【正文】 ogram is one which adjusts (optimizes) the damping factor, the factor is usually made quite small near an optimum, because the program is taking small steps and the situation looks quite linear。 when it is extended to a 10 or 20 dimension space, one can realize only that it is apt to be an extremely plex neighborhood. Local Minima Figure shows a contour map of a hypothetical twovariable merit function, with three significant local minima at points A, B, and C。 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 efficient as regards puting time, but requires careful design of the merit function. Still another type of merit function uses the variance of the wavefront to define the defect items. The merit function used in the various David Grey programs is of this type, and is certainly one of the best of the mercially available merit functions in producing a good balance of the aberrations. 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 length, 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 which somewhat offset the neat simplicity of this approach. One is that if the firstorder characteristics which are targeted are not initially close to the target values, the program may correct the image aberrations without controlling these firstorder characteristic。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。 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。 阻尼最小二乘法會涉及到的 數(shù)學中的矩陣反轉。 事實上，自動設計程序是極其有限的。 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。 圖 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）。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)，并且從該最小可唯一確定的值開始測定坐標。 人們可以想象只有兩個變量參數(shù)的情況。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。對評價函數(shù)產(chǎn)生變化的每一項進行計算。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。 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(zhì)量，這個數(shù)值是通過評價函數(shù)的缺陷項經(jīng)過加權求和計算出來的。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(zhì)量的處理效果。一些程序包括了隨圖像失真而變化的評價函數(shù)的項目。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)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)點也正是在于它追蹤了大量的光線，因此從某種意義上