## Abstract

The performance is reported of new optimization software that
maximizes the relative modulation transfer function (MTF) by
minimizing the merit function (1 minus the approximate relative
MTF). Contrary to the predictions of earlier studies, this merit
function, whose only variable part is the variance of the wave
aberration difference function, is shown to be effective for both
poorly and well-corrected systems. In addition, the new software is
significantly faster than our in-house software for the direct
optimization of the actual MTF.

© 1998 Optical Society of America

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### Equations (7)

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(1)
$$\mathrm{MF}=\sum _{i}{\left({\mathrm{\omega}}_{i}{g}_{i}\right)}^{2},$$
(2)
$$D\left(s,\mathrm{\psi}\right)=T\left(s,\mathrm{\psi}\right)expi\mathrm{\theta}\left(s,\mathrm{\psi}\right)=1/\mathrm{\pi}\int {\int}_{S}expi2\mathrm{\pi}\left[W\left(x,y\right)-W\left(x-scos\mathrm{\psi},y-ssin\mathrm{\psi}\right)\right]\mathrm{d}x\mathrm{d}y,$$
(3)
$${D}_{R}\left(s,\mathrm{\psi}\right)=D\left(s,\mathrm{\psi}\right)expi\mathrm{\theta}\left(s,\mathrm{\psi}\right)/{D}_{0}\left(s,\mathrm{\psi}\right)=M\left(s,\mathrm{\psi}\right)expi\mathrm{\theta}\left(s,\mathrm{\psi}\right),$$
(4)
$$M*\left(s,\mathrm{\psi}\right)=1-2{\mathrm{\pi}}^{2}{s}^{2}K\left(s,\mathrm{\psi}\right)\cong M\left(s,\mathrm{\psi}\right),$$
(5)
$$K\left(s,\mathrm{\psi}\right)=\left[1/S\left(s\right)\right]\int {\int}_{S}{V}^{2}\left(x,y;s,\mathrm{\psi}\right)\mathrm{d}x\mathrm{d}y-{\left\{\left[1/S\left(s\right)\right]\int {\int}_{S}V\left(x,y;s,\mathrm{\psi}\right)\mathrm{d}x\mathrm{d}y\right\}}^{2},$$
(6)
$$V\left(x,y;s,\mathrm{\psi}\right)=\left(1/S\right)\left[W\left(x,y\right)-W\left(x-scos\mathrm{\psi},y-ssin\mathrm{\psi}\right)\right].$$
(7)
$$K\left(s\right)=\sum _{i}\sum _{j}P\left(i,j;s\right){W}_{i}{W}_{j}.$$