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——光学设计何处去 Whither Optical Design? 原文作者 Douglas C. Sinclair 发表于 Optics and Photonics News, June 2000 X` #vH8
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由 小马过河 翻译，仅供学习参考，转载请站内信箱联系。 #8 rLB(
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20世纪可能见证了传统镜头设计的生与灭。我所指的传统镜头设计是平衡共轴球面系统的象差，获得尽可能好的象质。在传统的镜头设计中，物理光学仅仅提供了优化终点的条件。一旦达到瑞利极限，这个设计就足够好了。 _KLKa/3
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直到最近，典型的光学系统的尺度仍比波长长很多。几何光学的专业人士采用象差和光线的概念研究折射，物理光学方面的专业人士则使用波的概念来研究成像，两者并没有多少共同之处。现在的技术人员谈论光的波长，相比起他们设计的光学系统，并不像以前的人认为的那么短了。与此同时，跨越几何光学和物理光学领域进行设计的人却十分少有。我们拥有工具，可以处理比以前更大范围，更令人感兴趣的问题，但是真正知道如何使用这些工具的人越来越少。大概二十年前，Warren Smith写了一篇名为“镜头设计师的消失”的文章。今天，可以越来越强烈的感觉到专家级镜头设计人员数量减少的问题。 p~BE z?e
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上个世纪初，传统镜头设计的数学，物理框架已经建立得比较完备。早期的设计，如消色差胶合透镜，Petzval镜头已经被发展的很好了。但是，直到20世纪的前半，镜头设计的理论与实践才真正建立，主要是在欧洲。 7S}NV7
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到了计算机出现的1950年，今天使用的基本镜头设计形式已经发展完备。Cook式的三片镜，Petzval镜头和双高斯镜头直到今天还广为使用，当然具体的结构形式经由计算机优化而略有调整，这一事实是对当年的发明者工作的最佳肯定。当然，现代光学系统中也出现了一些全新的结构形式。渐变折射率透镜，衍射透镜以及普遍使用的变焦镜头早已为人知，但直到20世纪下半才发展完备。采用计算机优化，使得今天的镜头可以更加复杂。有意思的是，大多数镜头的结构或多或少的遵循了传统的设计准则，这一点并不令人惊讶。现在的平版印刷镜头就是一个典型。平版印刷镜头通常拥有纳米级的畸变象差容限，极高的照明和波前质量要求。这种镜头是递进发展中的一个重要环节--设计这种镜头用以制造更快的芯片，更快的芯片用以优化下一代的平版印刷镜头。从另一方面看，这种镜头是double-humped Gauss lenses这种典型结构的一种衍生结构。 lE'2\kxI?
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激光和计算机这两个上世纪中期的发明，极大的拓展了光学设计的视野，以至传统意义上的光学设计被推至一个次要地位。今天可以这样说，激光的存在，让光学设计人员有工作可做；计算机的存在则提供了必要的支持。激光的重要性不在于激光器本身的特性，而在于激光对光学系统的影响。除开有限的几个军事，视觉和成像应用，光学，直到最近，都是其它科学领域的服务学科。当我们进入新的世纪，光学迅速的演变成消费品技术。 为了取得市场成功，消费品技术必须同时“好”和“便宜”。大多数的设计者都好不适应工作在这种压力下：他们对“好”很熟悉，但不习惯于“便宜”。将来，设计者的任务不是设计出成像质量好到极至的镜头，而是设计象质令人满意，但制造成本最低的镜头。这是一个重要的不同点，它强调需要全新的设计方法论。如果一个消费品的镜头被过分设计了（象质过好），它就会太贵，而没有竞争力。然而针对镜头量产方面的优化已经超越了传统光学设计的边界。 ?
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公差，是极具挑战性，同时也是传统光学设计最为忽略的领域，如今它非常重要。从产品封装的角度而言，小尺寸越来越具有吸引力。尺寸不断缩小的需求已经将光学系统的尺寸推至非比寻常的结构尺度，随之而来的就是连同数值计算技巧在内的设计分析方法的转变，这些设计方法通常根据手头的项目不同而不同。在某些应用实例中，尺寸方面的要求使得镜头被放置在波长量级尺度的空间。在这种情况下，几何光学的设计方法已经无能为力，但是，现阶段的基于物理光学的计算速度太慢。这就是光学设计人员即将遇到的挑战。 MA6(VII
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如果光学设计人员对整个光学领域的知识缺乏一个整体的理解，他就无法解决上述问题。为了应对未来的问题，很有必要将镜头设计人员精细的方法论和光学工程师的广阔视野结合起来。在光学设计行业以外，有这么一种趋势：认为镜头设计是一个已经被解决的问题，那些人相信只要你买上一套光学设计软件，然后按一下“全局优化”的按钮，你就可以解决所有镜头设计的问题。当然，现实情况是相反的。 o7;lR?
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98年国际光学设计大赛的竞赛题目和色差的优化有关。根据竞赛规则，参加者可以有两种选择：只可以使用很少的面（玻璃空气接触面）和很多种不同的玻璃，或者是很少的几种玻璃和很多个玻璃空气接触面。和预期的一样，经验老道的设计者提供了top 5的结构。其中四个使用了商业光学设计软件，另外一个使用了内部专有的设计软件。尽管，其中三个人声称借助了软件的全局优化功能。但是他们的设计结果反映了他们对设计本身的掌控。从这一点来看，这一结果和过去二十年间的设计比赛是类似的。 C[6}
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下面的两个结构就是98年IODC的参赛答案（见下图）。上面John Isenberg的获奖答案性能极为优异，而下面不知名作者的答案看起来缺乏对复消色差的理解。图中，较高折射率的玻璃显示暖色调。 wQEsq<
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更令人感兴趣的是那些参赛答案中的失败作品。看起来，其中很多参赛者对复消色差的基本原理缺乏了解，或者是，他们试图让软件替他们思考--在这个设计案例中是行不通的。当然，镜头的复消色差并非普通工程师必须熟悉的，但是，我们讨论的是一群光学设计的专业人士。今天顶级的光学设计师消失以后，他们将接管光学设计工作。很有必要反思一下究竟发生了什么。很明显的是，光学设计软件无法提供设计结果：软件的标准内置功能是不充分的，它需要在设计者的指导下工作。 #p*D.We
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随着光学设计领域的拓展，这种情况越来越普遍。为了应对这种情况，我们有必要反思光学设计本身，确保我们采用正确的方式教育学生，使他们有能力应付这些挑战。值得注意的是，从几何光学开始，然后是物理光学的次序来教育学生不是个好主意。最好是从波的概念开始，然后介绍在器件尺度远大于波长的时候，光线是一种很有用的近似。让学生由易及难，学习会变得比较容易一点，这没有错。但问题的实质是和光线打交道不比和光波打交道容易。 F2QFQX(j
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事实上，从光线概念开始的教学意味着Snell定律的使用。Snell定律优雅而简洁，但当你使用Snell定律描述成像系统时，你会得到一系列的展开式，它们会很快变得难以处理。这种情况下，学生仅仅熟悉了一点近轴光学的知识，然后就是胡思乱想的假设只有嗜好代数运算的镜头设计专家才可以懂这一门学问，最后，大部分学生选择了放弃努力。光学设计真正的困难之处在于，采用了一些离散的数值来描述一个连续的、非线性的系统，而不是在于代数运算的复杂。代数运算可以交给计算机来完成。 u% !/-&?wF
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从光波的概念出发，意味着先接触Huygens原理，然后经由Fermat原理到几何光学。这种方法会促使学生去思考光的本质，而不是光线追迹的代数式。这样做的优点还有，让学生理解光波和光线是如何联系起来的，同时还能理解那些经由合理的，工程上决定出来的光学系统的工作实质。如果某天，你手头的设计任务超过了套装光学软件提供的功能，那么，理解你所做的工作的物理实质就至关重要。即使将来套装光学软件不断升级，自己动手，抓住物理实质，拓展需要的功能，这种需求仍然不会消失。 @IhC:Yc
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Jenkins和White的傻话 XXPn)kmWR
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Jenkins和White的“Fundamentals of Optics”出版于1937年，而后73年间不断重印，它可能是最为广泛使用的光学教材了。在光学领域，有很多衍生的教材，如同树的枝叶，“Fundamentals of Optics”则是树根，至少也是树干。每个进入光学领域的人都熟悉这本书。但是，这本书的开头两句话却让我们误入歧途。 VkdG GY
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书中写道：光学，研究光的学问，习惯性的被分为三个领域，每个领域都有各自不同的理论处理方法。它们是：a.几何光学，采用光线的方法，b.物理光学，关注光的本质，主要是波的理论，c.量子光学，处理光和物质原子的作用，精确的计算需要量子力学的方法。 HCfme<'
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问题出在哪儿呢？断言经典光学和量子光学是基于不同概念，这没有问题。问题在于宣称几何光学和物理光学之间的差异使得各自需要完全不同理论方法来处理。大家都知道，光的传播遵循Maxwell方程，无论你是采用波面的概念还是波面法线的概念，这一点都不会改变。尽管Jenkins和White的傻话对准备学习光学的学生是有害的，但真正的问题是，这本教材被某种程度上当作光学领域的圣经。真正的光学设计师不会采用Jenkins和White的教材。 =h0 vdi%{
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镜头设计和光学工程 eu={6/O
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几年前，Rudolf Kingslake被罗切斯特工程界提名为年度工程师，获得提名不是因为Kingslake在那一年里做了什么，而是褒奖他一生的专业成就。当我向他祝贺提名是名至实归时，他回答说，他感到非常荣幸，而且还有些意外，因为他一直认为自己是个镜头设计师，而不是光学工程师。 )Fon;/p
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Kingslake很清楚镜头设计师和光学工程师之间的区别。镜头设计师的主要工作就是平衡像差；光学工程师则处理系统布局，和市场部门，机械部门讨价还价，以获得足够的空间，使得在物理法则以内设计是可以实现的。当我们进入新千年时，这两者之间的区别消失了，同时，也形成了一个无人填补的空白。镜头设计师和光学工程师都必须直面这一问题。 %|j`z?i|
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镜头设计专业本质上很可能即将消失。今天的现实是没有几家公司能够雇佣传统模式下的全职镜头设计师。原因是这些公司面临的不仅仅是传统镜头设计中解决的像差平衡问题，它们遇到的问题更为广泛。而同时，光学系统的优化也不是一个很容易就可以解决的问题，最近的光学设计大赛结果就很清楚的说明了这一点。因此，现在非常需要这样的人，他既可以完成专业水准的光学设计，又具有工程上的广阔视野。 6~c#G{kc
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几年前，日本的贸易大臣提出了这样的口号：“电子是二十世纪的科学--光学是二十一世纪的科学”。现在，在世纪交替的时候，光学看起来发展得还不错，但我们还要确认一下我们走在正确的道路上。我们的确很有可能让光学成为二十一世纪的科学，但是，它主要还是一门工程科学。我们必须明白这一点。 ~- R%m
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将镜头设计包含到光学工程中去，这一点并不容易。尽管改变几何光学的教学方法有一定帮助，但这还不够。更重要的是，提升光学工程师的光学设计训练水平。过去的岁月中有很多值得吸取的经验，吸取这些经验非常重要。但同时，光学设计新的发展中也有很多激动人心的机会。可以肯定的是，世纪交替的现在就是年轻人进入光学设计的绝佳时机。▲ ]; xDXQd
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Whither Optical Design? @,Z0u2WLl6
Douglas C. Sinclair Optics and Photonics News, June 2000 .DNPL 5[v
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The twentieth century is likely to have witnessed both the birth and the death of traditional lens design. By traditional lens design I mean the process of balancing the aberrations of centered spherical systems to achieve maximum image quality. In traditional lens design, physical optics provides only a termination condition. When the Rayleigh diffraction limit is reached, the design is good enough. TZ&X0x8
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Until recently, the dimensions of typical optical systems were much greater than optical wavelengths. Specialists in geometrical optics studied refraction using aberrations and rays, and specialists in physical optics studied images using waves, with neither group having much in common with the other. Now, however, optical wavelengths are not considered as short as they used to be. At the same time, there is a lack of people competent in both geometrical and physical optics. We have the tools to tackle challenging and exciting problems of much greater scope and interest than ever before, but fewer and fewer people know how to use these tools. Nearly twenty years ago, Warren Smith wrote an article entitled “The Vanishing Lens Designer”; today, the dwindling number of expert lens designers has become a problem that is even more keenly felt. 0vETg'r
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At the beginning of the century, the mathematics and physics relevant to traditional lens design were already pretty well established, and early designs like achromatic doublets and the Petzval lens had already been developed. But it was during the first half of the twentieth century that the theory and practice of lens design were really established, chiefly in Europe. n,U? ]mr
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By the time computers appeared in the 1950s, the basic design forms used today were pretty well developed. It is a tribute to the inventors that lenses like the Cooke triplet, the Petzval and the Double-Gauss are still widely used, mostly in the form of computer-optimized derivatives. There are some new forms, of course. Gradient-index and diffractive lenses, and the ubiquitous zoom lens, were known but not well developed until the second half of the century. It is interesting but perhaps not surprising that although computers have made possible the development of lenses of greater complexity, today most lenses still operate within more or less conventional guidelines. The modern lithographic lens is a sterling example of such a design. With nanometer distortion tolerances, incredible illumination and wavefront requirements, lithographic lenses are part of a recursive cycle, in that they are designed to produce chips fast enough to design the next generation of lenses. On the other hand, they tend to be variations of double-humped Gauss lenses, an established form. 8Cs;.>75[
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Two mid-century inventions, the laser and the computer, have expanded the scope of optical design so much that optical design as it is traditionally conceived will likely soon be relegated to a minority position. Today, the laser provides the work for the optical designer, while the computer provides the necessary support. The importance of the laser is not to be found in the intrinsic characteristics of the device itself, but rather in its impact on optics. Until fairly recently—with the exception of a few established military, visual and photographic applications—optics was essentially a service discipline for other sciences. As we enter the new century, optics is rapidly becoming a consumer technology. d~1uK-L]*
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To meet with market success, consumer technology must be both “good” and “cheap.” Many lens designers are not used to working under such pressure: they’re comfortable with good—but not with cheap. In the future, designers will not be called upon to design the lenses that form the best images, but rather those that form satisfactory images and are cheapest to manufacture. This is an important distinction, one that under-scores the need for development of a whole new design methodology. If a lens for a consumer product is over designed, it will be too expensive to be competitive. Yet optimizing this aspect of production is outside the boundary of traditional optical design. ^/_Yk.w
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Tolerancing, the most challenging and traditionally the most neglected aspect of optical design, is obviously becoming more important. In packaging, small size is increasingly in demand. The quest for smaller and smaller sizes has led to unusual geometries, and the consequent replacement of analytic design methods with numerical techniques, often tailored to the particular task at hand. In some applications, size restrictions may necessitate placing lenses in spaces where they can have dimensions of only a few wavelengths. In this case, geometrical design methods are inadequate, but current physical optics methods are too slow. These are the types of problems that optical designers can expect to confront in the future. Ve2{;`t
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Designers won’t be able to solve these problems without wide-ranging knowledge of optics as a discipline. In the future, it will be necessary to combine the lens designer’s meticulous methodology with the broader perspective of the optical engineer. Outside the optical design community, there is a tendency to consider lens design a problem that has been solved: there are those who believe that if you purchase an optical design software package and press the “global optimize” key, you can be done with it. The reality, of course, is different. j$K*R."
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The optical design problem presented to participants in the 1998 International Optical Design Conference, involved the optimization of a system characterized by chromatic aberration. Participants had the choice of using a few surfaces but lots of different glasses, or a few glasses and lots of surfaces. As expected, experienced lens designers came up with the top five solutions. Four of the designers used commercial optical design software, one an in-house proprietary program. Although three of the designers noted that they had used the global exploration features of their software as an aid, all the solutions reflected the detailed personal involvement of the designer. In this respect, the results were comparable to those of similar contests held over the course of the past twenty years. ~)^'5^
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Two designs submitted as solutions to the lens design problem posed at the 1998 International Optical Design Meeting in Kona, HI. John Isenberg's winning design (top) achieved superb performance, but a typical solution from an unknown designer (bottom) lacked the essential apochromatic correction. In the drawings, higher index glasses are shown in warmer hues. (:aU"5M
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More interesting are some of the losing designs among the few dozen that were submitted. It is apparent that many of the designers were unaware of some of the basic principles of apochromatic correction, or else that they tried to let the software do the thinking for them—and in this case, it didn’t work. Of course, apochromatic correction of lenses is not something that you expect the average engineer to be familiar with, but we’re talking here about a group of optical design specialists. These are the people who presumably will take over optical design when today’s top lens designers vanish. It seems reasonable to ask what happened here. The obvious response is that the software didn’t provide the answer: its standard built-in capabilities were insufficient and needed to be supplemented by designer-developed workarounds. D"J',YN$
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As the scope of optical design widens, this type of situation will become increasingly common. To deal with it, we need to re-conceptualize optical design and ensure we are educating students in such a way as to provide them with the ability to meet the challenge. In particu-lar, it’s not a good idea to start by teaching geometrical optics and then progress to physical optics: better to start with waves and then introduce rays as a useful approximation when the dimensions of the elements are large compared to the wavelength. It’s true that learning is facilitated when students progress from simple to more complicated subjects, but the truth of the matter is that ray optics isn’t any simpler than wave optics. H4s~= iB
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In fact, starting with rays implies the use of Snell’s law. Snell’s law is elegant, but when you try to use it to describe imaging systems you are led to series expansions that very quickly become unmanageable. At this point, with a limited degree of familiarity with paraxial optics, and believing that only lens designers with a penchant for algebra can understand the subject, the vast majority of students opt out. Optical design is difficult because it involves modeling a continuous non-linear system using discrete numbers, not because the algebra is hard. Computers can do the algebra. M?!@L:b[
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Starting with waves means beginning with Huygens’ principle and arriving at geometrical optics through Fermat’s principle, an approach that leads students to think about the physics of light rather than the algebra of ray tracing. This is good because it helps them understand how waves and rays are related, as well as how the systems needed to make sensible engineering decisions really work. If your job will one day entail circumventing the limitations of canned software, it’s important to understand the physics of what you’re doing. And it’s not likely that this requirement will change in the future. MjU|XQS:
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Jenkins’ and White’s folly >!6|yk`GJ
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First published in 1937 and still in print 63 years later, Fundamentals of Optics by Jenkins and White is probably the most widely used optics text ever published.1 In a field sown with thousands of what are known as “twig books,” Fundamentals of Optics has been at the root, or at least the trunk, of the tree. Everyone trained in optics is familiar with it. Yet the first two sentences start us off on the wrong track: RN[I%^$"
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Optics, the study of light, is conveniently divided into three fields, each of which requires a markedly different method of theoretical treatment. These are (a) geometrical optics, which is treated by the method of light rays, (b) physical optics, which is concerned with the nature of light and involves primarily the theory of waves, and (c) quantum optics, which deals with the interaction of light with the atomic entities of matter and which for an exact treatment requires the methods of quantum mechanics. /TyGZ@S>m
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What’s the problem? It’s not in the assertion that classical and quantum optics are based on different concepts. It’s in the assumption that the difference between geometrical and physical optics requires a “markedly different method of theoretical treatment.” Everyone agrees that the propagation of light is governed by Maxwell’s equations: it doesn’t matter whether you think in terms of wave surfaces or the normals to these surfaces. Although Jenkins’ and White’s “folly” has been detrimental to students trying to learn optics, the real problem is that the text seems to have been adopted as some sort of bible by suppliers of optical components. Real optical designers don’t use Jenkins and White. <q8@a0e@
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Lens design vs. optical engineering MC* Hl`C
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A few years ago, Rudolf Kingslake was named Engineer of the Year by the Rochester Engineering Society, not for anything he did during that particular year, but for a lifetime of professional accomplishment. When I congratulated him on an award justly deserved, he replied that he felt indeed honored to have been selected, and was somewhat surprised, because he had always thought of himself as a lens designer, not an optical engineer. TG%B:^Yz!
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Kingslake had a clear picture of the difference between the two. The lens designer was the one who balanced the aberrations; the optical engineer worked on layouts and negotiated with the marketing and mechanical departments to get enough room for the design to be implemented within the laws of physics. As we enter the new century, that distinction is disappearing. At the moment, it is leaving a void that is not being filled. Both lens designers and optical engineers need to confront this issue. #L~i|(=U5
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The profession of lens design per se is likely to disappear. The reality today is that very few companies can afford to employ a full-time lens designer from the traditional mold. The problems that these companies face are not the aberration-balancing problems solved in traditional lens design—they’re much broader in scope. At the same time, the optimization of optical systems is not a problem that lends itself to casual solution, as the results of recent lens design contests demonstrate. There’s much demand for people who can work at a professional level in optical design, but who also have a broad engineering perspective. I |U'@E
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A few years ago, the Japanese trade ministry came up with the slogan “Electronics is the science of the twentieth century—Optics is the science of the twenty-first century.” Now, at the turn of the century, optics is looking pretty good, but we need to be confident that we’re working on the right agenda. We do indeed have the opportunity to make optics the science of the twenty-first century, but it will be primarily an engineering science, and we need to understand that. s U"%,Q5
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Including lens design as a part of optical engineering is not easy. Although changing the way that geometrical optics is taught may be of some help, it is not sufficient. More important is raising the level of optical design taught to optical engineers. There’s a great deal to be learned from the past, and it’s important to learn it. But there are wonderful opportunities in optical design, and surely there’s never been a better time for a young person to enter optics.
