Decomposition of the total wave aberration in generalized optical systems

TL;DR

The paper addresses decomposing the total wave aberration in generalized optical systems, including freeform elements, by introducing a numerical, surface-by-surface approach that segments the optical path along the chief ray. It defines surface contributions as wavefront changes between entrance reference spheres and further splits them into intrinsic, induced, and transfer components using multiple ray sets, independent of system symmetry. The method is combined with Zernike Fringe polynomials to analyze per-surface errors up to sixth order, and demonstrated on a two-surface configuration and a freeform-corrected mirror, revealing additive surface contributions and insights for optimization and tolerance analysis. This approach enables detailed surface-specific design feedback and robust analysis for complex, asymmetric optical designs, with practical relevance to freeform optics and high-precision imaging.

Abstract

The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the wave aberration function into field and pupil dependent coefficients is an analytical method used for that purpose. An alternative numerical approach utilizing data from the trace of multiple ray sets is proposed. The optical system is divided into segments of the optical path measured along the chief ray. Each segment covers one surface and the distance to the subsequent surface. Surface contributions represent the change of the wavefront that occurs due to propagation through individual segments. Further, the surface contributions are divided with respect to their phenomenological origin into intrinsic, induced and transfer components. Each component is determined from a separate set of rays. The proposed method does not place any constraints on the system geometry or the aperture shape. However, here we concentrate on near-circular apertures and specify the resulting wavefront error maps using an expansion into Zernike polynomials. Hence, for the first time additive surface Zernike contributions are obtained.

Figures (18)

• Figure 1: Locating the coordinate system of pupil vector (a) on the pupil plane and (b) on the pupil sphere oriented perpendicularly to the chief ray.
• Figure 2: Difference between exit pupil spheres (ExPSph) referred to the paraxial chief ray (PCR) and the real chief ray (RCR). In the latter case the information about the chief ray aberration $|\Delta H|$ is not present in the aberrated wavefront. The diameter of the paraxial exit pupil (ExP) is determined by the paraxial marginal ray (PMR).
• Figure 3: Preliminary trace of edge rays (ER) to determine the normalization aperture radius of the exit pupil sphere (ExPSph) located upon the real chief ray (RCR).
• Figure 4: Construction of intermediate image planes with trace of parabasal rays. (a) Location and orientation determined with trace of two arbitrary, orthogonally oriented pairs of rays PARy and PARx.(b) Orientation of local transverse axes determined with trace of parabasal ray in field PFRy launched from the tangential axis of the object plane.
• Figure 5: Alternative definition of surface contributions to the total wave aberration. Instead of dividing the system into subsystems bounded by intermediate pupils (EnP, stop, ExP) (blue color), surface contributions are defined as the segments of the optical path measured along the chief ray from the surface of interest until the subsequent surface (red color).