co-ordinates of./and M can be obtained as:(6MandFig.I The Delano diagram of an optical system with three com-From the relationship between the numerical aperture NAponents.and the object aperture angle uy given in Equation(8)(8)3 THE RELATIONSHIP BETWEEN THECONTROL POINTS AND DESIGN GOALthe object aperture angle can be calculated asNAIn this section,the relationship between the control points(9nJand the basic design goal is deduced.For a system with a fi-nite object distance and an infinite object distance,the con-Line JS'is the line that connects the object plane and thetrol points are different.In Section 3.1,the control points offirst optical component,thus the slope of IS'can be ob-the system with a finite object distance will be introduced,tained by Equation (2)as followsand in Section 3.2,the control points of the system withan infinite object distance will be introduced.The control?1994-2016 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.netAutomatic Generation of Optical Initial Configuration Based on Delano Diagram3In the Delano diagram,the coordinates of the entrance(18),the coordinates of the principal plane can be obtainedpupil can be obtained from the basic design goalas shown below2Qf'(hj -hM)D(11)DhM(19)The slope ofJS'can thus be denoted asFor a given system,the coordinate in the Delano diagramof the control points./,P and M have been obtained as de-(12)scribed by Equations (6),(7)and (19),which are entirelydetermined by the parameters for the design requirementsCombining Equations (9),(10)and (12),the angles of the(hJ,hM,NA,f',D),regardless of the values of the de-marginal ray and principal ray at the object plane can besign parameters.However,if the designers set the controlobtained aspoints J,P and M as constraints during the design pro-cess,the final outcome must fulfill the design requirementsNAarcsinas shown in this section.NAarcsin3.2 Control Points of a System with an Infinite ObjectDDistanceThe Lagrange invariant of a system with a finite ob-For an optical system with an infinite object distance,weject distance can be calculated at the object plane byhave established the basic design requirements that areEquations(1),(6)and (13)listed below:NAThe halffield of view:6.Q=-njhJarcsin(14)-The focal length:f.The entrance pupil diameter:D.Due to the fact that IS'and S'P are on the same line,theslopes ofJS'and the S'P are therefore equal,and satisfythe relation-0Component 10-hj(15)The coordinates of the principal plane calculated fromEquation (15)can be denoted asComponent_N2hJyp(16)MConstructing the line OF parallel to the line JP,and set-tingOF to intersect PM at F,the relation for F can beobtained as Equation (17),which is the focal plane of theFig3 Control points of a system with an infinite object distance.systemDFigure 3 is the Delano diagram correspondingto a sys-tem with an infinite object distance./represents the object(17)plane,and/P is the line connecting the object plane to theh-principal plane in the diagram.For this type of system,JPDis parallel to the axis.The entrance pupil plane is rep-resented by S',and its coordinates can be obtained fromAfter solving Equation(17),the coordinates of F'can bedefined asthe design requirements,as shown in Equation(11),where2yphMD is also the diameter of the entrance pupil.Because JPand PS'are on the same line,and J represents the objectplane with an infinite distance,the coordinates defining ob-ject plane J are as followsF=hM-hjThe focal length can be obtained in the Delano diagram byD(20)solving Equation (3).Combining Equations (3),(16)andJ=2?1994-2016 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.net