We have developed a new fundamental ray aberration analysis that extends conventional ray matrix analysis to the third-order region using a four-element fundamental ray vector. This analysis method can analyze the factors in the generation of the Seidel aberration coefficients by separating them into the transform characteristics of rays unique to the optical system and paraxial trace values representing the conjugate relationship. In establishing this analysis, we first introduce the fundamental ray aberration, and we present calculation formulae for the fundamental ray aberration coefficients of a co-axial rotationally symmetric optical system. Numerical examples employing these analysis results are shown, and it is confirmed that the causes of the Seidel aberration coefficients can be analyzed.
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