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Zoom lens design requires a very strong understanding of geometrical optics and how it directly relates to an optical system. Understanding both first-order optics and pupil conjugation is absolutely essential to ensure that a lens zooms correctly and avoids discontinuities. This tutorial paper explains these first-order considerations in detail and illustrates how to derive a starting configuration. The tutorial also shows how to proceed toward a final lens optimization.
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Richard N. Youngworth, Ellis I. Betensky, "Fundamental considerations for zoom lens design (tutorial)," Proc. SPIE 8488, Zoom Lenses IV, 848806 (19 October 2012); https://doi.org/10.1117/12.930618