Sky colors, rainbows, and halos are simulated using models that include light scattered as it passes through clear air and clouds of finite optical depth.
Vivid rainbows, ice crystal halos, coronas, iridescence, glories, mirages, sky colors, and crepuscular rays have always inspired awe and wonder. This makes simulating atmospheric optical phenomena both a scientific and aesthetic undertaking.(ProQuest: ... denotes formulae omitted.)Buying OnlineMuch simpler approximations to scattering can reproduce many of the principal features of most optical phenomena. Thus, for example, many features of rainbows and halos are explained by using the geometric optics of reflection and refraction as an approximation to scattering by spherical (or near spherical) raindrops and by simple hexagonal ice crystal prisms. In a similar manner, many features of coronas can be described using the Fresnel-Kirchhoff formula for diffraction as an approximation to light scattered by cloud droplets (Fowles 1989). Similarly, some features of sky color are explained by the simple theory first derived by Rayleigh to express light scattered by particles much smaller than the wavelength of light, such as air molecules, and by Mie theory to represent scattering by aerosol particles, even though most aerosol particles are neither homogeneous nor spherical.About Cooper Wiring DevicesIt's an understatement to say that cellular phones are ubiquitous. Whether you're on the subway, in a bookstore, or driving in a car, chances are good that you are either talking on a cell phone or overhearing another person's conversation. Now that we're always in touch, accessories like a Bluetooth headset are almost a necessity. Wireless connectivity is safer and more convenient, and a Bluetooth headset is like a fashion accessory.Cooper Lighting, a subsidiary of Cooper Industries (NYSE:CBE), is the leading provider of innovative, high quality lighting fixtures and related products to worldwide commercial, industrial, residential and utility markets. For more information, visit www.cooperlighting.com.The color and radiance of atmospheric optical phenomena, therefore, depend on the optical depth of the cloud and/or clear air and must be treated as problems in radiative transfer. A robust theory of atmospheric optical phenomena must include the role of multiple scattering of light. This article is, therefore, designed to develop simple radiative transfer models that show how the radiance and color of atmospheric optical phenomena depend on the optical depth of the cloud and clear air (Meyer 1929; Minnaert 1993). This approach is routinely taken in climate modeling (Lacis and Hansen 1974), remote sensing (Menzel et al. 1998), and models of skylight and color (Adams et al. 1974; Gedzelman 1975; Bohren and Fraser 1985; Gedzelman 2005), but not often in modeling rainbows, halos, coronas, and glories (Gedzelman 1980; Tränkle and Greenler 1987; Gedzelman 2003; Gedzelman and Lock 2003).GPS ReceiversAbout Cooper LightingWhen the angular distribution of radiance varies with particle size, shape, and orientation, it is necessary to integrate over all of the illuminated particles. Recent models of coronas, glories, and rainbows include the drop size distribution (Lock and Yang 1991; Cowley et al. 2005) and size-dependent flattening of drops (Fraser 1983), while models of complex halo displays include a number of ice crystal shapes and orientations (Greenler 1980). Even so, these theories still essentially treat light as if it were scattered once by a single "integrated" particle.Any rigorous theory involving multiple scattering is complex and cumbersome, but a model that treats atmospheric optical phenomena as beams of singly scattered sunlight that are depleted by a second scattering on their way to the observer provides a simple first-order approximation for two reasons. First, the brightest rainbows, halos, coronas, and glories are produced when the optical thickness of the light path through the atmosphere and/or cloud is small, so that relatively little light is scattered more than once. Second, rainbows, halos, coronas, and glories involve light scattering from particles with pronounced peaks of radiance in certain directions and hence are much brighter than multiply scattered light, which spreads more uniformly around the sky. When modeling these phenomena, we use simple, approximate expressions for multiply scattered background light. As a result, the theory developed here is simple enough and the resulting simulations are convincing enough to be presented in courses that treat atmospheric optics.About Cooper Industries
Colors of the sun and moon. The brightness and color of sunlight and moonlight constitute the simplest applications of radiative transfer theory for optical phenomena. Sunlight and moonlight dim and redden as they approach the horizon because they must pass through much more air to reach an observer (Fig. 1), and because shortwaves are scattered more efficiently than longwaves by air molecules and by most aerosol particles. Under typical conditions for an observer at sea level, a horizontal sunbeam must pass through about 38 times as much air as a vertical sunbeam, and the gradient of optical thickness is so large just above the horizon that the sun and moon exhibit a distinct color gradation from yellow at the top to red at the bottom when seen at the horizon. The horizon-level sun and moon Appear even redder for elevated observers (e.g., in an airplane or on a mountain peak), because the light must pass through up to twice as much air as that for observers at sea level. But, even when the sun appears at the horizon, its radiance is much greater than that of skylight except in extremely hazy air. This indicates that the predominant role of scattering for the appearance of sunlight is depletion.
Author: Gedzelman, Stanley David, Vollmer, Michael
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