現(xiàn)代光學(xué)設(shè)計(jì)外文翻譯(參考版)
2025-01-20 02:40本頁面
【正文】 other starting point can lead to one of the trivial minima. 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, 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 stagnate in one of the trivial minima at D, E, or F. It is this sort of minimum from which one can escape by “jolting” the 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。 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。 it is a function of the construction parameters which are designated as variables. Without getting into the details of the mathematics involved, we can realize that the merit function is an ndimensional space, where n is the number of the variable constructional parameters in the optical system. The task of the design program is to find a location in this space(.,a lens prescription or a solution vector) which minimizes the size of the merit function. In general, for a lens of reasonable plexity there will be many such locations i
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