Showing papers on "Fresnel equations published in 1970"

The optimum angle of incidence for determining optical constants from reflectance measurements

Abstract: The shape of the boundary enclosing analytical solutions to the generalized Fresnel reflectance equations for n and k in terms of reflectances and angle of incidence has been investigated and the optimum angle of incidence for experimental measurement determined to be 74°. The distribution of reflectance values for fixed n and k for which the method is accurate to within ±0·05 has been deduced to be n<3·0 and k<3·2.

Analysis of Optical- and Inelastic-Electron-Scattering Data. III. Reflectance Data for Beryllium, Germanium, Antimony, and Bismuth

Abstract: A procedure is described for simultaneously fitting reflectance data obtained for various photon energies and angles of incidence using a simple physical model for e(ω), the complex frequency-dependent dielectric constant. The mutual consistency of the model and of the experimental data is tested, within the accuracy of each measurement. As an example of the technique, reflectance data in the vacuum ultraviolet obtained by Toots, Fowler, and Marton for Be, Ge, Sb, and Bi have been satisfactorily fitted. The model parameters have been used to derive the optical constants n and k (in satisfactory agreement with conventional determinations) and can be readily related to other relevant experimental results or theoretical calculations of e(ω) if these are available.

On using holograms for test glasses.

Abstract: Holograms have been made of test glass surfaces and later used in place of the test glass to evaluate optics. The reconstructed virtual image of the test glass surface is superimposed on the surface of the optic to be evaluated and the resulting interference rings interpreted with regard to power error and irregularity. This paper describes the technique used to produce and employ such holograms for both positive and negative surfaces.

Analysis of a thin circular loop antenna over a homogeneous earth

Abstract: In this paper, the current distribution on a bare conducting loop, situated in free space over a semi-infinite medium, is obtained for arbitrary time harmonic excitations. The loop is assumed to be thin, perfectly conducting and the standard one-dimensional integral equation and its Fourier series solution are used as the starting points. The field due to the current in the loop, where the semi-infinite medium is absent, is expressed as a superposition of plane waves. The tangential component of the field reflected by the interface, of the semi-infinite medium, is evaluated using appropriate Fresnel reflection coefficients. This reflected field serves as a new source for the loop and induces a current on the loop. The field due to the induced current is treated in the same manner, and this process is repeated indefinitely. The summation of the original current and all the induced currents gives the steady-state current on the loop.

Analysis of Multilayer Optical Filters Using Signal Flow Graph Techniques

Abstract: Multilayer optical filters are characterized by a signal flow graph. Standard feedback–network analysis techniques are modified to yield an iterative algorithm to compute the transmission of filters with any number of layers. The use of iteration results in an economical use of computer storage. The algorithm can take into account the frequency, polarization, and angle of incidence of the incident light wave as well as the index of refraction and thickness of each layer. Dispersion effects can be incorporated. Working programs have been developed for the IBM 1130 computer.

Estimation of refractive indices by a spectrophotometric method.

Abstract: This note is presented in amplification of a method recently proposed by one of us for the estimation of the refractive indices of transparent materials from measurements of spectral transmittance. Specifically, we wish to emphasize that the application of this method to samples exhibiting light scattering, particularly in the visible or near ir wavelengths, can lead to errors which may be serious in some cases. Although scattering may well be neg­ ligible for the application originally proposed, namely determining the ir refractive indices of many polymers, salts, and glasses used as substrates in this region of the spectrum, it can be quite signifi­ cant in certain samples. Unlike the effects of absorption, loss of transmittance due to scattering is not accounted for directly by the mathematical treatment in the paper cited. The partial diffusion of light flux can lead, of course, to a more complex reflection coefficient than that given by the Fresnel equation, and to loss of light by devia­ tion into directions outside the angle of acceptance of many spectrophotometers or even integrating-sphere instruments. The magnitude of these effects cannot be predicted in any way known to us, except for the limiting case of complete diffusion of light flux within the sample where most people, we feel, would realize that the method under discussion is inapplicable. In applying the spectrophotometric method for the calculation of the refractive index of a sample exhibiting scattering, it is wise to perform calculations first at longer wavelengths, subsequently working toward progressively shorter wavelengths. Computed indices (except through absorption bands) should show a rather uniform trend. As wavelengths are considered where scattering shows a pronounced effect upon the precision of the method, de­ viations in index will be noted (in the absence of absorption bands) greater than those attributable to measurement error. Typically, computed indices will oscillate about the true value with varying wavelength. When this activity is noted the method, of course, is no longer applicable. Refractive indices were quoted in Table I of Ref. 1 for several common plastics at random wavelengths. These were described as first approximations only. The possibility always exists that these might be quoted, out of context, as accurate values. We have found at least one of these values, that for Kel-F at 2.0 μ wavelength, to be in serious error owing to error in the reference used in calculating this value. Therefore, the author of Ref. 1 has carefully applied the spectrophotometric method to the calcu­ lation of indices at several wavelengths for three of the plastics tabulated earlier. The results of these calculations, which should