Variable Neutral Density Filters: Why are they not calibrated for photography or videography?

Variable neutral density filters are useful for video or time-lapse work. However, they are infuriating—as I pointed out in my review here—because they are not calibrated in stops or Exposure Values (EVs). Instead, all that I have found for sale have a linear scale corresponding to the change of angle of rotation.

Here is the scale on a variable neutral density filter made by Gobe:

Variable neutral density filters comprise two sheets of polaroid material, one rotating on top of the other. When the angle of polarisation of one sheet is identical to that of the other, there is no reduction in the amount of light passing through (other than the basic reduction caused by the material itself). As the angle is increased up to 90 degrees, the amount of light transmitted is decreased until, with two ideal polarisers, no light is transmitted at all. Although polaroid material is not an ideal in terms of a perfect optical polarising material, it does follow pretty well the Law of Malus. The intensity of light transmitted by the filter can be calculated from the angle of rotation of one sheet with respect to the other. I have actually checked experimentally using an ordinary cheap variable neutral density filter (i.e. made of polaroid material) that there is close agreement between the actual curve of intensity against angle of rotation and the theoretical curve calculated from the Law of Malus.

The problem for photographers is that we do not work with a linear scale of light intensity. We work with stops or Exposure Values, a base-2 logarithmic scale. In other words, halving the light intensity is 1 EV (stop) difference; halve it again, 2EV differences and so on. If we look at the graph calculated from the Law of Malus, we can see that the angle of rotation between the two polaroid sheets needs to reach approximately 45 degrees for the light intensity to be reduced by half, i.e. 1 EV or stop. With a scale of say 14 steps on the rim of the variable ND filter, we have to get to number 7 just to get a 1 stop reduction in light transmitted over and above that caused by the material itself. Minus 2 EVs is reached at 60 degrees but then smaller and smaller changes in angle are needed to achieve a change in EV.

This diagram shows the reduction in transmitted intensity with change of rotational angle (calculated from the Law of Malus). Also shown are where changes in EV fall on the line.

So we know that moving the rotation by one point at one end of the scale does not have the same effect as rotating the upper layer by one point at the other end of the scale. Quite simply the photographer does not know which graduation to use to achieve a reduction of light transmission by, say, 4 EVs or stops.

This graph shows the calibration of a variable neutral density filter in photographic terms, i.e. in stops or EVs. This one (made by Gobe has a scale marked with 14 points together with ‘min’ and ‘max’ marked as bands placed non-linearly:

This graph shows the effect of the setting on the rim of a Gobe variable neutral density filter
on the decrease in Exposure Value (EV) (stops). EVs were measured to the nearest 1/3rd
of a stop. A was the arrow on the side of the 'Max' mark nearest the scale. The graph
serves as a calibration curve for the filter.

My simple question is: why do manufacturers of variable neutral density filters not calibrate their filters with decrease in EV? Is it because the calibrations would all be close together on the rim? Or that it would be difficult to engrave a marking that sits precisely on an EV difference? In that case simple markings for, say, 5 or 6 EVs should not be too difficult even if only one or two of the marks had values attached. Or have manufacturers not done so because variable neutral density filters were traditionally marked by and physicists, with the graduations indicating simply the change in rotation? The very least manufacturers could do would be start the markings at a point where there is a decrease of 1 EV beyond the basic decrease (of approximately 2 stops) produced by having the filter in place.

There is actually plenty of room on the rim for two scales. Since the rotational angles cover 0-90 degrees, there is the rest of the rim on which EVs could be marked.

I wondered if more expensive filters had markings in EV. It would appear not. I found the instructions for Tiffen:

The Tiffen Variable ND filter operates on the same principle as a Circular Polarizer [erm, no it doesn’t] – rotate until you reach your desired effect and shoot. It allows you to have continuous control over the amount of light coming through your lens in an approximate range of 2 (ND 0.6) to 8 (ND 2.4) stops – while maintaining the integrity of your image. Note: The evenly spaced indexing marks between MIN and MAX do not represent calibrated stops. They are for reference only, to be used as a density bench-mark to return to a previous setting.

What would a variable ND filter look like when calibrated for photographic use? Here is the same photograph as above but the upper one this time has marks added in Photoshop to indicate a scale marked in EVs:

A big improvement, I would submit.