Transformation equation from wavefront aberrations to ray aberrations based on coordinate frames in object space

Object and image spaces are widely used in geometrical optics to describe the functions of optical systems. However, the mapping between these two spaces is non-linear, meaning that a function expressed in coordinate frames in the image space cannot be directly applied in the object space, and vice versa. For example, the relationship between the wavefront and ray aberrations given by Rayces J. (1964) Opt. Acta 11, 85-88. https://doi.org/10.1080/713817854 is valid for coordinate frames in the image space but fails for coordinate frames in the object space. To overcome this limitation, this study converts the wavefront-ray aberration relationship using the chain rule so that it can also be applied to coordinate frames in the object space. The numerical results obtained for the primary ray aberrations using the proposed converted relationship are shown to be in close agreement with the Zemax simulation results.