現(xiàn)代光學設計外文翻譯

1、<p>　　畢業(yè)設計(論文)外文資料翻譯</p><p>　　系： 電子工程與光電技術系 </p><p>　　專 業(yè)： 光電信息科學與工程 </p><p>　　姓 名： </p><p&

2、gt;　　學 號： </p><p>　　外文出處：Smith W J. Modern lens design[M]. </p><p>　　New York: McGraw-Hill, 2005. </p><p>

3、;　　附 件： 1.外文資料翻譯譯文；2.外文原文。 </p><p>　　注：請將該封面與附件裝訂成冊。</p><p>　　附件1：外文資料翻譯譯文</p><p><b>　　現(xiàn)代光學設計</b></p><p><b>　　2.1評價函數(shù)</b></p><p>

4、;　　到底什么是大家所說的自動光學設計，當然，自動并不是指電腦能夠自己來完成設計。實際上它所描述的是使用計算機對光學系統(tǒng)進行優(yōu)化的程序，并通過評價函數(shù)（它不是一個真正的優(yōu)化函數(shù)，實際上是一個缺陷函數(shù)）定義的優(yōu)化方案。不管前面的免責聲明，我們將在下面的討論中使用被大家普遍接受的術語。</p><p>　　從廣義上說，評價函數(shù)可以描述為計算特性，其目的是用一個單純的數(shù)字來完整地描述一個給定的透鏡的質量或者功能。這顯然

5、是一個極其困難的事情。典型的評價函數(shù)是許多圖像缺陷值的平方之和，通常這些圖像的缺陷通過視場中的三個位置參數(shù)來進行評價（除非該系統(tǒng)包括一個非常大或非常小的視場角）。使用缺陷的平方來計算可以確保一個負值的缺陷不會抵消其它的正值的缺陷。</p><p>　　缺陷可以是許多不同種類的，它們中的大多數(shù)通常都涉及到圖像的質量。任何可以被計算的光學特性都會被分配一個目標值，然而，當實際值偏離這一目標值時該特性被視為存在缺陷。一

6、些不太復雜的程序利用三階（賽德爾）像差來計算缺陷；這提供了一種快速而有效的方式來調整設計。這種方法雖然沒有真正優(yōu)化圖像質量，但他們在普通鏡頭的糾正上有很好地效果。另一種類型的評價函數(shù)的原理是追跡從一個對象發(fā)出的大量光線。將所有的出射光線相交的圖心與圖像平面的交點的徑向距離視作圖像缺陷。因此，評價函數(shù)是光斑在幾個視場角的有效尺寸總和的均方根（RMS）。這種類型的評價函數(shù)的效率較為低下，因為它需要追跡大量的光線，但它所具有的優(yōu)點也正是在于它

7、追蹤了大量的光線，因此從某種意義上說它所包含的數(shù)據(jù)量很大，對于光線的反映十分的完整全面。還有一種評價函數(shù)，它計算出古典像差的值，并將其轉換（或計算）成等效的波振面的形變。（幾種常見的像差轉換系數(shù)見附錄F- 12第二段 ）。這種方式非常有效，它的優(yōu)點是節(jié)省了計算時間，優(yōu)化設計的功能更好。還有一種類型的評價函數(shù)的使用波陣面的方差來定義的缺陷項。這種類型的評價函數(shù)中使用各種“大衛(wèi)灰色”程序，當然這是</p><p>　

8、　凡涉及到圖像質量的特性都可以通過鏡頭設計程序控制。具體的結構參數(shù)如：半徑，厚度，空氣間隔以及焦距，工作距離，倍率，數(shù)值孔徑，光闌等，都是可以被控制的。一些程序包括了隨圖像失真而變化的評價函數(shù)的項目。但是有兩個缺點在一定程度上抵消了這種方法所帶來的簡便性。一個是，如果最初選定的計算對象的一階特性不足夠接近目標值，所述程序在校正圖像畸變的時候將不能控制這些一階特性，其結果可能是，例如，一個有著錯誤的焦距或數(shù)值孔徑的透鏡會被認為已經(jīng)被校正了

9、。程序往往認為這是一個局部最優(yōu)的方案而且不能解決掉這個錯誤。另一個缺點是，在評價函數(shù)中包含的各個項會帶來減緩我們改善圖像質量的處理效果。一種替代的方法是使用評價函數(shù)之外的約束系統(tǒng)。還要注意的是程序中有很多項可以被控制，包括幾乎所有的角度和高度的求解功能。用這些代數(shù)求解的半徑或空間來得到所需的射線斜率或高度。</p><p>　　通常情況下,評價函數(shù)用一個單純的數(shù)值來表示系統(tǒng)的質量，這個數(shù)值是通過評價函數(shù)的缺陷項經(jīng)

10、過加權求和計算出來的。評價函數(shù)的值越小，鏡頭越好。評價函數(shù)的數(shù)值取決于光學系統(tǒng)的建設，即函數(shù)的變量是光學系統(tǒng)的結構參數(shù)。不考慮所涉及的數(shù)學細節(jié)，我們可以意識到評價函數(shù)是一個n維空間，其中n是在光學系統(tǒng)中的可變結構參數(shù)的數(shù)目。設計方案的任務是找到一個空間位置(即鏡頭處理方法或解決方案的方向)它最大限度地減少了函數(shù)的大小。一般而言，一個具有合理復雜性的鏡頭在典型的價值函數(shù)空間內會有很多這樣的位置。自動設計程序將使鏡頭的設計趨向于最接近的、最

11、簡單的評價函數(shù)。</p><p><b>　　2.2優(yōu)化 　　</b></p><p>　　鏡頭設計程序通常這樣操作：每個變量參數(shù)變化(每次一個)的增量大小是選擇一個較大的值(以獲得良好的數(shù)值精度)和一個較小的值(獲得本地微分)之間的值。對評價函數(shù)產(chǎn)生變化的每一項進行計算。結果是一個相對于該參數(shù)的缺陷項的偏導數(shù)的矩陣。因為通常參數(shù)可變，所以會有許多項缺陷變量，針對這個

12、問題可以用經(jīng)典的最小二乘法來解決。它的基礎假設是，缺陷項目和變量參數(shù)之間的關系是線性的。然而在實際條件下這通常是一個錯誤的假設，一個普通的最小二乘法的計算結果往往會是一種無法實現(xiàn)的鏡頭或一個可能比開始設計更糟的鏡頭。針對這一情況可以使用阻尼最小二乘解，這實際上是增加了對于評價函數(shù)的參數(shù)進行加權平方這一計算，從而嚴格控制任何大的變化，因此限制了結果大小變化。斯賓塞對這一過程在“靈活的自動鏡頭校正程序”一文中進行了數(shù)學描述，該文發(fā)表在應用光

13、學,第二卷,1963年,1257 - 1264頁,史密斯,W.德里斯科爾(主編),光學手冊,麥格勞-希爾,紐約,1978年。</p><p>　　如果優(yōu)化結果的變化很小，非線性計算不會破壞過程以及結果，盡管是一個近似的結果，但程序對于設計上的優(yōu)化計算將開始不斷重復，直到最終使設計達到最近似的局部最優(yōu)解。</p><p>　　人們可以想象只有兩個變量參數(shù)的情況。然后可以把評價函數(shù)的空間比作一

14、個地形圖，其中緯度和經(jīng)度相對應的變量和仰角代表評價函數(shù)的值。因此，鏡片設計是在一個特定的初始位置，在設計中橫向將透鏡移動到最小值的優(yōu)化過程就像在下坡的過程中找到海拔最低的點。由于在下坡的過程中可能有許多凹陷的地形，一個凹陷里的最低點的未必是整個地形中的最低點，它是一個局部最優(yōu)但不能保證（除非在非常簡單的系統(tǒng)）我們已經(jīng)找到了全局最優(yōu)的評價函數(shù)。這個簡單的地形比喻有助于我們理解優(yōu)化過程的主要目標：程序找到最接近的最小的評價函數(shù)，并且從該最小

15、可唯一確定的值開始測定坐標。景觀比喻是很容易為人類的頭腦去理解，當它被擴展為10 - 或20 - 維空間，想要實現(xiàn)去逼近它是及其復雜的。</p><p><b>　　2.3局部極小</b></p><p>　　圖2.1表示了將一個兩變量評價函數(shù)想象成的一個等高線地形圖，用點A，B和C表示三個顯著的局部最小值，還有其他三個極小的D，E和F是顯而易見的，如果我們在Z點開始

16、優(yōu)化，B是唯一一個程序可以找到的最小點。若換做Y點開始優(yōu)化，最低的極值將變?yōu)镃。</p><p>　　圖2.1表示面形的一個兩變量評價函數(shù)，有三個主要極小值（A，B，C）和三個相對較不重要的極小值（D，E，F(xiàn)）。其中一個設計方案將最低的點設為該優(yōu)化過程開始的基準點?；鶞庶cX，Y和Z的不同分別導致了設計最小點的不同;其它起點會導致最小點變?yōu)橄鄬Σ恢匾狞c中的一個。</p><p>　　然而，

17、初始點換做X的時候，雖然它距離Y只有很短的距離，但是極小值會變?yōu)锳點。通過這個比喻就算我們對于評價函數(shù)只有一點模糊的知識，我們也可以很容易地把起點選在地圖的右下象限來保證最小點在A點處。另外還要注意的是任何三個出發(fā)點一點小的改變就可能導致程序在極小值的D，E或F中的一個停滯不前。為了在尋找最小值的過程中可以從這些極小值中“震蕩”逸出，設計如下所述。</p><p>　　事實上，自動設計程序是極其有限的。它對于鏡頭

18、設計的需要能給出最近似的最優(yōu)結果，但是這需要在一開始人為的選擇一個接近最優(yōu)的設計形式。這是一個自動程序可以設計一個良好系統(tǒng)的唯一途徑。如果程序在一個局部凹陷的附近開始優(yōu)化，其結果將是一個糟糕的設計。</p><p>　　阻尼最小二乘法會涉及到的數(shù)學中的矩陣反轉。盡管存在阻尼作用，這個過程會通過下列條件減緩或中止：(1)評價函數(shù)中的一個變量不改變(或僅產(chǎn)生很小的變化)。(2)兩個變量具有相同的或者幾乎相同的縮放效果

19、。幸運的是，這些條件都很少恰好滿足,并且他們可以很容易地被避免發(fā)生。</p><p>　　另一個經(jīng)常遇到的問題是一個設計會持續(xù)陷入到一個明顯的不良形式（當你知道有一個更好的，非常不同的，你想要的一個）設計中。通過固定透鏡中一項參數(shù)不變，再進行幾個周期的反復優(yōu)化的的方法通常會允許透鏡的其余參數(shù)降低到所需的最佳值的附近。例如，如果一個人試圖把一個庫克三片式鏡頭轉換為前端頂部分離的形式，這個過程可能會產(chǎn)生兩種情況，一個

20、形狀類似于在鏡頭前面出現(xiàn)了一個狹窄的空氣層間隔，另一個則是非?？鋸埖膹澰滦瓮哥R的形式。通常避免這種情況的一種局部優(yōu)化技術是將所述第二表面固定到一個平面上再進行幾個周期的優(yōu)化來確定前端元件的平凸形狀。當然，這些操作的前提是使用者必須知道哪種鏡頭形式是好的。</p><p>　　附件2：外文原文（復印件）</p><p>　　Modern Lens Design</p><

21、p>　　2.1 the merit function</p><p>　　What is usually referred to as automatic lens design is,of course,nothing of the sort. the computer programs which are so described are actually optimization programs

22、which drive an optical design to a local optimum, as defined by a merit function (which is not a true merit function , but actually a defect function). in spite of the preceding disclaimers, we will use these commonly ac

23、cepted terms in the discussions which follow.</p><p>　　Broadly speaking ,the merit function can be described as a combination or function of calculated characteristics, which is intended to completely descri

24、be, with a single number, the value or quality of a given lens design. This is obviously an exceedingly difficult thing to do. The typical merit function is the sum of the squares of many image defects; usually these ima

25、ge defects are evaluated for three locations in the field of view (unless the system covers a very large or a very small angular</p><p>　　The defects may be of many different kinds; usually most are related

26、to the quality of the image. However, any characteristic which can be calculated may be assigned a target value and its departure from that target regarded as a defect. Some less elaborate programs utilize the third-orde

27、r (Seidel) aberrations; these provide a rapid and efficient way of adjusting a design. These cannot be regarded as optimizing the image quality, but they do work well in correcting ordinary lenses. Another type </p>

28、;<p>　　Characteristics which do not relate to image quality can also be controlled by the lens design program. Specific construction parameters, such as radii, thicknesses, spaces, and the like, as well as focal l

29、ength, working distance, magnification, numerical aperture, required clear apertures, etc., can be controlled. Some programs include such items in the merit function along with the image defects. There are two drawbacks

30、which somewhat offset the neat simplicity of this approach. One is that if</p><p>　　In any case, the merit function is a summation of suitably weighted defect items which, it is hoped, describes in a single

31、number the worth of the system. The smaller the value of the merit function, the better the lens. The numerical value of the merit depends on the construction of the optical system; it is a function of the construction p

32、arameters which are designated as variables. Without getting into the details of the mathematics involved, we can realize that the merit function is an n-dim</p><p>　　2.2 optimization</p><p>　　T

33、he lens design program typically operates this way: Each variable parameter is changed(one at a time) by a small increment whose size is chosen as a compromise between a large value(to get good numerical accuracy) and a

34、small value (to get the local differential). The change produced in every item in the merit function is calculated. The result is a matrix of the partial derivatives of the defect items with respect to the parameters. Si

35、nce there are usually many more defect items than variable </p><p>　　If the change are small, the nonlinearity will not ruin the process, and the solution, although an approximate one, will be an improvement

36、 on the starting design. Continued repetition of the process will eventually drive the design to the nearest local optimum. </p><p>　　One can visualize the situation by assuming that there are only two varia

37、ble parameters. Then the merit function space can be compared to a landscape where latitude and longitude correspond to the variables and the elevation represents the value of the merit function. Thus the starting lens d

38、esign is represented by a particular location in the landscape and the optimization routine will move the lens design downhill until a minimum elevation is found. Since there may be many depressions in the t</p>&

39、lt;p>　　2.3 Local Minima</p><p>　　Figure 2.1 shows a contour map of a hypothetical two-variable merit function, with three significant local minima at points A, B, and C; there are also three other minima

40、at D, E, and F. It is immediately apparent that if we begin an optimization at point Z, the minimum at point B is the only one which the routine can find. A start at Y on the ridge at the lower left will go to the minimu

41、m at C. </p><p>　　Figure 2.1 Topography of a hypothetical two-variable merit function, with three significant minima (A, B, C) and three trivial minima (D, E,F). The minimum to whi

42、ch a design program will go depends on the point at which the optimization process is started. Starting points X, Y, and Z each lead to a different design minimum; other starting point can lead to one of the trivial mini

43、ma. </p><p>　　However, a start at X, which is only a short distance away from Y, will find the best minimum of the three, at point A. If we had even a vague knowledge of the topography of the merit function,

44、 we could easily choose a starting point in the lower right quadrant of the map which would guarantee finding point A. Note also that a modest change in any of the three starting points could cause the program to stagnat

45、e in one of the trivial minima at D, E, or F. It is this sort of minimum from which one</p><p>　　The fact that the automatic design program is severely limited and can find only the nearest optimum emphasize

46、s the need for a knowledge of lens design, in order that one can select a starting design form which is close to a good optimum. This is the only way that an automatic program can systematically find a good design. If th

47、e program is started out near a poor local optimum, the result is a poor design.</p><p>　　The mathematics of the damped least-squares solution involves the inversion of a matrix. In spite of the damping acti

48、on, the process can be slowed or aborted by either of the following condition: (1) A variable which does not change (or which produce only a very small change in) the merit function items. (2) Two variable which have the

49、 same, nearly the same, or scaled effects on the items of the merit function. Fortunately, these conditions are rarely met exactly, and they can be easily avoided.</p><p>　　If the program settles into an uns

50、atisfactory optimum (such as those at D, E, and F in Fig.2.1) it can often be jolted out of it by manually introducing a significant change which is in the direction of a better design form. (Again, a knowledge of lens d

51、esigns is virtually a necessity.) Sometimes simply freezing a variable to a desirable form can be sufficient to force a move into a better neighborhood. The difficulty is that too big a change may cause rays to miss surf

52、aces or to encounter total</p><p>　　Another often-encountered problem is a design which persists in moving to an obviously undesirable form (when you know that there is a much better, very different one—the

53、one that you want). Freezing the form of one part of the lens for a few cycles of optimization will often allow the rest of the lens to settle into the neighborhood of the desired optimum. For example, if one were to try