TAILIEUCHUNG - OPTICAL IMAGING AND SPECTROSCOPY Phần 8

Tham khảo tài liệu 'optical imaging and spectroscopy phần 8', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | RESONANT SPECTROSCOPY 355 Figure A Fabry-Perot etalon consists of a pair of partially transmissive surfaces separated by a gap of thickness d. reflected by the first surface and partially transmitted into the cavity. Once in the cavity the wave experiences an infinite series of partial reflection and transmission events at each surface. As always we approach analysis of an optical element by first considering the modulation that the device induces on a coherent input field. An FP resonator does not produce a local modulation of the incident field like a transmission mask or a lens. Rather the output field is a shift-invariant linear transformation of the input field. As always shift invariance means that if the field on the input aperture is Eị x y then the field on the output aperture is Eo x y n h x - X ỷ - y n Ei x y n 9 45 The coherent transfer function h u v n corresponding to the shift-invariant impulse response is derived by considering the transmittance for the incident plane wave Eie2pi ux vy ei2pzy 1 À2 -u2-v2. Assuming that the plane wave transmittance at each interface is T and that the reflectance is r the wave transmitted by the etalon is Et u v T2eifMEi T2r2ei3f u v Ei T2r4ei5f u v Ei T2r6ei7f u v Ei t2 eif u v 1 _ r2e v 9 46 356 SPECTROSCOPY where the phase delay in propagating through the etalon is f u v 2pndp 1 Á2 u- v2 n is the index of refraction of the cavity dielectric. We find therefore that the transfer function between the field on the input aperture of an etalon and the output aperture is t2eif u v h u v ----------- 1 _ r2ei2f u v In deriving Eqn. we have neglected the fact that T and r also depend on u v . While it is not difficult to account for this dependence in numerical analysis our analytic discussion is simpler without it. If the surfaces of the etalon consist of metal films or high-permitivitty dielectrics then the u v dependence of T and r is relatively weak. The reflectivities of practical surfaces as well as .

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