A rainbow is an atmospheric optical arc produced by refraction, internal reflection and wave dispersion of light in water droplets. Wavelength-dependent refractive index separates the colours. The primary arc involves one internal reflection, and the secondary arc involves two.
For the one-internal-reflection branch, Snell's law and give . At an interior stationary point, , hence . Another differentiation gives there. The interior minimum exists for . The internal specular reflection can be partial; total internal reflection is not required.
An optical halo is a ring, arc or other light pattern formed by refraction or reflection in atmospheric ice crystals. It is distinct from a dark-matter halo.
The common optical halo has a radius of approximately around the Sun or Moon. Refraction through a ice-crystal prism supplies a minimum-deviation edge. Nearby incident directions are concentrated near that edge, forming a caustic.[ref]
Atmospheric extinction attenuates starlight through absorption and scattering. It depends on wavelength and path length, and is described by an optical depth or an extinction coefficient in astronomical magnitudes per airmass.
The total extinction cross-section per unit volume of particles is a length-inverse coefficient. Its path integral is optical depth. It combines scattering and absorption and differs from the dimensionless imaginary part of a complex refractive index. For liquid droplets with size-independent , .
An atmospheric window is a wavelength interval of relatively high atmospheric transmission. Infrared photometric bands are largely chosen to lie in such windows.
Atmospheric refraction bends a ray through the vertical refractive index gradient, shifting its apparent direction. Because of optical dispersion, the shift varies with wavelength.
Atmospheric dispersion is the wavelength dependence of atmospheric refraction. It spreads a broadband stellar image along the vertical direction toward the zenith.
Atmospheric turbulence produces changing refractive index fluctuations. These alter optical path lengths, distorting wavefronts and causing astronomical seeing and atmospheric scintillation.
The timescale on which turbulent optical-path fluctuations decorrelate constrains short-exposure imaging and adaptive-optics control latency. In a frozen-flow approximation it scales as , with an effective turbulence-weighted wind speed. It is not the temporal coherence time set by the optical bandwidth.[ref]
NACO User Manual by European Southern Observatory. §3.1, printed p.13, atmospheric coherence length and time
Astronomical seeing is the atmospheric blurring of a stellar image, conventionally expressed as the angular full width at half maximum of its long-exposure point spread function, usually in arcseconds. For a large aperture in the ideal Kolmogorov model, it is approximately radians, with Fried parameter .
Calibrated Fourier statistics of short-exposure speckle patterns recover information suppressed by a long seeing-blurred exposure. A power spectrum constrains the modulus, while additional phase-sensitive statistics such as the bispectrum are needed for image reconstruction. The exposure must adequately freeze turbulence and the source must supply enough photons; noise and calibrator mismatch limit the reconstruction.
Many short frames freeze atmospheric image fluctuations. Selecting the sharpest frames, registering them and combining them can improve angular resolution. Selection discards photons and can create a read-noise penalty, so adequate reference-source photon counts are essential. It does not guarantee that every high-order wavefront error disappears.
The Fried parameter is the atmospheric coherence length for optical phase. In the standard inertial-range model, the phase structure function is . For unchanged atmospheric turbulence, . The NACO manual, section 3.1 describes this scaling and its role in adaptive correction.
Anisoplanatism is the loss of correlation between wavefront errors along different viewing directions. Correcting a guide star therefore leaves a larger residual for a sufficiently separated target.
The isoplanatic angle is the characteristic angular separation over which a single-direction atmospheric correction remains useful. It depends on the altitude distribution of atmospheric turbulence as well as on wavelength.
Atmospheric scintillation is the fluctuation of received stellar intensity produced by propagation through atmospheric turbulence. A phase-only deformable mirror does not generally remove these amplitude fluctuations.
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Atmospheric optics is the study of how light interacts with the Earth's atmosphere, leading to various optical phenomena. This field encompasses the understanding of how atmospheric conditions—such as the presence of particles, water vapor, and gases—affect the propagation and perception of light. Some key phenomena studied in atmospheric optics include: 1. **Refraction**: The bending of light rays as they pass through layers of air with different temperatures and densities, leading to phenomena like superior and inferior mirages.