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【正文】 n a typical merit function space. The automatic design program will simply drive the lens design to the nearest minimum in the merit function. optimization The 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 promise between a large value(to get good numerical accuracy) and a 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. Since there are usually many more defect items than variable parameters, the solution is a classical leastsquares solution. It is based oon the assumption that the relationships between the defect items and the variable parameters are linear. Since this is usually a false assumption, an ordinary leastsquares solution will often produce an unrealizable lens or one which may in fact be worse than the starting design. The damped leastsquares solution, in effect, adds the weighted squares of the parameter changes to the merit function, heavily penalizing any large changes and thus limiting the size of the changes in the solution. The mathematics of this process are described in Spencer, “A Flexible Automatic Lens Correction Program,” Applied Optics, , 1963, pp. 12571264, and by Smith in (ed.), Handbook of Optics, McGrawHill, New York, 1978. If the change are small, the nonlinearity will not ruin the process, and the solution, although an approximate one, will be an improvement on the starting design. Continued repetition of the process will eventually drive the design to the nearest local optimum. One can visualize the situation by assuming that there are only two variable parameters. Then the merit function space can be pared 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 design 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 terrain of the landscape, this optimum may not be the best there is。 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.) Thi
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