## An application of Berek's method to triplet design.

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http://hdl.handle.net/2144/11303##### Abstract

This thesis describes the investigation of Berekt's method of third order lens design as applied to the design of a flat field, photographic triplet. The fields of photographic triplets are usually flattened artificially by adjustment of the astigmatic image surfaces. This process results in degraded image definition in the zonal area of the film plane. The degree of degradation depends primarily upon the original curvature of the Petzval surface with which the astigmatic surfaces are intimately related. If the Petzval surface is steeply curved, then more degradation must be expected than if the Petzval surface is comparatively flat. Most photographic triplets have a Petzval surface whose radius
is between two and three times as long as the focal length. The ratio of these radii (called Petzval ratio) chosen for this project was 5.0, which is attained in the final thin lens solution. Use of the Berek basic equations is analyzed in detail. It is shown that with thirteen quantities involved in six equations, it is necessary to account for seven of them either as arbitrarily set values or as dependent variables, "leaving only
six true variables for the solution of the basic equations. This accounting is made; and each of the thirteen quantities is identified as an arbitrarily set quantity, a dependent variable, or a true variable. The six basic equations include expressions for focal length, Petzval sum, oblique (lateral) and axial color correction, distortion, and overall lens thickness. The distortion expression is based on the assumption that the diaphragm stop coincides with the second element in the thin lens system. Oblique and lateral color are to be set equal to zero. These two assumptions are justified on the basis of convenience and the lack of any valid method of assigning advantageous residuals.
The solution of the basic equations yields individual element powers, spacing, and the number ratio for the first and second elements.
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Thesis (M.A.)--Boston University