Compact folded imaging systems often require freeform surfaces to correct astigmatic and other off-axis aberrations. However, aberration theory for non-rotational symmetric systems is quite complex and it is especially hard to quantify individual surface aberration contributions. In this paper we develop a matrix method based on the propagation of a differential ray pair, which allows determining the aberration contribution of each individual surface for any ray. We can mathematically prove that the sum of the aberrations is identical to the exact ray-tracing result at the image plane. A head-mounted display lens is employed for testing and verification of this method. As will be shown, the method proves to be a universal tool for aberration calculations within freeform system.
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