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I teach physics at a community college, and due to the covid-19 epidemic, we're developing a lab kit for our students so that they can do labs at home in the fall. It's challenging but also kind of fun to try to figure out labs that are good educationally and give decent results, while also staying within our budget of $200 per student. For an activity in which the students investigate polarization and Malus's law, I found a technique that gives nice results, which involves photographing an image on an LCD screen and adjusting the orientation of a polaroid film until brightness A on a computer screen, seen through the filter, appears the same as brightness B. To avoid issues with the gamma correction of the screen, I use speckle patterns rather than the monitor's grayscale, and take the photos from far enough so that the pixels aren't resolved. The technique can actually be done without any electronic devices at all (eye instead of camera, printout instead of computer screen), but I got the best results using the photography technique. The vast majority of our students own both a laptop and a smartphone.

When I did the technique myself using a webcam to photograph my LCD monitor, the big issue I ran into was that the webcam's sensitivity was wildly mismatched to the extremely bright monitor. Through the camera, black on the monitor looked indistinguishable from white. I overcame this by screwing together a stack of neutral density filters to make 7 f-stops worth of attenuation, or about a factor of 1/100.

Even with the monitor's hardware controls set to minimum brightness, it was still much too bright without the filters. Although my webcam does allow software control of its brightness, that didn't seem to help enough either.

My question: is there some way to improvise a filter about this dark, either from very cheap materials that I could include in the kit or from household objects that my students would be likely to have? It can be lousy optical quality -- in fact, if it helps to blur out the pixels, that's a plus.

I tried placing one lens of a pair of sunglasses in front of the webcam (which made the webcam look really cool), but that only seemed to give about 1-2 stops of dimming. Looking around the house for colored plastic, most of what I found, like the lids of tupperwares, was either much too transparent or totally opaque. I did notice a jug of olive oil that looked promising, but I didn't want to cut it up.

I tried using a pair of crossed polaroids, and although it was easy to get about the right attenuation, this is unfortunately incompatible with the physics point of the lab -- it adds two more polarizers to the stack, which changes the math.

I did find a commercial product, described as a "gel sheet," that might work. They'll sell you a 21"x24" piece of ND1.2 (4 stops) for $23. This would probably work, with students possibly stacking two pieces to get 8 stops, but would be kind of a hassle to prepare for the kits, because I'd have to cut out 150 pieces for 75 students.

Is there any really simple option that I'm not thinking of, like maybe some substance from the kitchen spread on a piece of plastic, or some other common household item that hasn't occurred to me? Maybe thin onion-skin paper?

[EDIT] I found a couple of things that sort of worked, although they weren't optimal. (1) Put a tiny pinhole in a piece of paper and use it to reduce the camera's aperture. This worked pretty well, giving maybe 5 stops, but I had to position it by hand, and keeping it in position might be hard. (2) I have some poop bags for my dogs that are made of thin, black plastic. A single thickness of this looked like about 10 stops, but the image quality through it was pretty bad.

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Historically, filters were made using various techniques. Liquid filled cells were common. A rectangular clear glass cell, likely one centimeter cube, was filled with a solution, perhaps a specific percentage of copper sulfate, or dye, or pigment, or lamp black. Early photographers and many scientific instruments used such filter cells. They were also made using two pieces of thin glass fashioned with a gasket, making a flat, thin rectangular filter cell.

The English inventor, Frederick Wratten was a famous filter maker for scientific purposes. The firm of Wratten and Wainwright was purchased by Kodak in 1906. The Kodak filters bore the prefix Wratten for nearly a 100 years. This firm perfected gelatin filters. They maintained a catalog of recipes used to dye gelatin. They made sheets of gel filers lacquered for protection. Also, gelatin filters were made by sandwiching the gelatin between thin sheets of glass.

You can dye gelatin, or suspend lamp back in gelatin. The gelatin mixture is then poured into a basin of water. The gelatin floats and gels. This makes an optically flat filter. It is then scooped using a wire frame from beneath.

Ordinary photo roll film can also be used to make neutral density filters. Point the camera at a uniformly illuminated target and make a series of exposures in 1/3 f-stop increments. This makes a density series.

Filters are historically labeled using logarithmic notation. For example, a neutral density filter that blocks 2X = 1 f-stop or 50% reduction is labeled 0.30. Sometimes the decimal point is omitted. This value is the exponent base 10 -- thus the number 2, written as a log base 10 is 10 elevated to the 0.30 power – the 0.30 is the exponent.

0.05 = 1/6 f-stop = 90% Transmission = 1.11 Opacity 0.10 = 1/3 f-stop = 80% Transmission = 1.25 Opacity 0.15 = ½ f-stop = 70% Transmission = 1.43 Opacity 0.20 = 2/3 f-stop = 63% Transmission 1.58 Opacity 0.30 = 1 f-stop = 50% Transmission 2.0 Opacity 0.60 = 2 f-stop
0.90 = 3 f-stop 1.20 = 4 f-stop

It was common practice to visually compare using a split screen viewer. A filter of known value juxtaposed. Such readings are very accurate, as the human eye can make satisfactory judgements. Such readings are labeled “V” for visual. Modern electronic instruments are calibrated to read the same as a visual reading.

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  • Thanks, this is interesting, and now I know why they're called "gels." Floating the gelatin seems like it would be a fun thing to try, but doesn't seem like a practical way of saving time and money for me and my students. – Ben Crowell Jun 15 at 16:48
  • Early astronomers made a ND sun filter - Glass microscope slide held above a candle flame this deposits carbon black on the glass making an ND filter. – Alan Marcus Jun 15 at 17:07
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There are some fairly low-cost solutions.

  • Lower the display brightness. Every modern computer has brightness controls buried in settings somewhere. Most monitors have buttons to control brightness, and most laptops have button or key combinations that do the same.

    Most displays can dim to completely black, and it's highly unlikely that a display dimmed to that extent would overexpose a webcam.

  • Use a camera that can control exposure via aperture, shutter speed, ISO, or exposure compensation. Old compact cameras can be purchased for little more than the cost of shipping, much less than the cost of traditional textbooks.

    Also, the cameras built into smartphones are capable of this miraculous feat. You state, "The vast majority of our students own both a laptop and a smartphone."

  • Use webcam software that can control exposure. Your problem may be a software defect (auto exposure + exposure compensation). Try some different programs.

  • Use a different webcam. If not a software defect, your webcam may be defective.

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  • As stated in the question, I tried #1 and #3, and #2 is not possible, because students have to do this at home with their own camera. – Ben Crowell Jun 15 at 21:05
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    For 1 and 3, something is probably wrong with your computer, webcam, or software. Most displays can dim to completely black, and it's highly unlikely that a display dimmed to that extent would overexpose a webcam. For 2, you state, "The vast majority of our students own both a laptop and a smartphone." Students can also buy old compact cameras for little more than the cost of shipping, much less than the cost of traditional textbooks. – xiota Jun 15 at 22:08
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Replacement side-mirror glass for cars and trucks (e.g., https://shop.advanceautoparts.com/p/k-source-replacement-mirror-glass-driver-side-99255/10485267-p ) is cheap, is pretty good optical quality, and it transmits a small fraction of light (like mirrored sun-glasses do.) You could buy a few, cut them into squares, tape the sharp edges, and simply hold your home-made filter over the camera lens.

One down-side is, you'll have to hold it tight against the lens, or find some other way to stop light from entering behind the "filter." Any light that sneaks in there potentially is going to bounce around considerably because... It's a mirror!

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I have just tried the so called "space blanket" as a filter - looks awful and gives about 5-6 stops. (This piece was really worn out, perhaps the new one would be less hazy). space blanket filter

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