%A Simone FIORI %T Averaging over the Lie group of optical systems transference matrices %0 Journal Article %D 0 %J Front. Electr. Electron. Eng. %J Frontiers of Electrical and Electronic Engineering %@ 2095-2732 %R 10.1007/s11460-010-0121-z %P 137-145 %V %N %U {https://journal.hep.com.cn/fee/EN/10.1007/s11460-010-0121-z %8 2011-03-05 %X

Motivated by recent studies in ophthalmology about the computation of the average character of a set of eyes, the present manuscript discusses an iterative approach to tackle the problem of computing the average matrix out of a set of optical-system-transference matrices. The manuscript recalls how the optical features of a human eye may be described in terms of a linear optical model. The paper also shows that the linear optical models form a Lie group under appropriate algebraic and geometric settings. An averaging algorithm that copes with Lie groups is recalled from the scientific literature and described. The present paper also recalls a previous non-iterative averaging rule by Harris [Harris W F. Ophthalmic and Physiological Optics, 2004, 24(6): 580-585]. Numerical results about the averaging of optical transference matrices suggest that Harris’ rule is nearly optimal, as Lie-group averaging iteration can improve Harris’ result only slightly.