## Polarimetry

Posted by .

Polarimetry is the technique of measuring the degree and direction of polarization. Here, we focus specifically on how polarimetry is used to measure linear polarization.

We (almost*) can’t detect polarization with the naked eye. Normal detectors of visible light are not normally able to detect the polarization properties of the measured light. To find the degree and direction of polarization of the incident light we will have to manipulate (or modulate) the light before it falls on a detector. There are several different techniques to measure linear polarization.

*) Some people are able to detect polarization with their eyes in the form of two small butterflies in the centre of their field of view. These butterflies, one yellow, one blue, are known as Haidinger’s Brush.

### Polarizer

The most basic part of every polarimetric instrument (polarimeter) is the polarization filter, also known as polarizer. Polarizers consist in several different forms, all with the same goal: letting light in one direction of polarization through and blocking the perpendicularly polarized light. An ideal polarizer completely blocks the unwanted radiation and has no loss in the wanted radiation. The orientation the polarizer has when parallel to the light released is called the polarization axis of the polarizer.

In the description of polarization, we explain that a bundle of unpolarized light consists of many different completely polarized beams whose directions of polarization cancel each other. If we let an unpolarized beam fall on a polarizer, it will cancel exactly half of the light (with the wrong direction) and let the other half pass through.

### Polarimetric method 1: Temporal Modulation

In the simplest and most obvious polarimetric method a polarizer is rotated during a measurement series, with the polarization axis perpendicular to the travel direction of the light. Let us imagine a set-up where the light travels in the horizontal direction, called the ‘x’ direction. The light is captured at the end of its path by a detector. Now we will measure the light in the following steps.

1. We place the polarizer in front of the detector in the path of the light, with the axis of polarization in the vertical (‘z’) direction. All the light which falls on the detector is now polarized in the z direction, independently of the original degree and direction of polarization.
2. We turn the polarizer around the x direction, until the axis of polarization lies on the horizontal plane (‘y’) perpendicular to the x direction. All the light which falls on the detector is now polarized in the y direction, independently of the original degree and direction of polarization.

Now imagine that the light was originally polarized for 50% in the z direction. To calculate how much light an ideal polarizer would let pass through, we can divide the light in a polarized and an unpolarized part. The polarized part is passed entirely in step 1. The unpolarized light is passed for 50% in this step. In total this means that 75% of the light falls on the detector during step 1.

During step 2 all the polarized light is blocked, the unpolarized part is once again let through, leaving 25% of the original light to fall on the detector. The difference that we measure (75% – 25% = 50%) shows us the original degree of polarization in the vertical direction.

If the original direction of polarization is unknown beforehand, it can be found by adding two measurements to the series: one rotated 45 degrees from the x-axis and one 135 degrees. With some calculations this allows us to find the exact degree and direction of polarization of the original light.

Because the light is modulated for every measurement, and the different modulator values are measured after each other, we call this temporal modulation. Temporal modulation is also possible my rotating the source of light in stead of the polarizer. Since this is essentially the same technique we will not go into the details.

### Polarimetric method 2: Spatial Modulation

This method is similar to temporal modulation, because the light is modulated once again by changing the angle of the polarizers. The difference between the two techniques is that the polarizer doesn’t rotate between the different measurement steps, but that we use two (or four) different unmoving polarizers that all modulate the light for a part of a detector or for a detector of their own.

Because the different modulated parts are eventually measured at different places in space we call this method spatial modulation. To find the degree and direction of polarization the same calculations have to be done as during the previous method.

The advantage of spatial modulation is that measurements can be made simultaneously which has the advantage of knowing that we won’t miss any changes during the measurements. A disadvantage of this method is however that we measure light which falls on different (parts of the) detectors, these might have different properties making it more difficult to compare them.

To remove these disadvantages it is possible to combine both methods. A measurement set-up will in this case have have multiple moving polarizers.

### Polarimetric method 3: Spectral Modulation

There is a third method of measuring the polarization properties of light. In this method we will not modulate in time or space, but in the spectral direction. Both iSPEX and SPEX deploy this polarimetric technique.