Fermat’s Principle and Third-Order Aberrations

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Starting from Fermat’s principle, Hamilton introduced characteristic functions for analyzing the behavior of rays in a general optical system (see [17]). Subsequently, Seidel [18] and Schwarzschild [19] defined a new characteristic function termed Schwarzschild’s eikonal. This is related to the Hamiltonian angle characteristic, but it depends on the use of suitable nondimensional variables. Using this function, the authors succeeded in developing a complete analysis, with evident geometrical meaning, of the third-order monochromatic aberrations of a compound optical system with a symmetry of revolution about the optical axis.


Optical System Optical Path Length Object Point Spherical Aberration Gaussian Image 
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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università degli Studi di Napoli “Federico II”NapoliItaly

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