現(xiàn)代光學(xué)設(shè)計(jì)外文翻譯

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

2、gt;　　學(xué) 號(hào)： </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(qǐng)將該封面與附件裝訂成冊(cè)。</p><p>　　附件1：外文資料翻譯譯文</p><p><b>　　現(xiàn)代光學(xué)設(shè)計(jì)</b></p><p><b>　　2.1評(píng)價(jià)函數(shù)</b></p><p>

4、;　　到底什么是大家所說(shuō)的自動(dòng)光學(xué)設(shè)計(jì)，當(dāng)然，自動(dòng)并不是指電腦能夠自己來(lái)完成設(shè)計(jì)。實(shí)際上它所描述的是使用計(jì)算機(jī)對(duì)光學(xué)系統(tǒng)進(jìn)行優(yōu)化的程序，并通過(guò)評(píng)價(jià)函數(shù)（它不是一個(gè)真正的優(yōu)化函數(shù)，實(shí)際上是一個(gè)缺陷函數(shù)）定義的優(yōu)化方案。不管前面的免責(zé)聲明，我們將在下面的討論中使用被大家普遍接受的術(shù)語(yǔ)。</p><p>　　從廣義上說(shuō)，評(píng)價(jià)函數(shù)可以描述為計(jì)算特性，其目的是用一個(gè)單純的數(shù)字來(lái)完整地描述一個(gè)給定的透鏡的質(zhì)量或者功能。這顯然

5、是一個(gè)極其困難的事情。典型的評(píng)價(jià)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(guò)視場(chǎng)中的三個(gè)位置參數(shù)來(lái)進(jìn)行評(píng)價(jià)（除非該系統(tǒng)包括一個(gè)非常大或非常小的視場(chǎng)角）。使用缺陷的平方來(lái)計(jì)算可以確保一個(gè)負(fù)值的缺陷不會(huì)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(zhì)量。任何可以被計(jì)算的光學(xué)特性都會(huì)被分配一個(gè)目標(biāo)值，然而，當(dāng)實(shí)際值偏離這一目標(biāo)值時(shí)該特性被視為存在缺陷。一

6、些不太復(fù)雜的程序利用三階（賽德?tīng)枺┫癫顏?lái)計(jì)算缺陷；這提供了一種快速而有效的方式來(lái)調(diào)整設(shè)計(jì)。這種方法雖然沒(méi)有真正優(yōu)化圖像質(zhì)量，但他們?cè)谄胀ㄧR頭的糾正上有很好地效果。另一種類型的評(píng)價(jià)函數(shù)的原理是追跡從一個(gè)對(duì)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(diǎn)的徑向距離視作圖像缺陷。因此，評(píng)價(jià)函數(shù)是光斑在幾個(gè)視場(chǎng)角的有效尺寸總和的均方根（RMS）。這種類型的評(píng)價(jià)函數(shù)的效率較為低下，因?yàn)樗枰粉E大量的光線，但它所具有的優(yōu)點(diǎn)也正是在于它

7、追蹤了大量的光線，因此從某種意義上說(shuō)它所包含的數(shù)據(jù)量很大，對(duì)于光線的反映十分的完整全面。還有一種評(píng)價(jià)函數(shù)，它計(jì)算出古典像差的值，并將其轉(zhuǎn)換（或計(jì)算）成等效的波振面的形變。（幾種常見(jiàn)的像差轉(zhuǎn)換系數(shù)見(jiàn)附錄F- 12第二段 ）。這種方式非常有效，它的優(yōu)點(diǎn)是節(jié)省了計(jì)算時(shí)間，優(yōu)化設(shè)計(jì)的功能更好。還有一種類型的評(píng)價(jià)函數(shù)的使用波陣面的方差來(lái)定義的缺陷項(xiàng)。這種類型的評(píng)價(jià)函數(shù)中使用各種“大衛(wèi)灰色”程序，當(dāng)然這是</p><p>　

8、　凡涉及到圖像質(zhì)量的特性都可以通過(guò)鏡頭設(shè)計(jì)程序控制。具體的結(jié)構(gòu)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(píng)價(jià)函數(shù)的項(xiàng)目。但是有兩個(gè)缺點(diǎn)在一定程度上抵消了這種方法所帶來(lái)的簡(jiǎn)便性。一個(gè)是，如果最初選定的計(jì)算對(duì)象的一階特性不足夠接近目標(biāo)值，所述程序在校正圖像畸變的時(shí)候?qū)⒉荒芸刂七@些一階特性，其結(jié)果可能是，例如，一個(gè)有著錯(cuò)誤的焦距或數(shù)值孔徑的透鏡會(huì)被認(rèn)為已經(jīng)被校正了

9、。程序往往認(rèn)為這是一個(gè)局部最優(yōu)的方案而且不能解決掉這個(gè)錯(cuò)誤。另一個(gè)缺點(diǎn)是，在評(píng)價(jià)函數(shù)中包含的各個(gè)項(xiàng)會(huì)帶來(lái)減緩我們改善圖像質(zhì)量的處理效果。一種替代的方法是使用評(píng)價(jià)函數(shù)之外的約束系統(tǒng)。還要注意的是程序中有很多項(xiàng)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(lái)得到所需的射線斜率或高度。</p><p>　　通常情況下,評(píng)價(jià)函數(shù)用一個(gè)單純的數(shù)值來(lái)表示系統(tǒng)的質(zhì)量，這個(gè)數(shù)值是通過(guò)評(píng)價(jià)函數(shù)的缺陷項(xiàng)經(jīng)

10、過(guò)加權(quán)求和計(jì)算出來(lái)的。評(píng)價(jià)函數(shù)的值越小，鏡頭越好。評(píng)價(jià)函數(shù)的數(shù)值取決于光學(xué)系統(tǒng)的建設(shè)，即函數(shù)的變量是光學(xué)系統(tǒng)的結(jié)構(gòu)參數(shù)。不考慮所涉及的數(shù)學(xué)細(xì)節(jié)，我們可以意識(shí)到評(píng)價(jià)函數(shù)是一個(gè)n維空間，其中n是在光學(xué)系統(tǒng)中的可變結(jié)構(gòu)參數(shù)的數(shù)目。設(shè)計(jì)方案的任務(wù)是找到一個(gè)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(gè)具有合理復(fù)雜性的鏡頭在典型的價(jià)值函數(shù)空間內(nèi)會(huì)有很多這樣的位置。自動(dòng)設(shè)計(jì)程序?qū)⑹圭R頭的設(shè)計(jì)趨向于最接近的、最

11、簡(jiǎn)單的評(píng)價(jià)函數(shù)。</p><p><b>　　2.2優(yōu)化 　　</b></p><p>　　鏡頭設(shè)計(jì)程序通常這樣操作：每個(gè)變量參數(shù)變化(每次一個(gè))的增量大小是選擇一個(gè)較大的值(以獲得良好的數(shù)值精度)和一個(gè)較小的值(獲得本地微分)之間的值。對(duì)評(píng)價(jià)函數(shù)產(chǎn)生變化的每一項(xiàng)進(jìn)行計(jì)算。結(jié)果是一個(gè)相對(duì)于該參數(shù)的缺陷項(xiàng)的偏導(dǎo)數(shù)的矩陣。因?yàn)橥ǔ?shù)可變，所以會(huì)有許多項(xiàng)缺陷變量，針對(duì)這個(gè)

12、問(wèn)題可以用經(jīng)典的最小二乘法來(lái)解決。它的基礎(chǔ)假設(shè)是，缺陷項(xiàng)目和變量參數(shù)之間的關(guān)系是線性的。然而在實(shí)際條件下這通常是一個(gè)錯(cuò)誤的假設(shè)，一個(gè)普通的最小二乘法的計(jì)算結(jié)果往往會(huì)是一種無(wú)法實(shí)現(xiàn)的鏡頭或一個(gè)可能比開(kāi)始設(shè)計(jì)更糟的鏡頭。針對(duì)這一情況可以使用阻尼最小二乘解，這實(shí)際上是增加了對(duì)于評(píng)價(jià)函數(shù)的參數(shù)進(jìn)行加權(quán)平方這一計(jì)算，從而嚴(yán)格控制任何大的變化，因此限制了結(jié)果大小變化。斯賓塞對(duì)這一過(guò)程在“靈活的自動(dòng)鏡頭校正程序”一文中進(jìn)行了數(shù)學(xué)描述，該文發(fā)表在應(yīng)用光

13、學(xué),第二卷,1963年,1257 - 1264頁(yè),史密斯,W.德里斯科爾(主編),光學(xué)手冊(cè),麥格勞-希爾,紐約,1978年。</p><p>　　如果優(yōu)化結(jié)果的變化很小，非線性計(jì)算不會(huì)破壞過(guò)程以及結(jié)果，盡管是一個(gè)近似的結(jié)果，但程序?qū)τ谠O(shè)計(jì)上的優(yōu)化計(jì)算將開(kāi)始不斷重復(fù)，直到最終使設(shè)計(jì)達(dá)到最近似的局部最優(yōu)解。</p><p>　　人們可以想象只有兩個(gè)變量參數(shù)的情況。然后可以把評(píng)價(jià)函數(shù)的空間比作一

14、個(gè)地形圖，其中緯度和經(jīng)度相對(duì)應(yīng)的變量和仰角代表評(píng)價(jià)函數(shù)的值。因此，鏡片設(shè)計(jì)是在一個(gè)特定的初始位置，在設(shè)計(jì)中橫向?qū)⑼哥R移動(dòng)到最小值的優(yōu)化過(guò)程就像在下坡的過(guò)程中找到海拔最低的點(diǎn)。由于在下坡的過(guò)程中可能有許多凹陷的地形，一個(gè)凹陷里的最低點(diǎn)的未必是整個(gè)地形中的最低點(diǎn)，它是一個(gè)局部最優(yōu)但不能保證（除非在非常簡(jiǎn)單的系統(tǒng)）我們已經(jīng)找到了全局最優(yōu)的評(píng)價(jià)函數(shù)。這個(gè)簡(jiǎn)單的地形比喻有助于我們理解優(yōu)化過(guò)程的主要目標(biāo)：程序找到最接近的最小的評(píng)價(jià)函數(shù)，并且從該最小

15、可唯一確定的值開(kāi)始測(cè)定坐標(biāo)。景觀比喻是很容易為人類的頭腦去理解，當(dāng)它被擴(kuò)展為10 - 或20 - 維空間，想要實(shí)現(xiàn)去逼近它是及其復(fù)雜的。</p><p><b>　　2.3局部極小</b></p><p>　　圖2.1表示了將一個(gè)兩變量評(píng)價(jià)函數(shù)想象成的一個(gè)等高線地形圖，用點(diǎn)A，B和C表示三個(gè)顯著的局部最小值，還有其他三個(gè)極小的D，E和F是顯而易見(jiàn)的，如果我們?cè)赯點(diǎn)開(kāi)始

16、優(yōu)化，B是唯一一個(gè)程序可以找到的最小點(diǎn)。若換做Y點(diǎn)開(kāi)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(gè)兩變量評(píng)價(jià)函數(shù)，有三個(gè)主要極小值（A，B，C）和三個(gè)相對(duì)較不重要的極小值（D，E，F(xiàn)）。其中一個(gè)設(shè)計(jì)方案將最低的點(diǎn)設(shè)為該優(yōu)化過(guò)程開(kāi)始的基準(zhǔn)點(diǎn)?；鶞?zhǔn)點(diǎn)X，Y和Z的不同分別導(dǎo)致了設(shè)計(jì)最小點(diǎn)的不同;其它起點(diǎn)會(huì)導(dǎo)致最小點(diǎn)變?yōu)橄鄬?duì)不重要的點(diǎn)中的一個(gè)。</p><p>　　然而，

17、初始點(diǎn)換做X的時(shí)候，雖然它距離Y只有很短的距離，但是極小值會(huì)變?yōu)锳點(diǎn)。通過(guò)這個(gè)比喻就算我們對(duì)于評(píng)價(jià)函數(shù)只有一點(diǎn)模糊的知識(shí)，我們也可以很容易地把起點(diǎn)選在地圖的右下象限來(lái)保證最小點(diǎn)在A點(diǎn)處。另外還要注意的是任何三個(gè)出發(fā)點(diǎn)一點(diǎn)小的改變就可能導(dǎo)致程序在極小值的D，E或F中的一個(gè)停滯不前。為了在尋找最小值的過(guò)程中可以從這些極小值中“震蕩”逸出，設(shè)計(jì)如下所述。</p><p>　　事實(shí)上，自動(dòng)設(shè)計(jì)程序是極其有限的。它對(duì)于鏡頭

18、設(shè)計(jì)的需要能給出最近似的最優(yōu)結(jié)果，但是這需要在一開(kāi)始人為的選擇一個(gè)接近最優(yōu)的設(shè)計(jì)形式。這是一個(gè)自動(dòng)程序可以設(shè)計(jì)一個(gè)良好系統(tǒng)的唯一途徑。如果程序在一個(gè)局部凹陷的附近開(kāi)始優(yōu)化，其結(jié)果將是一個(gè)糟糕的設(shè)計(jì)。</p><p>　　阻尼最小二乘法會(huì)涉及到的數(shù)學(xué)中的矩陣反轉(zhuǎn)。盡管存在阻尼作用，這個(gè)過(guò)程會(huì)通過(guò)下列條件減緩或中止：(1)評(píng)價(jià)函數(shù)中的一個(gè)變量不改變(或僅產(chǎn)生很小的變化)。(2)兩個(gè)變量具有相同的或者幾乎相同的縮放效果

19、。幸運(yùn)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(gè)經(jīng)常遇到的問(wèn)題是一個(gè)設(shè)計(jì)會(huì)持續(xù)陷入到一個(gè)明顯的不良形式（當(dāng)你知道有一個(gè)更好的，非常不同的，你想要的一個(gè)）設(shè)計(jì)中。通過(guò)固定透鏡中一項(xiàng)參數(shù)不變，再進(jìn)行幾個(gè)周期的反復(fù)優(yōu)化的的方法通常會(huì)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(gè)人試圖把一個(gè)庫(kù)克三片式鏡頭轉(zhuǎn)換為前端頂部分離的形式，這個(gè)過(guò)程可能會(huì)產(chǎn)生兩種情況，一個(gè)

20、形狀類似于在鏡頭前面出現(xiàn)了一個(gè)狹窄的空氣層間隔，另一個(gè)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?jī)?yōu)化技術(shù)是將所述第二表面固定到一個(gè)平面上再進(jìn)行幾個(gè)周期的優(yōu)化來(lái)確定前端元件的平凸形狀。當(dāng)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(fù)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