Encyclopedia of Color Science and Technology

Living Edition
| Editors: Renzo Shamey

Umov Effect

  • Ken TappingEmail author
Living reference work entry
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

When randomly polarized light is obliquely incident on particles in a dusty surface or layer, the scattered or reflected light becomes partially polarized to a degree that is dependent upon the viewing direction with respect to the incident light (phase angle) and, if the particles are irregularly shaped, their orientation. Since the geometry of the source-scatterer-observer light path is the same for all single-particle scattering events, this component of the light is polarized. For light scattering involving a large number of particles, the geometries are many and widely different, so that even though each scattering event might produce a net polarization, the integrated scattered light from these particles will be randomly polarized. The higher the reflectivity of the individual particles, the larger the contribution to the randomly polarized light reaching the observer from the multiple-particle scattering events. This means the higher the general reflectivity (albedo) of the dust particles, the lower the net degree of polarization of the light reaching the observer. This relationship is described by the following inverse correlation:
$$ P\propto \frac{1}{A} $$
where 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 (Pmax) 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

Figure 1 shows a beam of randomly polarized light coming from the far background in the upper left propagating toward the lower right foreground. It is incident upon a particle, which is assumed to be “small” and “spherical,” and is scattered. The light that continues with its direction unchanged retains its initial polarization. However, in general the scattered light changes its polarization to a degree that depends on the direction in which it is scattered. Light deviated by 90 degrees with respect to the direction of the incident light becomes totally linearly polarized in a sense tangential to a circle centered on the particle and normal to the direction of the incident ray. In an arbitrary direction (the thick line in the figure), the light will be partially polarized to some degree depending upon the scattering angle. If the illumination source and the observer are a large distance from the scatterers, light from a collection of particles reaching the observer after a single interaction would follow the same path geometry, and their individual polarization components would be additive and give a calculable increase in the degree of polarization seen by the observer.
Fig. 1

Polarization of light by 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

In general, when incident light encounters a dust cloud or dusty layer, it interacts with a very large number of particles. In this discussion, the term “particle” refers to an “average particle,” combining the scattering properties of the ensemble of particles. Each of these scatters light onto an even larger number of particles, which, in turn, give rise to further scattering. This makes it possible to consider an average scattering event, involving an average cascade of secondary scattering, leading to the following simplifying approximations:
  1. 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. 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. 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. 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. 5.

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

     
This scattering scenario is represented in Fig. 2.
Fig. 2

A ray of light interacting with a single particle and triggering many cascades of multiple particle scattering

Albedo

Light from the source hits a particle. A fraction 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:
$$ A\propto a+{a}^2n+{a}^3{n}^2\dots {a}^k{n}^{k-1}\dots $$
(1)
where 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:
$$ A\propto \frac{a}{1- an} $$
(2)

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

The first encounter between the light and a particle has the same geometry as all the other first encounters. However, the large number of ray paths of the encounters with second and subsequent particles will contribute a net randomization of the polarization. We define the degree of linear polarization, P, by:
$$ P=\left|\frac{I_y-{I}_x}{I_y+{I}_x}\right| $$
(3)
where 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.
Since the observer sees the sum of a very large number of cascades, we can assume the first scatter in each cascade yields some level of linear polarization 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:
$$ P\propto \frac{P^{\ast }+0+0+0+0\dots }{a+{a}^2n+{a}^3{n}^2+\dots {a}^k{n}^{k-1}\dots }={P}^{\ast}\left(\frac{1- an}{a}\right) $$
(4)
So substituting from the albedo eq. (2) where 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:
$$ P\propto \frac{1}{A} $$
(5)

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. 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. 2.
    Umov, N.: Chromatische Depolarisation durch Lichtzerstreung. Phys. Z. 6, 674–676 (1905)Google Scholar
  3. 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. 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. 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

Copyright information

© Springer Science+Business Media LLC 2019

Authors and Affiliations

  1. 1.D.R.A.ONational Research CouncilPentictonCanada

Section editors and affiliations

  • Joanne Zwinkels
    • 1
  1. 1.National Research Council CanadaOttawaCanada