Second-order axial color of thin lenses in air

In present research, the influence of higher-order aberrations on the correction of secondary axial color is under investigation. Analytical solutions have so far been restricted to special cases and simple optical systems. Common theories require the tracing of rays of different wavelengths. Such numerical approaches do not support the comprehension of the underlying physical effects. In this paper, a formula for second-order axial color contributions is derived which is based on paraxial ray data for the reference wavelength only. Therefore, it allows the determination of second-order axial color in early paraxial design stages without further numerical ray trace. For systems of thin lenses in air, three second-order effects are identified and discussed using simple examples. A quantitative comparison with intrinsic secondary axial color is given.