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In case of the optical camera system with an infinite object distance, optical designs different from previous systems are required to speed up the auto-focus. As the number of lens groups is increased due to this, the conventional analytic method found it difficult to calculate the locus, and even the one-step advanced calculation method also had the trouble of taking a lot of time. In this paper, we suggested an analytic method for calculating the zoom loci by analyzing movement of one or two groups for situations corresponding to the given back focal length and effective focal length after taking a spline interpolation for each lens group. With this method, we would not only calculate the analytic zoom loci without iterations in every optical system without placing a limit on the group number at the zoom lens systems with the infinite object distance, but we would also show the utilities of this method through many examples.

We investigate the properties of the moiré fringes of matched radial-parallel (MRP) gratings that are useful for the fine visual indication of angular displacements. Moiré patterns formed by overlapping two different MRP gratings of angular pitches, P(theta) and P(theta)? (