Decomposition of the total wave aberration in generalized optical systems

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.

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

“…The expansion of the wave aberration function into the field-and pupil-dependent coefficients is an analytical method used for that purpose; see Section 2.1. In the following chapter, an alternative numerical method utilizing data from the trace of multiple ray sets is described [48]. Surface contributions are divided with respect to their phenomenological origin into intrinsic, induced and transfer components.…”

It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations

“…The wavefront and ray aberrations of axis-symmetrical systems have attracted significant attention in the literature [1][2][3][4][5][6][7][8][9][10][11][12]. The usual equation for decomposing the monochromatic wavefront aberration 0 W (h , , )   into different orders and components is given as (e.g., Eq.…”

The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems

“…Aberrations result in significant blurring or distortion of the image.Consequently, effective methods for quantifying their effects during the optical design stage are of paramount importance. The literature contains many approaches for determining the Seidel primary aberration coefficients[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. One of the most widely used methods in optical software (e.g., Zemax[6]) is that proposed by Buchdahl[8].…”