使用ZEMAX"於設計、優化·公差和分析Design,optimization,tolerancing and analysis using ZEMAX摘要光學設针軟體ZEMAX的功能討論可藉由使用ZEMAX去設計和分析一個投影系統來討論，包括使用透镜陣列(lenslet arrays)來建構聚光镜(condenser)。ABSTRACTA discussion of the capabilities of the optical design program ZEMAX is followed by adiscussion of using ZEMAX to design and analyze a projection system to include thecondenser made using lenslet arrays.ZEMAX以非序列性(non-sequential)分析工具來結合序列性(sequential)描光程式的傅統功能，且爲一套能夠研究所有表面的光學設計和分析的整合性套装軟體，並具有研究成像和非成像系統中的雜散光(stray light)和鬼影(ghosting)的能力·從簡單的繪圖(Layout)一直到優化和公差分析皆可達成。根據過去的經驗，對於光學系統的端對端(end to end)分析往往是需要雨種不同的殷計和分析工具。一套序列性描光軟體，可用於設計、優化和公差分析，而一套非序列性或未受限制的(unconstrained描光軟體，可用來分析雜散光、鬼影和一般的非成像系統分析，包括照明系統。序列性描光程式這個名嗣是與定義一個光學系統爲一連串表面的工具有關。所有的光線打到光學系統之後，會依序的從一個表面到另一個表面穿過這個系統。在定義的順序上，所有的光線一定會交到所有的表面，否則光路將怒止。光線不會跳過任何中間的表面；光線只能打在每一個已定義的表面一次。若實際光線路徑交到一個表面上超過一次，如使用在二次描光(double pass))中的元件，然後在序列性列表中，必須再定義超過一次的表面参敷。大部份成像光學系統，如照相機镜頭、望遠鏡和顯微鏡，可在序列性模式中完整定義。對於這些系統，序列性描光具有許多優點：非常快、非常彈性和非常普逼。幾乎任何形状的光學表面和材質特性皆可建構。在成像系統中，序列性描光最重要的優點爲使用簡單且高精確的方法來做優化和分析。序列性描光的缺點，包括無法追跡所有可能的光路徑（即鬼影反射）和許多無法以序列性方式來描逃的光學系統或元件。非序列性描光最常用來分析成像系統中的雜散光和鬼影，甚致分析照明和其他非成像系統。在非序列性描光中·光線入射光學系統後·是自由的沿著實際光學路徑追跡；一條光線可能打到一個物件(objc)許多次，而且可能完全未打到其他物件。此外，非序列性方法可用來分析從光學或機構元件產生的表面散射(scatter),和從場丙(in-field)和場外(out-of-field)的光源所產生的表面反射而形成的鬼影成INTRODUCTIONZEMAX combines the traditional capabilities of sequential ray tracing programs withnon-sequential analysis tools in an integrated package capable of studying all facets ofoptical design and analysis,from initial layout through optimization and tolerancing withthe ability to study stray light and ghosting in imaging as well as non-imaging systems.Historically,two different design and analysis tools were required for end to end analysisof optical systems.A sequential ray tracing program for design,optimization andtolerancing,and a non-sequential,or unconstrained,ray tracing program to analyze straylight,ghosting,and for general non-imaging system analysis,including illuminationsystems.The term sequential ray tracing program refers to a tool that defines an optical system asa sequential series of surfaces.All rays entering the optical system proceed through thesystem from surface to surface in a defined,sequential order.All rays must intercept allsurfaces in this defined order or the ray path will be terminated.Rays can not skip overany of the intermediate surfaces;rays can only strike each defined surface once.If theactual ray path would intercept a surface more than once,such as a component used indouble pass,then the surface parameters must be defined more than once in thesequential listing.Most imaging optical systems,such as camera lenses,telescopes,and microscopes arewell defined by the sequential model.Sequential ray tracing has many advantages forthese systems:it is very fast,very flexible and very general.Optical surfaces of almostany shape and material properties can be modeled.The most important advantage ofsequential ray tracing in imaging systems is that it leads to a straightforward and highlyaccurate method for optimization and analysis.The disadvantages of sequential raytracing include the inability to trace all possible light paths (i.e.ghost reflections)andthere are many optical systems or components which can not be described in a sequentialfashion.Non-sequential ray tracing is most often used to analyze stray light and ghosting inimaging systems,as well as to analyze illumination and other non-imaging systems.Innon-sequential ray tracing rays entering the optical system are free to follow any realoptical path;a ray may strike an object multiple times and may entirely miss other objectsAdditionally,non-sequential methods can be used to analyze surface scatter from opticalor mechanical components as well as visualizing ghost images formed due to surfacereflections from in-field and out-of-field sources.ZEMAX的功能ZEMAX可以用於一個完全序列性模式中、一個完全非序性模式中和一個混合模式中，混合模式對分析具有大部分序列性而卻有一些元件是作用在非序列性方式・管(light pipes)(roof prisms)o序列性系統需定義視锡角(field of view)、波長範圍和表面資料。序列性設計的最重要参敷之一，爲系統f孔徑(system aperture)。系統f孔徑，常指入瞳(entrancepupi或孔徑光欄(aperture stop),它限制可從已定義視場入射光學系統的光線。光學表面可以是折射、反射或繞射。透镜可以是由均匀或漸變折射率材質所製成。表面的下灣(sag)可以是球面、圓錐面(conic)、非球面(aspheric)或藉由多項式或其他参敷函數來定義。也包含了許多繞射光學元件模型。此外，一個使用者自定表面的功能，允許設計者以撰寫程式的方式來建構任何實際的表面下灣或相位分佈。些功能可以用來分析系統，包括敷個系統繪圖(layouts)類型·匯出CAD格式資訊(spot diagrams)(ray fan)和光程差丶繞射調變轉移函數(modulation transfer function,MTF和點擴散函數(point spread function,PSF)圆、包圍圓(encircled)和包圍矩形(ensquared)的能量資訊、像差計算（塞德(Seidel)和策尼克（亿ernike))、理想或偏斜(skew)高斯光束参數計算、極化描光和波前傅播工具。ZEMAX FEATURESZEMAX can be used in a fully sequential mode,a fully non-sequential mode as well as ahybrid mode which is useful for analyzing systems which are largely sequential withsome components which behave in a non-sequential fashion,such as light pipes and roofprisms.Sequential systems are defined by a field of view,wavelength range and surface dataOne of the most important parameters of the sequential design is the system aperture.The system aperture,often the entrance pupil or the aperture stop,limits the rays that canenter the optical system from the defined field.The optical surfaces can be refractive,reflective or diffractive.Lenses can be made of homogeneous or gradient index materials.The sag of the surface can be spherical,conic,aspheric,or defined by a polynomial orother parametric function.Many surface models for diffractive optical elements are alsoincluded.Additionally,a user defined surface capability allows designers to programvirtually any arbitrary surface sag or phase profile.Some of the features available to analyze systems include several forms of system layoutswith the ability to export surface information in CAD format,spot diagrams,ray fan andoptical path difference plots,diffraction based modulation transfer function(MTF)andpoint spread function(PSF)plots,encircled and ensquared energy information,aberrationcalculations (Seidel and Zernike),ideal or skew Gaussian beam parameter calculation,polarization dependent ray tracing and a wavefront propagation tool.3