Lens Designing by Electronic Digital Computer: I

The Calculation of the Optical Transfer Function Using Gaussian Quadrature

“…Similar considerations apply in the tangential case, for which it can easily be shown that D(s)=A f f exp {ik(W(x+s/2, y)-W(x-s/2, y))} dx dy (12) In both of these cases, then, the integration only needs to be performed over onehalf of the area, so that the new area of integration is as shown in figure 5 (a), for the sagittal case, and figure 5 (b) for the tangential case . …”

“…. ., b lo can be calculated once, for a given spatial frequency, and it is then possible to calculate the integrand in equation (15) by calculating a total of 17 terms, which is to be compared with the 60 terms that have to be calculated if the integrand of equation (12) were calculated twice . Further simplification is possible, however, because the integration is actually carried out as a pair of single integrals, using equations (5) and (16) or (7) and (8), and in each case either x or y is constant for the inner integral .…”

<title>Optimization of the Cooke triplet with various evolution strategies and damped least squares</title>

“…It was introduced into optics by Rosen and Eldert [7], Merion [8,9], Wynne [10] and others. Damped least squares optimization evolved after a period of intensive research and experimentation in late 1950s and mid 1960s.…”

Determination of Initial Variable Derivative Increments Using Genetic Algorithm in Damped Least-Squares Automatic Lens Design Problem

“…Lens design is formulated as a minimization problem of a merit function; ip (X)=F(X)TF(X) , (1) where F(X)~R" means performance functions and XE R" denotes variables. The superscript T means matrix transposition.…”