tailieunhanh - Nonimaging Optics Winston Episode 2

Tham khảo tài liệu 'nonimaging optics winston episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-r mi T 1TÍÍ1 1 . T T . 1 The Generalized Etendue or Lagrange Invariant 19 Figure The étendue for a multielement optical system with an internal aperture stop. Figure The generalized étendue. from obvious geometrical considerations d cannot exceed p 2 this suggests p 2ớ 2 as a theoretical upper limit to the concentration. Unfortunately this argument is invalid because the étendue as we have defined it is essentially a paraxial quantity. Thus it is not necessarily an invariant for angles as large as p 2. In fact the effect of aberrations in the optical system is to ensure that the paraxial étendue is not an invariant outside the paraxial region so that we have not found the correct upper limit to the concentration. There is as it turns out a suitable generalization of the étendue to rays at finite angles to the axis and we will now explain this. The concept has been known for some time but it has not been used to any extent in classical optical design so it is not described in many texts. It applies to optical systems of any or no symmetry and of any structure refracting reflecting or with continuously varying refractive index. Let the system be bounded by homogeneous media of refractive indices n and n as in Figure and suppose we have a ray traced exactly between the points P and P in the respective input and output media. We wish to consider the effect of small displacements of P and of small changes in direction of the ray segment through P on the emergent ray so that these changes define a beam of rays of a certain cross section and angular extent. In order to do this we set up a Cartesian coordinate system Oxyz in the input medium and another O x y z in the output 20 Chapter 2 Some Basic Ideas in Geometrical Optics dM Figure The generalized étendue in the y section. medium. The positions of the origins of these coordinate systems and the directions of their axes are quite arbitrary with respect to each other to the directions of the ray

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