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Tham khảo tài liệu 'nonimaging optics winston episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5.6 The CPC Designed for Skew Rays 79 Figure 5.11 Transmission-angle curves for concentrators designed for nonzero skew invariant h. All the concentrators have exit apertures of diameter unity. double-arrowed segment AB rotated around the axis so that A reaches D. Thus the segment reflected from D touches the circle of radius h sin di. We can show that this segment meets the exit aperture at the same point C as the segment BC reflected at B by calculating the angles subtended at the center by the various ray segments the proof is given in Appendix C. The design is completed by requiring that all rays that leave the exit aperture at its rim shall have entered at the input angle di. These rays in the projection of Figure 5.10 are typified by the three-arrowed segments that is reflection at some point E along the concentrator to emerge at F on the exit rim. It turns out that the rays do not in general emerge at the same point on the exit rim. Thus we have a situation where the edge-ray principle is less restrictive than say a requirement for imaging at the exit rim. This process completely determines the concentrator as a surface of revolution but it does not seem to be possible to represent it by any analytical expression. We show in Appendix C how the differential equation of the surface which is first-order nonlinear is obtained. But it can only be solved numerically. P. Greenman computed the solution for several values of the input angle di and skew invariant h. The results are briefly that the shapes are very similar to those of the basic CPC for the same di but that the overall lengths are less and the transitions in the transmission-angle curves are correspondingly more gradual. Figure 5.11 shows some of these curves. The overall length of this concentrator is determined as for the basic CPC by the extreme rays as in Figure 5.12. This figure shows the rays aDC and aBC of Figure 5.10 both inclined at the extreme input angle to the axis and both grazing the exit
