The Scatter Works (United States)

As the authoritative resource on optical scattering, this book was developed from many years of teaching light-scatter measurement and analysis courses to optical engineers. Dr. Stover covers scattering beginning with its basics and covering surface roughness calculations, measurements, instrumentation, predictions, specifications, and industrial applications. Also included are appendices that review the basics of wave propagation and Kirchhoff diffraction. Whether you're an optical engineer currently investigating roughness-induced haze in the semiconductor industry, or just entering the fiel

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In recent years paper have been published on the limitations of the Rayleigh Rice vector perturbation theory relating scattering (given by the bidirectional reflectance distribution function or BRDF) to surface roughness (given by the power spectral density function or PSD). In addition to the restrictions that the surface be optically smooth, clean and front surface reflective, the Rayleigh-Rice relationship has been criticized because calculations of the PSD from the BRDF often produce a high frequency (high scatter angle) peak. Variations in the wavelength and/or incident angle produce variations in the peak, so it is clear that the peak is not truly a part of the surface PSD. Recently a change was suggested to the expression that removes the peak. This paper presents data proving that the original expression is correct and implies that the peak is the result of scatter from non-topographic sources. In other words the surface is not clean, or is not front surface reflective.

For over three decades the Rayleigh Rice Perturbation Theory has been the method of choice for relating the surface power spectral density function (PSD) of smooth, clean, front surface reflectors to corresponding scatter patterns. This paper explores limitations with this traditional approach. In particular the annoying (anomalous) "hooks" at the high frequency (near grazing) end of a calculated PSD are investigated. In addition the smooth surface requirement is also probed for its limit. Experimental data involving different materials and wavelengths as well as variations in source polarization and incident angle are presented. The same data set is also used in a follow-on paper suggesting theoretical variations that may solve some of these issues.

Some of you are probably old enough (like me) to remember when polaroid sunglasses first became available. They were a sensation. Glare light is reduced by more than the background light with the result that you actually have better vision—not just less light in your eyes. They work best in situations where the sun is more or less in front of you and the combination of reflected light and near-specular scatter causes a bright glare that dominates your field of view. Because reflectance is a function polarization, the glare light (which has been reflected once) often has a horizontal polarization component that is much stronger than the vertical component. Normal background light (which has been reflected many times, at many angles) is more evenly divided between the two polarizations. Polaroid sunglasses simply discriminate against the horizontal component to reduce the fraction of glare light. If you look at the blue sky, which is a source of scattered light, through your sunglasses, you will find that rotating the glasses 90 degrees causes the sky to look dimmer (i.e., the sky has a strong vertical component). This effect is most strongly pronounced if you look in a direction perpendicular to the sun's rays. These two examples clearly demonstrate that scattering is polarization sensitive. When light is scattered, its polarization, as well as its amplitude and direction, is changed. The changes depend on the sample shape and material, as well as the polarization, amplitude, and direction of the incident beam. All three quantities must be considered to examine the effect of a sample on the reflected and transmitted light. A complete description of the polarization characteristics of an EM wave, before or after sample interaction, can be accomplished by straightforward measurements. Comparison of polarization amplitude and direction, before and after interaction with the sample, allows information about the sample material to be obtained. The trick is to relate the before-and-after changes to useful, or needed, sample characteristics. Chapters 3 and 4 discussed the relationship between smooth reflector topography and the resulting changes in the reflected light.