The Delano Diagram,a powerful design toolMarkus Schwab*,Dr.Alois Herkommer*,Carl Zeiss SMT AG,Oberkochen,GermanyABSTRACTA power density model is introduced into the Delano diagram.The correlation of the system length and the peak powerdensity are outline especially for 2-f-systems with a low Lagrange invariant and high energy transfer.Keywords:Delano diagram,Power density1.INTRODUCTIONA helpful tool for paraxial optical design is the Delano diagram [1,2,3,4].It can also be used to calculate the maximumpower density on elements of the system will be shown in this article.The Delano Diagram (DD)is a plot of the rayheight y of the paraxial marginal ray (green )over the ray height y of the paraxial chief ray (red)(see Fig.1).The linearcombination of these two rays can be interpreted as one skew ray (blue)in Gaussian optics (see Fig.2 )The Delanodiagram is the projection of this skew ray onto the xy-plane.The DD can illustrate many properties of the opticalsystems and of its subsystems.For example one can visualize the focal length,the focal points,the principal planes,theaxial length,the ray height,vignetting,magnification and more in one diagram only.In addition,it is very useful toclassify optical systems in terms of their functionality.Before introducing a maximum power density model into the DD,some of its basic properties are recapitulated.Note,that the whole article is based on the paraxial approximation,disregarding diffraction-,vignetting-and absorption effects.LensfStopImageMarginal ray●7Chief rayFig.I Paraxial optical systems can be described completely with the marginal ray and the chief ray.The marginal ray goesfrom the edge ofthe pupil stop to the center of the image plane.The chief ray goes from the center of the pupil stop tothe edge of the image plane.Optical Design and Engineering lll,edited by Laurent Mazuray,Rolf Wartmann,Andrew Wood,Jean-Luc Tissot.Jeffrey M.Raynor,Proc.of SPIE Vol.7100.71000U.2008 SPIECCCc0de:0277-786XW08/s18·do:10.1117112.797672Proc.of SPIE Vol.7100 71000U-1Downloaded From:http://proceedings.spiedigitallibrary.org/on 10/31/2013 Terms of Use:http://spiedlorg/termsX,ycyMycensStopddImageDelano diagramy (or yM)(or yc or x)Fig.2 Construction of the Delano diagram.In order to construct the DD we introduce the Delano ray(blue),which is thelinear combination of the chief ray (red)along the x-Axis and the Marginal ray (green)along to the y Axis.TheDelano diagram is the projection of the Delano ray onto the xy-plane,substitutingx with y.The Delano Diagramshows the ray height of the chiefray on the abscissa,which is the field coordinate and the marginal ray height on theordinate,which is the pupil coordinate.2.FEATURES OF DELANO DIAGRAMSFig.3 shows some general properties.The Delano diagram contains the complete information of the paraxial opticalsystem like a Gaussian optic does.In addition,the axial distance between two points in the Delano diagram can becalculated byd=-with n being the refractive index at the distance d,and LI n EPR NAO being the Lagrange invariant of the system.EPR is the entrance pupil radius and NAO is the object numerical aperture.Therefore,the axial distance is proportionalto the triangular area defined by the two points and the origin.Next,a lens power changes the direction of the Delanoray,a tumn to the right is a positive lens power,a turn to the left a negative lens power.Note,that the change of directionis limited by the line through the origin,since the lens power becomes infinite.Further,the object ray and the image raydefine the properties of the optical system such as focal length,magnification,object-,pupil-and image size,the focal-and principal planes.Any optical system with the first lens on the object ray and the last lens on the image ray fulfils allparaxial conditions.Proc.of SPIE Vol.7100 71000U-2Downloaded From:http://proceedings.spiedigitallibrary.org/on 10/31/2013 Terms of Use:http://spiedlorg/termsDistanced1d2Object rayImage rayFig.3 Properties of Delano diagram:The Delano diagram includes as much information as Gaussian optics.The distancebetween two elements is proportional to the area of a triangle defined by the onigin and the two elements (see bottomleft).A change of direction in the Delano diagrams indicates a lens power (see top right).The great advantage of theDelano diagram is that the functionality of the optical system is defined by the object ray and the image ray.Anyoptical system with the first lens on the object ray and the last lens on the image ray has the same paraxial focal lengthand numerical aperture but different lenses and different geometry.1-Lens SystemEntrance PupilPrincipal Planes PP'Optical System3 lensesobjFObjectimImageProc.of SPIE Vol.7100 71000U-3Downloaded From:http://proceedings.spiedigitallibrary.org/on 10/31/2013 Terms of Use:http://spiedlorg/terms