Related Experiment Video
Updated: Jun 16, 2026
09:16
Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
Published on: January 9, 2017
Spherical particle populations: approximate analytic relationship between size distribution parameters and integral
Applied Optics
|February 19, 2010
Summary
This study presents a simple formula to calculate light absorption and scattering by spherical particles. The method allows estimation of particle size distribution from optical measurements, useful for atmospheric aerosol analysis.
Area of Science:
- Atmospheric optics
- Aerosol science
- Radiative transfer
Background:
- Spherical particles' optical properties are crucial for understanding atmospheric radiative transfer.
- Accurate characterization of aerosol size distributions is essential for climate modeling and air quality assessment.
Purpose of the Study:
- To develop an analytic relationship between optical coefficients (extinction, scattering, adsorption) and log-normal particle size distribution parameters.
- To enable approximate calculations of optical coefficients using mean radius, standard deviation, and number concentration.
- To demonstrate a method for estimating size distribution parameters from optical measurements at multiple wavelengths.
Main Methods:
- Approximation of particle absorption and scattering efficiencies using a three-parameter formula.
- Development of an analytic formula linking optical coefficients to log-normal size distribution parameters.
- Inversion technique to estimate size distribution parameters from measured optical coefficients.
Main Results:
- An analytic relationship was established between optical coefficients and log-normal size distribution parameters.
- The technique allows for approximate calculation of optical coefficients from basic size distribution parameters.
- Size distribution parameters can be estimated by inverting optical measurements at three wavelengths.
Conclusions:
- The developed technique provides a computationally simple method for analyzing aerosol optical properties.
- The method is suitable for hand calculations, making it accessible for various applications.
- This approach is validated for atmospheric aerosol particles and visible radiation scenarios.
Related Concept Videos
01:26Gauss's Law: Spherical Symmetry
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
01:14Gravitation Between Spherically Symmetric Masses
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
01:27Triple Integrals in Spherical Coordinates
Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: 𝜌, 𝜃, and 𝜑. Here, 𝜌 is the distance from the origin, 𝜃 is the angle in the xy-plane measured from the positive x-axis, and 𝜑 is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...
01:26Spherical and Cylindrical Capacitor
A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
01:23Spherical Coordinates
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
01:20Maxwell-Boltzmann Distribution: Problem Solving
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by