The wave aberration expressed as the power series of pupil coordinates is frequently used to evaluate the physical-optical image quality of an optical system. However, the relations between the expansion coefficients and the traditional eiconal-based aberration coefficients are not known exactly to the 6th-order of wave abberration. The purpose of this paper is to present an approach to derive exactly the relationship between these two kinds of coeffcients.
The starting point of this derivation is the Herzberger's 5th-order aberration theory. In the Herzberger's theory, the aberration coefficients are derived from the eiconal function which represents the optical path length along a ray initiated from an object point and terminated at an exit pupil point. In order to derive the wave aberration function, it is only necessary to add this eiconal function to the optical path length between the exit pupil and the center of reference sphere, and to remove the constant term.
Theoretically, the derivation process is rather simple, but the final results can only be obtained after some complicated transformations. An example showing the usefulness of these results is also presented.

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The general characters and the peculiarities of the lenses for producing the IC are described from the standpoint of lens design. An aspect is explained that the demand for the new lenses, with the extreme resolution to attain micron or submicron photographic line width, is coming into being in relation to the recent advance of microelectronics.
A lens was designed and produced for such a purpose, which was considered to provide the photographic resolution power of about 800 line pairs per one millimeter, or line width of about 0.6 micron, with the OTF of 50% over the image circle of diameter 4 millimeters for photoresist or emulsion. The progress of development and the result of design, and some of the problem in regard to the design process are described in this report.

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