【正文】 個。 然而，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)?A 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。 事實上，自動設計程序是極其有限的。它對于鏡頭設計的需要能給出最近似的最優(yōu)結(jié)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(jié)果將是一個糟糕的設計。 阻尼最小二乘法會涉及到的 數(shù)學中的矩陣反轉(zhuǎn)。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。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。 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(zhuǎn)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，另一個則是非常夸張的彎月形透鏡的形式。通常避免這種情況的一種局部優(yōu)化技術(shù)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。 附件 2：外文原文 （復印件） Modern Lens Design the merit function What is usually referred to as automatic lens design is,of course,nothing of the sort. the puter programs which are so described are actually optimization programs 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 monly accepted terms in the discussions which follow. Broadly speaking ,the merit function can be described as a bination or function of calculated characteristics, which is intended to pletely describe, 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 image defects are evaluated for three locations in the field of view (unless the system covers a very large or a very small angular field). The squares of the defects are used so that a negative value of one defect does not offset a positive value of some other defect. The defects may be of many different kinds。 usually most are related 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 thirdorder (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 of merit function traces a large number of rays from an object point. The radial distance of the image plane intersection of the rat from the centroid of all the ray intersections is then the image defect. Thus the merit function is effectively the sum of the rootmeansquare(rms) spot sizes for several field angles. This type of merit function, while inefficient in that it requires many rays to be traced, has the advantage that it is both versatile many rays to be traced, has the advantage that it is both versatile and in some ways relatively foolproof. Some merit functions calculate the values of the classical aberrations, and convert (or weight) them into their equivalent wavefront deformations. (See Formulary Sec. F12 for the conversion factors for several mon aberrations.) This approach is very