2. Selecting and Buying Linear Polarizing Film

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Polarized beacons are simply light bulbs or LEDs with polarizing filters placed in front of them. Polarized light sensors are simply photoresistors, photodiodes, or phototransistors with polarizing filters placed in front of them. So, most robot builders already have most of the materials they need other than the polarizing filters.

Relatively inexpensive polarizing material can be found by searching the web for “linear polarizing film”. The word “linear” is important.

Photographers often use circular-polarizing filters that eliminate glare by combining a linear-polarizing filter with an additional material (called a retarder) that twists some of the light into a different orientation to properly process the light inside the camera. You need to avoid having the beacon light get twisted, because the filter on the sensor needs a nice clean vertical-only or horizontal-only signal.

Therefore, the specific type of polarizing filter applicable to these robotic devices is a linear-polarizing filter, not a circular-polarizing filter. (If you’re really careful, you can use a circular polarizing filter if it is installed with the linear polarizer facing outward.)

Extinction Ratio

Real-world polarizers are imperfect. That is, they let in some light that they should block, and they block some light that they should let in.

There are a couple of terms that specify the actual polarizing capabilities of the filter material as compared to the ideal. The resulting values allow you to objectively compare the quality of different polarizing materials.

Ideally, vertically-polarized light should 100% pass through a vertically-oriented polarizing filter. The actual percentage passed is called “parallel transmittance”. This number should be as high as possible.

Ideally, horizontally-polarized light should be 100% blocked by a vertically-oriented polarizing filter. The actual percentage blocked is called “extinction”. This number should be as high as possible.

Or, conversely, the percentage of undesired light that leaks through is called “crossed transmittance”. This number should be as low as possible.

Within your budget, you’d like to purchase a polarizing film that has a high parallel transmittance (passes desired polarized light) and a low crossed transmittance (blocks undesired polarized light). The mathematical comparison between the parallel and crossed transmittance is called the “extinction ratio”.

The extinction ratio is the most critical specification, because the other values are irrelevant on their own. Here’s why...

Clear glass allows a lot of desirable light through, but it also allows a lot of undesirable light through. So, it is not a good polarizing filter. A piece of black paper blocks a lot of undesirable light, but also blocks a lot of desired light. So, it is not a good polarizing filter.

Therefore, the comparison between good light passed and bad light blocked (the extinction ratio) is the most critical specification for linear polarizing material.

Calculating Extinction Ratio

There are at least three different ways of calculating and expressing extinction ratio. (Some readers may want to skip this next section out of fear of math. But remember: the math is more scared of you than you are of it.)

#1 Extinction ratio = (crossed/parallel) / 2
The smaller the result, the better.
Example: ER = (0.15% / 24%) / 2 = 0.003125 or 3.125 * 10-3

#2 Extinction ratio = parallel/crossed
Usually expressed as result:1. The larger the result, the better.
Example: ER = 24% / 0.15% = 160:1

#3 Extinction ratio in decibels = 10 log(parallel/crossed) or 10 log(crossed/parallel)
The larger the absolute value, the better.
Example: ER = 10 log(24% / 0.15%) = 22 dB or 10 log(0.15% / 24%) = -22 dB

Signal to noise ratios are often expressed in decibels. Expressing the extinction ratio in decibels is appropriate since this is a comparison of the light we want to see (signal) versus the leaked light we didn’t want to see (noise).

Since all three formulas are ratios, it doesn’t really matter which one you use, so long as you compare filters using the same formulas. Since the results are written differently (0.something, something:something, or something dB), you can tell which formula the polarizing film manufacturer used.

Simple Visual Tests of Polarizing Film

If the polarizing film vendor doesn’t specify the extinction ratio (or other values), then you can obtain some samples and perform a couple of simply visual tests.

Left: Two pieces of polarizing film overlapped parallel. Right: Two pieces overlapped orthogonally.

Left: Two pieces of polarizing film overlapped parallel. Right: Two pieces overlapped orthogonally.

You can observe the limitations of the filters by aligning two polarizing filters in the same orientation (parallel). If the filters were perfect, adding the second filter would not be any darker than looking through the first filter by itself. But, in reality, it’s a little bit darker. (See the middle of the pair on the left side of the above photo.)

Another test is to cross the polarizing filters orthogonally (90 degrees difference) such that one filter is only allowing vertically-polarized light and the other filter is only allowing horizontally-polarized light. If the filters were perfect, adding the second filter would block all remaining light. But, in reality, you can still see some light come through if you look at a bright-enough light source. (Not apparent in the above photo.)

By performing these tests side-by-side to a competitor’s polarizing film, you can make a rough comparison of relative polarizer quality.

Shopping for Polarizing Film

Knowing the specifications of the polarizing film may provide you with a way to comparison shop. For the purposes of a robot contest, it probably isn’t worth paying a premium for laboratory-quality polarizing film. Instead, try to get the required amount of linear-polarizing film for the lowest price.

I purchased Industrial Fiber Optics #IF-PF1 from web-tronics.com for $4.95. It consists of two thick sheets (50 mm x 50 mm x 0.67 mm thick).

I purchased #P630 from 3DLens.com for $57.99. It’s a really large sheet (630 mm x 900 mm x 0.30 mm thick).

In informal testing, the extinction ratios were approximately as advertised (about 20 db or 100:1). Both films are below professional laboratory grade polarizing film, but are more than adequate for amateur robotic tasks.

For the same total area, the various 3DLens films are between 1/5th and 1/10th the cost per square millimeter than the various Industrial Fiber Optics films. However, the 3DLens films are thinner and the vendor doesn’t offer much else.

If you’re making sensors for only one robot and there are other things you want to order from the vendor selling the Industrial Fiber Optics film (spreading the shipping cost), then #IF-PF1 is a good choice. If you’re making beacons and sensors for a bunch of robots, #P630 will save you a lot of money.

After buying the polarizing film, you'll need to determine which orientation is vertical and which is horizontal. Here’s how...