【正文】 design, as described below. The fact that the automatic design program is severely limited and can find only the nearest optimum emphasizes 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 the program is started out near a poor local optimum, the result is a poor design. The mathematics of the damped leastsquares solution involves the inversion of a matrix. In spite of the damping action, 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 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. If the program settles into an unsatisfactory optimum (such as those at D, E, and F in ) 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 designs 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 surfaces or to encounter total internal reflection, and the optimization process may break down. Conversely, too small a change may not be sufficient to allow the design to escape from a poor local optimum. Also, one should remember that if the program 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。 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 r