Progressive addition lenses are prescribed to patients who need
correction for both far and near visions. A progressive lens needs to
have power that gradually changes from the far vision zone, used for
example in driving, and the near vision zone, used for example in
reading a map. The basics of optics and lens design will be
described. In particular, it will be shown that the problem can be
reduced to one of surface design. The surface design problem itself is
solved by a variational approach, which can be further simplified by
linearization, leading to a fourth order elliptic PDE. Numerical
results are presented to illustrate the process of lens design.
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