Biomedical Optics

Chapter 2 - Rayleigh Theory and Mie Theory for a Single Scatterer

2.1.   INTRODUCTION

Both the Rayleigh and the Mie theories, which are based on the Maxwell
equations, model the scattering of a plane monochromatic optical wave by a
single particle. Even if the particle size is much greater than the optical wavelength,
the wave is diffracted by the particle with an effective cross section that
is usually different from the geometric cross section. The Rayleigh theory is
applicable only to particles that are much smaller than the optical wavelength,
whereas the Mie theory is valid for homogeneous isotropic spheres of any size.
The Mie theory reduces to the Rayleigh theory when the particle is much smaller
than the wavelength.

2.2.   SUMMARY OF RAYLEIGH THEORY

The Rayleigh theory (Appendix 2A) models the scattering of light by particles
that are much smaller than the optical wavelength. Figure 2.1 shows the spherical
polar coordinates used for light scattering. The incident light propagates along
the z axis; the scatterer is located at the origin; field point P is located at (r, θ, φ).
The distribution of the scattered light intensity for unpolarized incident light is
given by

 

Here, α denotes the polarizability of the particle; I0 denotes the incident light
intensity; k denotes the propagation constant (also referred to as the magnitude of
the wavevector
or the angular wavenumber) in the background medium. We have

 

Figure 2.1. Spherical polar coordinates used for light scattering, where θ denotes the polar angle and φ denotes the azimuthal angle.

where nb denotes the refractive index of the background medium and λ denotes
the wavelength in vacuum. Substituting Eq. (2.2) into Eq. (2.1), we obtain I (r, θ)
α 1/λ4. This strong wavelength dependence explains the blue sky in broad daylight
because blue light is scattered much more strongly than red light.

 

UNLIMITED FREE
ACCESS
TO THE WORLD'S BEST IDEAS

SUBMIT
Already a GlobalSpec user? Log in.

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.

Customize Your GlobalSpec Experience

Category: X-ray Instruments and X-ray Systems
Finish!
Privacy Policy

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.