Visibility of natural tertiary rainbows

Piston-Type Optical Modulator for Dynamic Thermal Radiation Tuning Applications

This study introduces a movable piston-like structure that provides a simple and cost-effective avenue for dynamically tuning thermal radiation. This structure leverages two materials with dissimilar optical responses-graphite and aluminum-to modulate from a state of high reflectance to a state of high absorptance. A cavity is created in the graphite to house an aluminum cylinder, which is displaced to actuate the device. In its raised state, the large aluminum surface area promotes a highly reflective response, while in its lowered state, the expanded graphite surface area and blackbody cavity-like interactions significantly enhance absorptance. By optimizing the area ratio, reflectance tunability of over 30% is achieved for nearly the entire ultraviolet, visible, and near-infrared wavelength regions. Furthermore, a theoretical analysis postulates wavelength-dependent effectivenesses as high as 0.70 for this method, indicating that tunabilities approaching 70% can be achieved by exploiting near-ideal absorbers and reflectors. The analog nature of this control method allows for an infinitely variable optical response between the upper and lower bounds of the device. These valuable characteristics would enable this material structure to serve practical applications, such as reducing cost and energy requirements for environmental temperature management operations.

Analyzing colors and spectra of natural rainbows with hyperspectral imaging

Few colorimetric analyses of natural rainbows (i.e., bows seen in rain showers) have been published, and these are limited either to approximate techniques (colorimetrically calibrated red-green-blue (RGB) cameras) or to rainbow proxies (bows seen in sunlit water-drop sprays). Furthermore, no research papers provide angularly detailed spectra of natural rainbows in the visible and near-IR. Thus some uncertainty exists about whether the published spectra and colors differ perceptibly from those in natural rainbows. However, battery-powered imaging spectrometers now make possible direct field measurements of the observed chromaticities and spectra in such bows. These data (1) show consistent spectral and colorimetric patterns along rainbow radii and (2) let one subtract additively mixed background light to reveal the intrinsic colors and spectra produced by rainbow scattering in nature.

Rainbows by elliptically deformed drops. I. Möbius shift for high-order rainbows

Using ray theory, the Möbius shift of the (p-1)-order rainbow angle for a particle having an elliptical cross section is obtained to first order in the ellipticity as a function of the tilt of the ellipse with respect to the propagation direction of the incoming rays. The result is then adapted to the geometry of scattering of light rays from the sun by a falling water drop as a function of sun height angle. The variation in the angular spacing between the supernumeraries is determined as a function of location along the rainbow arc, the conditions under which the rainbow angle is insensitive to drop flattening were determined, and the dependence of the Möbius shift on the drop refractive index is shown for rainbows up to fourth order (p=5).

Tropospheric haze and colors of the clear twilight sky

At the earth's surface, clear-sky colors during civil twilights depend on the combined spectral effects of molecular scattering, extinction by tropospheric aerosols, and absorption by ozone. Molecular scattering alone cannot produce the most vivid twilight colors near the solar horizon, for which aerosol scattering and absorption are also required. However, less well known are haze aerosols' effects on twilight sky colors at larger scattering angles, including near the antisolar horizon. To analyze this range of colors, we compare 3D Monte Carlo simulations of skylight spectra with hyperspectral measurements of clear twilight skies over a wide range of aerosol optical depths. Our combined measurements and simulations indicate that (a) the purest antisolar twilight colors would occur in a purely molecular, multiple-scattering atmosphere, whereas (b) the most vivid solar-sky colors require at least some turbidity. Taken together, these results suggest that multiple scattering plays an important role in determining the redness of the antitwilight arch.

Rainbows by elliptically deformed drops. II. The appearance of supernumeraries of high-order rainbows in rain showers

The appearance of supernumeraries of high-order rainbows in heavy rain showers is explored for rainbows up to order five (p=6). This is done by using a combination of the ray-theory-based first-order Möbius approximation for high-order rainbows with the Airy approximation of the rainbow radiance distribution. We conclude that supernumerary formation of rainbows of order three, four, and five is possible in natural rain showers. Supernumeraries of the third-order and fourth-order rainbows are preferentially formed near the bottom of these rainbows. A strategy for observing supernumeraries of high-order rainbows is proposed.

Spectral measurement and modeling of natural rainbows

Although quantitative observations of rainbow spectra, colors, and luminances are needed for any comprehensive analysis of rainbow scattering theory, very little such data has been published. But new remote sensing tools now make possible the detailed spectral and colorimetric measurement of natural rainbows, which here are defined as bows seen in sunlit rain or water-drop sprays. To measure these often short-lived phenomena, both multispectral tools (colorimetrically calibrated RGB cameras) and hyperspectral tools (imaging spectrometers) are used to examine the spectral and angular fine structure of natural rainbows. Airy theory for aerodynamically flattened drops helps to explain some of these bows' observed features, such as the reduced color gamuts caused by smaller drop sizes and low sun elevations h₀. However, other features such as the distinct blues seen in rainbows at higher h₀ are not well explained.

Intensity distribution of the parhelic circle and embedded parhelia at zero solar elevation: theory and experiments

We describe the individual contributions to the intensity distribution of the parhelic circle for plate-oriented hexagonal crystals at exactly zero solar elevation using geometrical optics. An experimental as well as theoretical study of in-plane ray paths provides details on the mechanism for several halos, including the parhelia, the 120° and 90° parhelia, a blue edge, and the Liljequist parhelia. Azimuthal coordinates for associated characteristic features in the intensity distribution are compared with experimental data obtained using a spinning hexagonal glass prism.

Polarization and visibility of higher-order rainbows

The degree of polarization of rainbows of order k with k≥3 is bounded in the interval [75%, 78%], where 75% is the limit for k→∞. A polarization filter can improve the signal-to-background ratio of the third and fourth rainbows by a factor of 2, which may lift their visibilities in natural circumstances above the threshold of human visual perception. Under optimal circumstances, the latter may be true for the recently photographed green fingerprint of the fifth rainbow, even without the aid of a polarization filter. The prospects for observing the sixth rainbow are unclear. There exists a possibility that the signal of the natural seventh rainbow (appearing at 64° from the Sun) may be separated from its background if photographed under perfect conditions through a polarization filter.

Photographic observation of a natural fifth-order rainbow

A photograph has been obtained of a natural fifth-order (quinary) rainbow. The photograph was acquired on 8 August 2012 with a digital camera and a polarization filter to maximize contrast of the rainbows with the background. The quinary rainbow, together with its first supernumerary, appears in a contrast-enhanced version of the photograph as broad green and blue-violet color bands within Alexander's dark band between the primary and secondary rainbows. The red band of the quinary rainbow is obscured by the much brighter secondary rainbow. A comparison with a numerical simulation using the Debye series confirms that the color bands of the quinary rainbow appear at the expected location. The numerical simulation produces a good match with the photograph for a droplet radius of 0.46 mm. The green band of the quinary rainbow is even faintly discernible in the unprocessed photograph, suggesting that under exceptional viewing conditions the green band of the quinary rainbow may be observed visually with the aid of a polarization filter.

Photographic observation of a natural fourth-order rainbow

We report what is believed to be the first photographic recording of a quaternary rainbow in nature. It appears on the Sun side of the sky with its red arc at a radius of about 45° from the Sun. The original pictures have been subjected to various forms of image processing to reveal the tertiary rainbow as well as the quaternary rainbow, which are separated by only a few degrees with their colors reversed and their red arcs adjacent to each other.