A Brief  History of Lens Design O;uG?.\  
Since about 1960, the way lenses are designed has changed profoundly  as a result of  the introduction of  electronic digital computers and numerical optimiz-ing methods. Nevertheless, many of  the older techniques remain valid. The lens designer still encounters terminology and methods that were developed even in previous centuries. Furthermore, the new methods often  have a strong classical heritage. Thus, it is appropriate to examine, at least briefly,  a history of  how the techniques of  lens design have evolved. p3(2?UO!  
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A.2.1 Two Approaches to Optical Design L|j%S  
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The equations describing the aberrations of  a lens are very nonlinear func-tions of  the lens constructional parameters (surface  curvatures, thicknesses, glass indices and dispersions, etc.). Boundary conditions and other constraints further complicate the situation. Thus, there are only a few  optical systems whose con-figurations  can be derived mathematically in an exact closed-form  solution, and these are all very simple. Examples are the classical reflecting  telescopes. @N@F,~[RR2  
This predicament has produced two separate and quite different  approaches to the practical task of  designing lenses. These are the analytical approach and the numerical approach. Historically the analytical dominated at first,  but the numer-ical now prevails. YJeyIYCs<  
Neither approach is sufficient  unto itself.  A lens designed analytically using aberration theory requires a numerical ray trace to evaluate its actual perfor-mance. In addition, an analytically designed lens can often  benefit  significantly from  a final  numerical optimization. Conversely, a lens designed numerically cannot be properly understood and evaluated without the insight provided by ab-erration theory. Yk!/ow@.  
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A.2.2 Analytical Design Methods &@FhR#pUQ  
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The first  lenses made in quantity were spectacle lenses (after  about 1285). c9"r6j2m5  
Later (after  1608), singlet lenses began to be made in quantity for  telescopes and microscopes. Throughout the seventeenth and eighteenth centuries, optical instru-ments were designed primarily by trial and error. As might be expected, optical flaws  or aberrations remained. Note that, aberrations are fundamental  design shortcomings, not fabrication  errors. Eventually it became clear that understand-ing and correcting aberrations required greater physical understanding and a more rigorous analytical approach. zi@]83SS#  
At first,  progress was slow and the methods largely empirical. Later, math-ematical methods were introduced, and these were much more effective.  The most outstanding early work on optical theory was done by Newton in 1666. Among the somewhat later pioneers were Fraunhofer,  Wollaston, Coddington, Hamilton,and Gauss. A major advance was made by Petzval in 1840. Petzval was a mathemati-cian, and he was the first  to apply mathematics to the general problem of  design-ing a lens with a sizable speed and field  for  a camera. The techniques he devised were new and fundamental.  His treatment of  field  curvature based on the Petzval sum is still used today. Just as unprecedented, he was able to completely design his very successful  Petzval Portrait lens on paper before  it was made. V)ig)(CT  
In 1856, Seidel published the first  complete mathematical treatment of  geo- metrical imagery, or what we now call aberration theory. The five  primary or third-order monochromatic aberrations are thus known today as the Seidel aber-rations. They are: <ABX0U[*  
1. Spherical aberration X{xBYZv4  
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3. Astigmatism yLE7>48  
4. Field curvature zAzP,1$?  
5. Distortion. Z @ dC+0[=  
There are also two primary chromatic aberrations. These are wavelength-de-pendent variations of  first-order  properties, and they are often  included with the Seidel aberrations. They are: 6w8">~)Z  
6. Longitudinal chromatic aberration 2Os1C}m  
7. Lateral chromatic aberration. j$7|XM6  
Petzval, Seidel, and many others in subsequent years have now put aberra-tion theory and analytical lens design on a firm  theoretical basis.注釋1 B;>{0 s  
Until about 1960, the only way to design lenses was by an analytical ap-proach based on aberration theory. Unfortunately,  by its nature, aberration theory gives only a series of  progressively better approximations to the real world. Thus, the optical designs derived from  aberration theory are themselves approximate and usually must be modified  to account for  the limitations in the process. ~^jq(:d)  
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Today, most lenses are designed, not with analytical methods, but with com-puter-aided numerical methods. Nevertheless, the analytical methods remain ex-tremely valuable for  deriving or identifying  potentially useful  optical configurations  that can serve as starting points for  further  numerical optimization. DyJ.BQdk)  
Even more important, aberration theory can explain what is happening. It is only through aberration theory that a lens designer can understand the underlying op-eration of  lenses. /D&%v*~E  
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A.2.3 Numerical Evaluation Methods  u$#Wv2| 大安市| 辽源市| 新巴尔虎右旗| 灌南县| 绵阳市| 吐鲁番市| 新平| 牟定县| 安徽省| 贺州市| 漠河县| 奇台县| 蓝山县| 林芝县| 涟水县| 龙井市| 华阴市| 北安市| 德惠市| 温宿县| 调兵山市| 白山市| 长白| 惠东县| 藁城市| 沾益县| 财经| 尉氏县| 长治市| 札达县| 达孜县| 新源县| 班戈县| 白河县| 通州区| 大洼县| 娱乐| 石台县| 冕宁县| 沙田区| 中山市|