Atmospheric Optics - Dan Bruton
The purpose of this page is to provide introductory information for
students interested in atmospheric optics. The software link below can be used to download
and Mueller Matrix software.
[ MUELLER MATRIX DEMONSTRATION SOFTWARE ]
Note: Richard Hill [email@example.com] provided the following info:
The definition of Stokes Vector components on (this) site is in error.
Wolfram has it wrong also.
The easiest way to see that it is wrong is to take horizontally polarized
light (1, 1, 0, 0) and solve for the intensities.
The total intensity I0 is ½ and the horizontal intensity I1 is 1. That obviously doesn't add.
The Wikipedia explanation is consistent (Lord help us).
S0 = I0 = I(horizontal) + I(vertical)
S1 = I(horizontal) - I(vertical) = 2*I(horizontal) - I0
S2 = I(+45) - I(-45)
Please correct as desired.
Mueller Matrix Information - June 2002
The original Stokes parameters were defined by letting
I0 be the total intensity,
I1 the intensity of horizontal linear polarization,
I2 the intensity of linear polarization at a 45° angle, and
I3 the intensity of left-handed circularly polarized light, and then defining
S0 = 2I0
S1 = 2I1 - 2I0
S2 = 2I2 - 2I0
S3 = 2I3 - 2I0
So the Stokes vector is
Table 1: Stokes Vector Examples
|Linear Horizontal |
|Linear Vertical |
|Linear +45° |
|Linear -45° |
|Circular, Right-Handed |
|Circular, Left-Handed |
Optical elements can be applied to Stokes vectors using Mueller matrices.
The Stokes vector describes the polarization of a plane wave, and
the Mueller matrix describes how the polarization changes upon scattering at a change in electrical or magnetic properties.
The Mueller Matrix contains everything optically one can obtain from a system of scatterers in a turbid medium.
It is a matrix that can be used to reproduce the effect of a given optical element when applied to a Stokes vector.
Radiance (or brightness)
The brightness is the intensity of a radiating source (i.e., the energy flux per solid angle per unit of frequency), also called the radiance or surface brightness. In MKS, it is measured in units of J m-2 s-1 Hz-1 ster-1.
Irradiance (or flux)
The flux of a quantity is defined as the rate at which this quantity passes through a fixed boundary per unit time. In various contexts, flux is called the exitance, irradiance, or radiancy. Energy flux, one of the most common types encountered, has units of energy per unit area per unit time (in MKS, J m-2 s-1, or W m-2).
Shadowband Radiometer - June 2002
In addition to compiling the information above, we have installed a
YESDAS Shadowband Radiometer for measuring the solar irradiance.
The Multi-Filter Rotating Shadowband Radiometer (Model MFR-7) is a field instrument that simultaneously measures global, diffuse, and direct normal components of spectral solar irradiance. The MFR-7 uses independent interference filter-photodiode combinations, mounted in a temperature-controlled enclosure, to detect spectral irradiance at six wavelengths and in one broadband channel. An automated, microprocessor-controlled shadowband is used to alternately shade and then expose the entrance aperture of the instrument, allowing for the measurement of the three solar radiation components. The global and diffuse components are measured directly and the direct-normal component is computed from the difference of the two measured components.
Acknowledgments and References
- Advanced Research Program (ARP)
- The Structure of Polarized Light in an Atmosphere-Ocean System, Jim Adams, Dissertation
- Atmospheric Temperature Profiles from Sunset Images, Dan Bruton, Dissertation (2600K PostScript File)
- Absorption and Scattering of Light by Small Particles, Bohren, C. F. and Huffman, D. R., New York: Wiley, pp. 53-56, 1983.
- Radiative Transfer, Chandrasekhar, S., New York: Dover, pp. 25-37, 1960.
- Light Scattering by Small Particles, van de Hulst, H. C., New York: Dover, pp. 41-44, 1981.
- "Matrix Methods in Optics" by Gerrard and Burch, pp 202-207