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Chapter 11:
Seidel and the Pegel Diagrams
11.1 Introduction In 1856, Ludwig von Seidel published his famous formulae for the primary aberrations. They are based on the truncation of the series expansion for the sine of an angle to sinx≅x−x 3 ∕6 . That is why these calculations are also referred to as third-order aberration calculations. This method has been applied in evaluating the performance of the presented examples in the previous chapters. Besides providing relatively quick answers, one additional important feature of these calculations is that they point out the individual surface aberration contributions. This, in turn, indicates the sensitivity to radii, thickness, and spacing tolerances. The desire is to have the “work” equally divided among the surfaces; meaning one likes to avoid wild swings between under correction and overcorrection from surface to surface. While the sheer numbers of these surface contributions give the full information, a graphic depiction, which is called a Pegel diagram, is even more telling (Pegel is the German word for level). Another name for this form of representation may be “aberration distribution diagram.” Of course, the ideal case would be if all surfaces would be free of aberrations. Since this is not the case, aberration balancing rather than aberration correction more accurately describes the effort to improve the image quality. 11.2 Triplet for the LWIR Region We shall demonstrate aberration balancing by analyzing a triplet with a cold stop for the LWIR. The layout of the objective is shown in Fig. 11.1.
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