First-Order Design and the y, y¯ Diagram

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Abstract
A new method is described for graphically representing the first-order layout of any optical system of axially symmetric refracting or reflecting surfaces. Such a system can be uniquely defined by the actual path of an arbitrary paraxial skew ray traversing it, provided the value of the Lagrange invariant is also known. This paper describes some interesting properties of the diagram obtained by projecting the ray onto the object plane. The diagram has proved to be a very useful aid in first-order design, particularly in systems where lens diameters and locations are severely constrained.

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