Polarimetry

Polarization is the characteristic of a light wave that describes the orientations of its oscillations as it propagates through space. Light waves can be randomly polarized, linearly polarized, circularly polarized, and elliptically polarized. Light directly from the sun is unpolarized, or in other words randomly polarized, but when sunlight interacts with the atmosphere or reflects off of physical objects, it usually becomes polarized. Some birds, insects and marine animals exploit this effect to navigate or to improve vision contrast. Human eyes are incapable of distinguishing unpolarized light from polarized light such as glare. But glare, which is simply light reflecting off of shiny objects, is always polarized and is significantly reduced by the linear polarizing filters used in our sunglasses.

What is Polarimetry?

The way in which the polarization of light waves change when they interact with objects reveals details about those objects. Polarimetry is the field of science that utilizes these polarization changes to reveal or measure specific properties of an object.

Often with polarimetry, an object is illuminated with light that has been polarized in a specific, known way, often linear. While many lasers are inherently linearly polarized, it is relatively straight-forward to generate linearly polarized light from unpolarized light sources such as incandescent bulbs or LEDs. Unpolarized light consists of many different random oscillations of light. When you pass unpolarized light through a linear polarizer (like your polarized sunglasses), all the vibrations except one are filtered out (or rejected) and it becomes linear polarized. The figure below illustrates this concept. The light exiting the linear polarizer oscillates in one plane.

To achieve non-linearly polarized light, such as circular or elliptical, you need to retard the light in an asymmetric way. This can be done with birefringent materials, which are often crystalline and have different indices of refraction depending on the orientation of the material. This asymmetric refractive index retards the light such that polarization change occurs. For example, a birefringent retarder plate with a quarter wave of retardation will change a linearly polarized beam to circular. Circular polarized light can be used to measure the birefringence of an unknown material by measuring how the circularly polarized light is changed after passing through the material.

Polarimetry

PolarCam cameras, with PolarView software, provide real-time display and calculation of key polarization parameters, including Degree of Linear Polarization (DoLP), Angle of Linear Polarization (AoLP), linear Stokes parameters (S₀, S₁ and S₂) and more. Use the many included tools to process and analyze the data, then save images and movies of each parameter for comprehensive analysis.

Quantifying Polarization

Traditional polarimeters characterize the polarization of an imaged scene or object by capturing multiple images with a linear polarizer rotated between each image. From the captured information, one can quantify polarization parameters, such as degree of linear polarization (DoLP) and angle of linear polarization (AoLP), and amount of birefringence through a transparent material.

The Stokes vector is commonly used to describe the polarization state of a light beam. The Stokes vector is fully characterized from 6 measurements of the light beam. There are four linear polarization measurements, nominally: vertical (0°), horizontal (90°), and diagonal (45°) and diagonal (135°). And since light can also polarize in a circular way—having a clockwise twist or a counterclockwise twist—two additional circular measurements are required.

To better understand this, understand that I₀ is the intensity of light reaching the sensor after passing through a linear polarizer at zero degrees (vertical), I₉₀ is the intensity with the polarizer at 90 degrees (horizontal), I₄₅ and I₁₃₅ are intensities with the polarizer at 45 and 135 degrees, respectively. The first Stokes parameter (S₀) comes from adding the horizontal and vertical intensities together, while the second parameter (S₁) is the difference between the same two. The third parameter (S₂) is the difference between the two diagonal intensities. The fourth Stokes parameter (S₃) is the difference between the two circular polarizations.

Using linear stokes parameters

Pixelated polarization cameras like PolarCam capture the linear polarization measurements: I₀, I₉₀, I₄₅ and I₁₃₅ instantaneously in every video frame. The circular polarization components; however, cannot be captured without an externally mounted retarder plate and additional video frames. Fortunately, circularly polarized light is rare in nature and circular polarization is not required for making retardance or birefringence measurements. Furthermore, with only the linear Stokes parameters, one can generate two other useful parameters: the Degree of Linear Polarization (DoLP, i.e., the relative propensity and direction of linear polarization) and the Angle of Linear Polarization (AoLP, i.e., the angle of the polarization of the light as it reaches the imaging sensor’s plane).