Fundamental-ray aberration analysis of off-axial optical systems: analytical formulae of first-order aberrations

In our previous paper [ Appl. Opt. 59 , 4466 ( 2020 ) 10.1364/AO.389600 ], we presented a fundamental-ray aberration analysis that extends ray matrix analysis to the third-order aberration region. The analysis results shown in that paper were applicable to coaxial rotationally symmetric optical systems. This time, we have extended the fundamental-ray aberration analysis so that it can be applied to off-axial optical systems. Here we present new analysis formulae for fundamental-ray aberration analysis of the first-order aberration region. In addition, we newly present first-order aberration expansion formulae for four-element fundamental-ray aberrations and calculation formulae for the fundamental-ray aberration coefficients of the first order, which are necessary for this extension.