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| Radiometry: Optical invariants | Prev topic | Next topic Fig. 1 |
Let a pencil of radiation rays cross an interface between two uniform media with real refractive indices mS and mR, respectively, separated by a (locally) plane interface. Consider an elementary area, dApS, within a normal cross section of the pencil at the source be imaged at a receiving normal cross section to an elementary area dApR (Fig. 1). Solid angles dωS in the source medium, dωR in the receiving medium represent the imaging sub-pencil. Let us neglect reflection losses at the interface. This allows us to simplify the radiance law in non-uniform media as follows:
| dApS dωS mS 2 = dApR dωR mR 2 |
It follows that a product dAp dω m2 is a constant. This constant is referred to as an optical invariant or throughput (for example, Wyatt CL 1991, p. 36).
Note that the invariance of dAp dω m2 yields the invariance of product θhm of the marginal ray angle, θ, emitted from an object (or admitted at an image) of height h, in the optics of an axially symmetrical system in the paraxial approximation (θ << 1). This product is referred to as the Lagrange invariant. Indeed, in this approximation, one has:
| dω dAp m2 | ≈ πθ 2 πh2 m2 | |
| = π2 (θhm)2 | (2) |
Hence, the invariance of the left side of this equation implies the invariance of θhm.
| CITATION: Jonasz M. 2007. Radiometry: Optical invariants (www.tpdsci.com/Tpc/RdmOptInva.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 06-Mar-2009 Modified: 06-Mar-2008 Peer-reviewed: PENDING |
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