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Interference Filter

# Interference Filter - INTERFERENCE FILTERS An elementary...

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Unformatted text preview: INTERFERENCE FILTERS An elementary thin ﬁlm interference ﬁlter is shown in Fig. 1. The thin ﬁlm of refractive index n is sandwiched between slabs of higher refractive index n2. Fig. 1 Rays passing through thin ﬁlm interference ﬁlter. The operation of the interference ﬁlter may be described in terms of the rays shown in Fig. 1. An incident wave from the left-hand region is partially transmitted and partially reﬂected at the second surface. The reﬂected wave then propagates backwards and is reﬂected at the ﬁrst surface. After propagating again through the thin ﬁlm, it is trans- mitted into the right-hand region (2). where it then interferes with the ﬁrst transmitted wave (1). A 7r phase shift occurs at (O) and (3) shown in Fig. 1. The optical path length (0) —> (3) -——> (2) is given by (0PL)032 = 2n(PL)03 where (PL)03 is the physical path length from (0) to (3) and is (PL)03 = d/cosﬂ and so (OPL)032 = 2nd/cosﬁ. The optical path length (0) —* (1) is given by (0PL)01 = 712 sin a (PL)02, where (PL)02 is the physical path length from (0) to (2) and is (PL)02 = 2 dtanﬁ. and so (OPL)01 = 2 722 d sina tanﬁ. Using Snell’s law n2 sina = nsinﬁ, then (OPL)01 = 2 n d sinﬁ tanﬂ. The optical path difference between the output rays is 2 n d cosﬂ (OPD) = (0PL)032 -- (0PL)01 = — 2ndsinﬂtanﬁ 1 sin2,8 coszﬁ — 2nd<cosﬁ_ cosﬂ) — 2nd c033 — 2ndcos,8 Therefore the condition for maximum transmission is m A = 2 nd cos ﬂ maximum in transmission From this condition, it is seen that increasing B (by increasing the angle of incidence) decreases the wavelength transmitted. A schematic of a thin ﬁlm interference ﬁlter is shown in Fig. 2 and deﬁning char- acteristics in Figs. 3. Semireflecﬁve layers Dielectric Fig. 2 Schematic representation of a thin ﬁlm interference ﬁlter. x"Kl! Fig. 3 Characteristics of a ﬁlter: Amaz measured in run: Tm” measured in percent; and HW measured in nm. The separation of the metallic coatings, usually half a wavelength or a multiple thereof, determines the color of the light which the ﬁlter will transmit. Most of the light that is not transmitted is reﬂected. Thus damage due to overheating is rare. Maximum trans- mission for normal incidence occurs when 2nd = m A. Two types of color ﬁlters are compared in Table 1. Table 1. Typical Characteristics of Two Types of Color Filters Absorption Filter Interference Filter HW 50 nm 0.1 nm Tmaz 30% 90 % l0 l0 2 9 3 5 05 0.5 V) 2 <1 (I )— 0 .5 IO l5 0 [0 I5 2.0 '0 WAVELENGTH I.0 0.5 05 0 0.6 08 1.0 l2 0 8 9 IO II I? [3 Fig. 4 Transmission of typical evaporated interference ﬁlters plotted against wavelength in arbitrary units. Upper left: Short wavelength pass ﬁlter (note that dashed portion of curve must be blocked by another ﬁlter if low transmission at long wavelengths is nec- essary. Upper right: Long wavelength pass ﬁlter. Lower left: Band pass ﬁlter. Lower right: Narrow band pass (spike) ﬁlter. ...
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Interference Filter - INTERFERENCE FILTERS An elementary...

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