I’ve always tried my best to be a continual learner in this field of lighting, deepening my understanding of the craft and continually refining my practice of it. In all of my readings or conversations with others in the industry, the concept of an even stage wash has always been assumed as a goal. However, while many have sought it, referenced it, taught methods of achieving it, I cannot say that I have to this date come across anyone to ever define it. Toward that end, I am taking the foolhardy task under hand. And if I may be wrong, hopefully I can in this writing begin the dialogue that leads the industry toward quantifying this goal that we have heretofore only assumed.

It seems right to me to turn toward cameras as a lens through which we can view the topic¹. Aside from the obvious pun, this approach is valuable because the camera is less forgiving in terms of contrast than the human eye. In other words, just because the stage looks good to the eye doesn’t mean it will look good to the camera, but if it looks good on camera, it will almost always look good to the eye. I won’t go into detail on this since the topic has been expertly covered in a recent book by James L. Moody and Jeff Ravitz. It is their discussion that sparked this one.

Another impetus to this discussion has been recent conversations with audio techs in modeling speaker deployments for venues. Many are quick to define an even coverage as falling within a 3dB range. They may disagree whether this is to be understood as ±3dB or a 3dB total range (i.e. ±1.5dB), but the idea of 3dB as being the range that most can discern as being different is key to the speaker modeling process. Their question to me was for how one would define the equivalent in the lighting realm.

In summary, the authors above look at the mechanism of the camera in terms of its relatively limited contrast compared to the human eye. This is not only in totem but also what can be discerned at any single time. The control of this brightness for the camera is the iris, its openness, and thus the amount of brightness is measured in f stops. If we want the evenness of our stage washes to be defined by unnoticeable deviations in intensity, then it would make sense to use the commonly referenced limits of what is noticeable in photography. Most can recognize the difference between a half stop of light but the trained eye sets it discernment on a third of a stop as the minimum distance between proper exposure and over/under exposure. Thus it seems appropriate to set the goal of our range considered to be an even intensity to a third of a stop from top to bottom.

What is operative for both the audio definition of even coverage and for the same of lighting is the understanding that these are both psychophysical effects, which is to say that our psychological intuition toward differences in intensity of stimuli is different than the measured differences in intensity. Going back to audio, doubling the power of an audio source as measured in watts will yield a barely noticeable difference to the ear, whereas to have a perceived doubling in volume would require ten times the power.

The foundational research in this was done in the mid twentieth century by Stanley Smith Stevens, after whom the resultant Steven’s Power Law was named². He investigated several stimuli, including tastes and vibrations, that showed that there was almost always a non-linear relationship between the measured change of magnitude of a stimulus and the the perceived magnitude of that change. Each type of stimulus then would need some correcting factor to relate the measured and perceived differences.

It will suffice to say that there is a difference between the measured and perceived at this point. For practical purposes, this gives us the confidence that there is some acceptable range where we do not perceive the differences, even if we can find them on our illuminometers. There is a deficiency of Stevens’ model, however, at least for our purposes. His four categories of light measurements yielded different correcting factors based on how the lights were presented. He used a 5˚ target, a point source, a flash and a point source flash. There have been critics of the methodology, the least of which is that there are many other factors that can influence the perception, such as the time between flashes or if the two point sources are viewed at the same time, and if so at what distance from each other.

Keeping it close to our immediate needs none of these match our use case of light dispersed continuously across a large area. But again, knowing that there is some difference between perception and measurement, whatever that correcting factor may be, frees us from the nearly impossible task of making our foot-candles match to the number across the stage. I would contend that using the camera as a guide is useful insofar as it bridges the gap between the perceived and measured–itself mechanically measuring the light, yet re-presenting the contrasts to the eye with a vocabulary that we in the lighting field can adopt, namely f stops.

Defining the Range

I had considered writing out an entire section called “Skip If You Don’t Like Math,” that would have reconstructed the math behind f stops. However, there is an internet full of pages explaining this with lovely graphics that I don’t need to reproduce here. So, let’s skip that math and get directly to the math we need to consider.

In short, the equation for exposure differences in terms of stops can be expressed thusly:
∂x=2^∂y
where X is the exposure, which for us lampies is analogous to intensity, and Y is the stops. The equation can be read as, “The change in intensity is equal to 2 to the power of the change in stops.” For the change in stops, we’ll simply use terms like up a stop or down a half stop rather than the difference from f/1.4 to f/2 (one stop). The reason is that this simplifies the math without having to introduce correcting factors, namely pi and the square root of two. This also means we can speak in relative terms appropriate for any lighting level.

So, if we want to go up one stop, which is to say that ∂y=1, this yields the following:
∂x=2¹
∂x=2

Going up two stops yields:
∂x=2²
∂x=4

This is the same as saying that going up two stops lets in 4 times the amount of light. Going down stops gives us negative exponents. For instance, going down a stop is expressed in this manner:
∂x=2^-1
∂x=1/2

This matches what we know, which is that going down a stop reduces the light intake by half.

We stated above that we want to investigate using a third of a stop as a guideline to what we might consider an even exposure since that is the smallest range that photographers and videographers generally take into consideration. This gives us fractional exponents and anxiety as we struggle to remember ninth grade math (or whenever it was). A third of a stop is expressed as follows:
∂x=2^1/3
∂x=1.2599…..

This would be to say that for any give light level, anything lit up to close to 25% brighter would remain within the minimum exposure difference that most cameras can correct for. It would take a keen eye to see the difference between the top of that range and the bottom, and even then in a controlled circumstance like across a single colored cyc or similar lighting subject with little variation.

The difficulty with that range is that it is from the bottom to the top of the range, assuming that the starting point is at the bottom. In practice, this is uncommon. We commonly have a target and then set our margins on either side of that target rather than on only one side, such as here in the top.

That’s not to say that there aren’t appropriate applications of this rule. I commonly have to set up house light designs where there is a specced minimum brightness, whether per code or internal standards. So, if I want to have an auditorium’s house light levels to be able to hit 25 fc as people move about, then I’d have 25 fc as the bottom of the range and 125% of that, 31.25 fc as the maximum. Granted, cameras probably won’t be taking much footage at those times, but we’re setting initial baselines that we can further refine.

More commonly on a stage, we have a target intensity and want to have our margins set on either side of it. So, if we want a third of a stop as a total range, then we want our margins to be one sixth of a stop both above and below. So, we want to define according to these equations:
∂x=2^1/6
∂x=1.122
and:
∂x=2^-1/6
∂x=.891

Since this is an exponential function, the answer isn’t as simple as taking the number in the middle of the third of a stop range. However, since we’ve reduced our range, we find that we’re fairly close, and maybe even close enough for practical needs. The equations tell us that for any target exposure, the higher margin within that total third range would be 112% and the bottom margin would be 89%.³

So, if we have a target intensity of 70 fc for a stage, as much as we’d love to see our illuminometers read right at 70 fc unwaveringly as we meter across the width of the stage, we can have a definable margin that should be acceptable on camera. 89% of 70 is 62.3 and 112% of 70 is 78.5. This means that if our target is 70 fc, then we should be accepting of readings anywhere between 63 and 78 fc.

Now, that may seem like a lot. It does to me. But let’s remember that we’re trying to define the maximum margin that can be considered acceptable. That range, although larger than is intuitive to those of us that want to be very precise, should at least define the minimum acceptability for creating an even stage wash. And with as many contingencies as we often face setting up our lights in real world situations, we at least have a starting point of discussion. Or, at the least, I have proved an equation that you can plug your own margins into.

Further, the method here is defined in terms of stops but doesn’t require us to constantly think in those terms. The terms of stops are tailored for the needs of photographers and our needs are different. We now have a way to get to the numbers we work with. Percentages help us with that. And we’ll take all the help we can get, because it only gets muddier from here with realities like dimming curves where raising a fader on a console ten percent raises the measured intensity of a light differently depending on the starting point. Or worse, different colors or color temperatures can have different perceived intensity differences, such as is the case with the Purkinje Effect.

Moving Forward

This may not be a perfect solution, although it may point us in the right direction. As was mentioned above, I have never encountered any attempt to define this in our field, and if all this does is spur further conversation on the matter, then I think we would have advanced just that little bit more.

Beyond that, while it may remain a goal to have an even stage wash, the reality is that we don’t always want to have the same amount of light hitting everything anyway. We work with a variety of clients and talent, each of whom bring a diversity of skin tones to our stages. Set pieces might need less focus than our subjects and require less intensity. A presenter may have a white shirt one day and a black one the next. We’ll have to adjust our finely-tuned stage washes to accommodate what is on the stage because, as I always say, I don’t light stages; I light people, i.e. the subjects on the stage.

And that may be enough to spur on another writing about how to get to what really matters, foot lamberts. The camera, or even our eyes, doesn’t care how many lumens you’re blasting at a subject. It only cares how many reflect off. But that’s a next step. A stage that can be washed evenly, whether according to the definitions presented here or by any other definition, should be able to be adjustable to match the needs of whatever rolls across our stages.

¹In a simple sense, a camera is like a lighting fixture in reverse. A light might have an RGB array that projects light through a lens to hit an object, off of which that light bounces, passes through a camera lens that focus the light onto a RGB sensor. In the same way, the optics of f stops can be reverse engineered to get to the intensity needs we need to project from our lights. Since the numbering system system of f stops is geared toward the end user of cameras, we will have to reverse the math to get at the intensity levels we’re more familiar with on the lighting side.

²Stevens, S. S. “On the Psychophysical Law.” Psychological Review 64:3 (1957): 153-181.

³To get ahead of any objections that this gives a range of 23% as opposed to the almost 26% of the third of a stop range defined earlier, we need to remember that the 26% is relative to the lower number whereas the 23% is relative to the target number. 1.122 is 126% of .891.