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where I0 is the irradiance of the incident wavefront and T is the transmittance If there is no absorption (nonmetallic coating), T % 1 R and there is a maximum value of I for R T 1=2 If one of the two mirrors has a higher re ectance than the other, for example if one of the them is a highly re ective mirror and the other is still uncoated, the intensity of one of the two interfering beams can be about 25 times higher than the other Under these conditions, the fringe contrast is greatly reduced A solution is to use a beam splitter with a different re ectivity Another possibility is to use both mirror without coating 221.



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Optical Path Difference Introduced by a Beam Splitter Plate We can show with a few algebraic steps and the law of refraction that a beam splitter or compensating plate shifts the optical axis laterally and parallel to itself by the following amount: " # cos y d t sin y 1 ; 2:2 n2 sin2 y 1=2 where y is the incidence angle, t is the plate thickness, and n is the refractive index The light going to the observer from mirror M1 has traversed the beam splitter only once, whereas the light from mirror M2 has gone through it three times An interferometer that has more glass in one arm than in the other, as in this case, is said to be uncompensated The interferometer can be compensated by inserting another piece of glass in front of mirror M1 as shown in Figures 21 and 22.





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The importance of compensating an interferometer is clearly seen in the following section Adjustable compensators for Williams con gurations (Steel, 1963) and Twyman Green con gurations (Connes, 1956; Mertz, 1959; Steel, 1962) have been described in the literature As pointed out before, an interferometer is said to be uncompensated when it has more glass in one of its arms than in the other, because (a) an optical component (lens or prism) is present in one arm in order to test it or (b) the light travels once through the beam splitter in one path and three times in the other path, and the compensating plate is absent Both of these situations can be included in a general case in which an inclined plane glass plate is placed in one of the arms The unfolded optical paths for both arms of the interferometer.

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The statement Em,n := E0 sin( n t) simulates an antenna that broadcasts a sinusoidal electromagnetic wave from the location x = m x (0, L) Of course, the antenna must be located in free space The FDTD algorithm is an explicit difference scheme, and so it may have stability problems However, it can be shown that the algorithm is stable provided we have x t 1 or t , (12123) e=c x c Thus, the CFL condition of Section 124 applies to the FDTD algorithm as well A justi cation of this claim appears in Ta ove [8] A MATLAB implementation of the FDTD algorithm may be found in Appendix 12A (see routine FDTDm) In this implementation we have introduced the parameters sx and st (0 < sx , st < 1) such that x (12.

124) t = st x = s x 0 , c Clearly, c t/ x = st , and so the CFL condition is met Also, spatial sampling is determined by x = sx 0 , which is some fraction of a free-space wavelength 0 [recall (1255)] Note that the algorithm simulates the eld for all t [0, T ], where T = N t If the wave is propagating only through free space, then the wave will travel a distance (12125) D = cT = N st sx 0 , that is, the distance traveled is N st sx free-space wavelengths Since L = Msx 0 (ie, the computational region spans Msx free-space wavelengths), this allows us to make a reasonable choice for N .

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A problem with the FDTD algorithm is that even if the computational region is only free-space, a wave launched from location x = m x (0, L) will eventually strike the boundaries at x = 0 and/or x = L, and so will be re ected back toward the source These re ections will cause very large errors in the estimates of H , and.

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