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Anomalous diffraction theory (also van de Hulst approximation, eikonal approximation, high energy approximation, soft particle approximation) is an approximation developed by Dutch astronomer van de Hulst describing light scattering for optically soft spheres.
The anomalous diffraction approximation for extinction efficiency is valid for optically soft particles and large size parameter, x = 2πa/λ:
where in this derivation since the refractive index is assumed to be real, and thus there is no absorption (). is the efficiency factor of extinction, which is defined as the ratio of the extinction cross section and geometrical cross section πa2.
p = 4πa(n – 1)/λ has a physical meaning of the phase delay of the wave passing through the center of the sphere;
a is the sphere radius, n is the ratio of refractive indices inside and outside of the sphere, and λ the wavelength of the light.
This set of equations was first described by van de Hulst. [1] There are extensions to more complicated geometries of scattering targets.
The anomalous diffraction approximation offers a very approximate but computationally fast technique to calculate light scattering by particles. The ratio of refractive indices has to be close to 1, and the size parameter should be large. However, semi-empirical extensions to small size parameters and larger refractive indices are possible. The main advantage of the ADT is that one can (a) calculate, in closed form, extinction, scattering, and absorption efficiencies for many typical size distributions; (b) find solution to the inverse problem of predicting size distribution from light scattering experiments (several wavelengths); (c) for parameterization purposes of single scattering (inherent) optical properties in radiative transfer codes.
Another limiting approximation for optically soft particles is Rayleigh scattering, which is valid for small size parameters.
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.
In optics, the refractive index of a material is a dimensionless number that describes how fast light travels through the material. It is defined as
Rayleigh scattering, named after the nineteenth-century British physicist Lord Rayleigh, is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering particle, the amount of scattering is inversely proportional to the fourth power of the wavelength.
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
Atoms or molecules which are exposed to light absorb light energy and re-emit light in different directions with different intensity. This phenomenon is an example of scattering, a general physical process where quanta of some form, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergoes scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections.
Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element is described by a 2×2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.
The Mie solution to Maxwell's equations describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of spherical multipole partial waves. It is named after Gustav Mie.
The resolution of an optical imaging system – a microscope, telescope, or camera – can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to the physics of diffraction. An optical system with resolution performance at the instrument's theoretical limit is said to be diffraction-limited.
In physics, Bragg's law, or Wulff–Bragg's condition, a special case of Laue diffraction, gives the angles for coherent and incoherent scattering from a crystal lattice. When X-rays are incident on an atom, they make the electronic cloud move, as does any electromagnetic wave. The movement of these charges re-radiates waves with the same frequency, blurred slightly due to a variety of effects; this phenomenon is known as Rayleigh scattering. The scattered waves can themselves be scattered but this secondary scattering is assumed to be negligible.
An acousto-optic modulator (AOM), also called a Bragg cell or an acousto-optic deflector (AOD), uses the acousto-optic effect to diffract and shift the frequency of light using sound waves. They are used in lasers for Q-switching, telecommunications for signal modulation, and in spectroscopy for frequency control. A piezoelectric transducer is attached to a material such as glass. An oscillating electric signal drives the transducer to vibrate, which creates sound waves in the material. These can be thought of as moving periodic planes of expansion and compression that change the index of refraction. Incoming light scatters off the resulting periodic index modulation and interference occurs similar to Bragg diffraction. The interaction can be thought of as a three-wave mixing process resulting in Sum-frequency generation or Difference-frequency generation between phonons and photons.
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed by means of the intensity or photon auto-correlation function. In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transformation of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions.
Single-scattering albedo is the ratio of scattering efficiency to total extinction efficiency. Most often it is defined for small-particle scattering of electromagnetic waves. Single-scattering albedo is unitless, and a value of unity implies that all particle extinction is due to scattering; conversely, a single-scattering albedo of zero implies that all extinction is due to absorption.
Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.
Light scattering by particles is the process by which small particles scatter light causing optical phenomena such as rainbows, the blue color of the sky, and halos.
Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient A2, can be calculated.
Multiangle light scattering (MALS) describes a technique for measuring the light scattered by a sample into a plurality of angles. It is used for determining both the absolute molar mass and the average size of molecules in solution, by detecting how they scatter light. Collimated light from a laser source is most often used, in which case the technique can be referred to as multiangle laser light scattering (MALLS). The insertion of the word “laser” was intended to reassure those used to making light scattering measurements with conventional light sources such as Hg-arc lamps that low angle measurements could now be made. Until the advent of lasers and their associated fine beams of narrow width, the width of conventional light beams used to make such measurements prevented data collection at smaller scattering angles. In recent years, since all commercial light scattering instrumentation use laser sources, this need to mention the light source has been dropped and the term MALS used throughout.
In the small wavelength limit, the total scattering cross-section of an impenetrable sphere is twice its geometrical cross-sectional area.
Atmospheric lidar is a class of instruments that uses laser light to study atmospheric properties from the ground up to the top of the atmosphere. Such instruments have been used to study, among other, atmospheric gases, aerosols, clouds, and temperature.
Rayleigh–Gans approximation, also known as Rayleigh–Gans–Debye approximation and Rayleigh–Gans–Born approximation, is an approximate solution to light scattering by optically soft particles. Optical softness implies that the relative refractive index of particle is close to that of the surrounding medium. The approximation holds for particles of arbitrary shape that are relatively small but can be larger than Rayleigh scattering limits.