tailieunhanh - Nonimaging Optics Winston Episode 5

Tham khảo tài liệu 'nonimaging optics winston episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Hamiltonian Formulation 109 Figure Flow lines with refractive components AA are a Lambertian source. The arrows indicate row lines the plain lines rays. are symmetrical transverse to the optic axis. As already noted in Section the étendue H generalizes to the difference of optical path lengths up to an overall constant . This remains true even in the presence of refractive media provided the optical path lengths are measured along rays. These rays need not be straight lines. Thus in Figure the étendue H from Lambertian source AA to section PP is proportional to I API - AP where the brackets indicate optical path lengths. It follows that the lines of flow indicated by arrows in the figure lie along contours of H constant. Since the detailed balance condition holds in 2D we may construct concentrators by placing mirrors along the flow lines. However it does not follow that the 3D construction obtained by rotating the 2D flow line about the optic axis will automatically satisfy detailed balance. Specific cases will have to be checked with respect to detailed balance before the usefulness of the 3D designs can be evaluated. HAMILTONIAN FORMULATION Introduction The principles of Geometrical Optics can be formulated in several ways all of them being equivalent in the sense that they can provide the same information. Nevertheless there are some particular problems for which one formulation is better than the others for example the problem is more easily stated and sometimes more easily solved using one of the formulations. This is common to disciplines having more than one mathematical model. Probably the most well-known formulation of Geometrical Optics is the variational one Fermat s principle . In Section we will see another well-known formulation the Hamiltonian equations. This formulation will be useful for stating and solving some nonimaging design problems both in 2D and 3D geometry with the Poisson Brackets method. This method

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