# Umov Effect

**DOI:**https://doi.org/10.1007/978-3-642-27851-8_376-1

## Synonyms

## Definition

When light is scattered off particles in a dusty surface or cloud, it becomes polarized. The more reflective (higher albedo) the dust particles, the lower the overall degree of polarization in the scattered light. This inverse relationship was first noted by Nikolay Umov and has accordingly become known as the “Umov effect.”

## Introduction

*P*is the degree of polarization and

*A*the overall (geometric) albedo of the object. Consequently, light scattered by dim, dusty objects will be more polarized than light from bright, dusty objects.

The relationship was first described by Russian physicist Nikolay Umov in 1905 [2] and has become widely referred to as the **Umov effect** and the inverse relationship between maximum degree of polarization and geometric albedo as **Umov’s Law.** It is usually described as giving a straight line with negative slope in a log-log plot of log (P_{max}) versus log(A), in a so-called linear **Umov diagram**. The degree and directional properties of the scattered light depend upon the shapes and sizes of the scattering particles and are a useful tool for investigating dusty surfaces such as the surface of the Moon or asteroids or even cosmic and interplanetary dust clouds.

## One Light Ray, Scattering Off a Single Particle

In the diagram the black arrows indicate relative degrees of polarization in the horizontal and vertical directions. Totally linearly polarized light will have just one component. Unpolarized light will have its orthogonal components of equal magnitude. In general there is some degree of polarization, in which case the longer arrow indicates the dominant plane of polarization.

## Scattering in an Ensemble of Many Particles

- 1.
The total scattering process in the cloud or dust layer can be treated as a very large number of average scattering cascades, added together.

- 2.
A very large number of irregular, randomly oriented particles can be treated, on average, as spherical, isotropically scattering particles in a scattering cascade. Each particle is assumed to have an individual albedo

*a*, which is the same magnitude in all directions. - 3.
For scattering paths involving only one particle between the light source and the observer, the geometries will be identical and all contributing the same polarization components to the observer, so these polarizations will be additive.

- 4.
The geometries of the secondary scattering events will differ widely and can be assumed random. We assume here there is a very large number of these that will all contribute different polarization effects to the light sent in the direction of the observer, so collectively these will average out and contribute to a randomization of the polarization.

- 5.
That every ray of light ultimately encounters a particle unless it is directly scattered from the source in the direction of the observer.

### Albedo

*a*of this is scattered in the direction of the observer. This fraction depends on two main factors, firstly the reflectivity of the particle and secondly the geometry of the interaction, i.e., that the light is now being scattered in all directions. We assume that apart from the light directly scattered in the direction of the observer, all rays of light eventually encounter a particle. Then if each scattering event illuminates

*n*particles on average, and each particle sends some light in the direction of the observer, the observed geometric albedo,

*A*, of the cloud or dust layer is given approximately by:

*an*< 1 and we assume the scattering process proceeds ad infinitum, although the contributions to the redirected light eventually become vanishingly small, so the equation becomes:

This geometric albedo, *A*, is a relative property that refers to the ratio of the reflectance of the particle to that of a perfectly reflecting Lambertian surface with the same area.

### Polarization

*P*, by:

*x*and

*y*are orthogonal directions with respect to the direction of the scattering plane defined by the location of the source-scatterer-observer. In this case

*P*varies between zero for a randomly polarized (unpolarized) wave and unity for one that is fully linearly polarized.

*P*∗ say, but all subsequent scatterings, with their various scattering geometries, yield randomly polarized radiation, the net observed polarization will be weighted for the albedo-related decreases as the cascade is descended:

*P∗*is a constant for the particle population, we have that the observed polarization is decreased in proportion to the contribution of increased interparticle scattering that increases albedo:

This is “Umov’s Law,” and the inverse relationship, where the linear polarization of the scattered light is a maximum for weakly absorbing, low albedo particles, is known as the “Umov effect.”

## Practical Uses of the Umov Effect

The scenario described here involves the integrated contributions of a large number of quasi-random or at least unpredictable events, and according to the central limit theorem, fluctuations in the amplitude and polarization have the properties of a Gaussian process. If the scatterers are non-spherical, but their orientations are random, and there are many of them, the results of the calculation would be similar. Under these conditions it is possible to detect in some cases differences in surfaces, such as in lunar soils, but little can be inferred about the scattering media involved.

However, when the particles are fewer in number or the cascade of scattering is not extensive (e.g., the scatterers have a low individual albedo), the probability density functions of individual fluctuations will deviate from a Gaussian distribution, although they might integrate to this normal distribution, given sufficient time. Some inferences can be made about the scattering particles from observations, but in many cases, the easiest approach is through laboratory measurements and simulations aimed at duplicating the observations. The practical value of the Umov effect has been primarily for evaluating the size of distant celestial objects that appear as a point source to the observer [3].

The Umov effect has also proved useful in investigating the scattering particles producing the zodiacal light, i.e., interplanetary dust particles [5], and the regolith, i.e. dust, gravel, and small rock fragments covering solid rock, on asteroids and the Moon. Other studies include terrestrial aerosols and pharmaceuticals, paints and coatings, and remote sensing through scattering media. It has also been shown to provide a quantitative estimation of the reflectance of small irregularly shaped particles in a two-component mixture, which are commonly found in stratospheric aerosols, desert sands, and thin clouds of cosmic dust [4].

## Cross-References

## References

- 1.Merzbacher, E., Feagin, J.M., Wu, T.-H.: Superposition of the radiation from
*n*independent sources and the probability of random flights. Am. J. Phys.**45**, 964 (1977)ADSCrossRefGoogle Scholar - 2.Umov, N.: Chromatische Depolarisation durch Lichtzerstreung. Phys. Z.
**6**, 674–676 (1905)Google Scholar - 3.Zubko, E., Videen, G., Shkuratov, Y., Muinonen, K., Yamamoto, T.: The Umov effect for single irregularly shaped particles with sizes comparable with wavelength. Icarus.
**212**, 403–415 (2011)ADSCrossRefGoogle Scholar - 4.Zubko, E., Videen, G., Subko, N., Shkuratov, Y.: The Umov effect in application to an optically thin two-component cloud of cosmic dust. Mon. Not. R. Astron. Soc.
**477**, 4866–4873 (2018)ADSCrossRefGoogle Scholar - 5.Zverev, A.: The Umov Effect: space dust clouds and the mysteries of the universe – FEFU scientists are developing and methodology to calculate the ratio of dust and gas in the comas and tails of comets. Eur. Secur. (2018)Google Scholar