Aberration analysis for freeform surface terms overlay on general decentered and tilted optical surfaces

Aberration theory helps designers to better understand the nature of imaging systems. However, the existing aberration theory of freeform surfaces has many limitations. For example, it only works in the special case when the central area of the freeform surface is used. In addition, the light footprint is limited to a circle, which does not match the case of an elliptical footprint for general systems. In this paper, aberrations generated by freeform surface term overlay on general decentered and tilted optical surfaces are analyzed. For the case when the off-Axis section of a freeform surface is used, the aberration equation for using stop and nonstop surfaces is discussed, and the aberrations generated by Zernike terms up to Z_17/18 are analyzed in detail. To solve the problem of the elliptical light footprint for tilted freeform surfaces, the scaled pupil vector is used in the aberration analysis. The mechanism of aberration transformation is discovered, and the aberrations generated by different Zernike terms in this case are calculated. Finally we proposed aberration equations for freeform terms on general decentered and tilted freeform surfaces. The research result given in this paper offers an important reference for optical designers and engineers, and it is of great importance in developing analytical methods for general freeform system design, tolerance analysis, and system assembly.