About incident light metering

Incident-light exposure metering is a valuable technique for placing the photometric exposure of different scene elements at points along the entire "tonal scale" that correspond to their reflectance.


Faking it

If we do not have a competent incident-light exposure meter, we can still use the technique by having the exposure metering system in our camera regard (with "spot" metering) a diffuse, neutral ("gray"), uniform-reflectance "card" placed in the scene at the place where we want to measure the incident illuminance.

But what should the reflectance of this metering card be? There are several ways to get at that.

One approach is to say that we would trust the recommendations of a competent incident light exposure meter, and want to use a card that will cause the (reflected-light) metering system in our camera to give the same result. Let me pursue that approach.

The "calibration" of a reflected-light exposure meter (or automatic exposure control) can be characterized in terms of the reflected light exposure meter calibration constant. K. The "calibration" of an incident-light exposure meter can be characterized in terms of the reflected light exposure meter calibration constant, C.

The international standard for inbuilt automatic exposure control systems in effect prescribes a value of 12.5 for K (although nowhere does that appear in the standard).

The international standard for free-standing incident-light exposure meters allows a fairly wide range of values of C. Often, for respected incident-light meters, a value of 340 is stated by the manufacturer.


If we consider a C of 340, and a K of 12.5, then to make the result of the camera's "incident-light" metering system, regarding a metering card, comparable to the result of the incident-light meter, the reflectance of the metering card would need to be about 11.5%.

We all know that metering cards with a nominal reflectance of 18% are, for various historical reasons, often used. The result would be that the result of the camera's metering system, regarding the card, would be about 0.3 stop lower than the result of the hypothetical incident light meter.

If we indeed want to make the camera-plus-card rig comparable to the hypothetical incident light meter, we would need to apply an exposure compensation of about +0.30 (say, + 1/3 stop).

The matter of exposure index

Headroom and its eating

The classical definitions in the field of exposure metering standards assume that the exposure index that is an input to the meter's "computer" is the ISO speed of the film or digital sensor.

The underlying predicate of the standard for reflected light exposure metering is this: for a scene in which the average reflectance is 18%, the photometric exposure for a 100% reflectance area (probably brighter than the brightest realistic object) would be about 1/2 stop shy of saturation. This so-called "1/2 stop headroom" is primarily intended to avert the possibility of overexposure by a high-reflectance area in a scene where the average reflectance is substantially lower than 18% (a pretty arbitrary value anyway).

The underlying predicate of the standard for reflected light exposure metering is this: the photometric exposure for a 100% reflectance area (probably brighter than the brightest realistic object) would be about at saturation. No headroom? No need. That system does not depend on any assumption about average scene reflectance. It deals with each area as it is.

Noe, the sophisticated reflected-light metering modes in modern digital cameras do not merely work on the basic of a measured overall average scene luminance, but rather meter the luminance at multiple points and, from that collection of data, attempt to predict the brightest area. Accordingly, the "1/2-top headroom" is not really profitable, and in fact represents "burning" of part of the camera's dynamic range.

So camera manufacturers decided that, in general, an exposure should be used that is about 1/2 stop "hotter" than that which would be suggested by the traditional exposure equations. They could do that in three ways:

A. In effect, bump the K of the metering system by 1/2 stop from that suggested by the international standard.


B. In effect, feed into the exposure metering algorithm an exposure index that was about 1/2 stop lower than the actual ISO speed of the sensor. This wouild be like a hidden exposure compensation of +0.5 stop.


C. Rate the ISO speed of the sensor at about 1/2 stop less than it would be as described by the ISO specification, and feed that into the system as the exposure index.


So the camera manufacturers arranged for the ISO to do this:

D. Define a mew measure of digital camera sensor sensitivity, the ISO Standard Output Sensitivity (ISO SOS) that was essentially 1/2 stop lower than the ISO SOS. Then, if that was fed into the exposure control algorithm, the result would be the desired "1/2-stop" hotter exposure, "spending the headroom".

So if people said, "The ISO speeds announced for the Canon EOS 40D are a half stop too low", the response, is "No, no, those are ISO SOS values, and are accurate.

Back to the story

Now returning to our harmonizing the results from an actual incident-light exposure meter and our camera regarding a metering card.

We saw earlier that to theoretically harmonize those, when using a metering card with a reflectance of 18%, we would need to "bump" the exposure in the digital camera by about +1/3 stop from that given by a "standard" (i.e, K=12.5) metering system.

But the use of ISO SOS, rather than ISO speed, as the exposure index, essentially imposes a +1/2-stop bump in exposure.

So for openers, we should just go with the result from the 18% reflectance card.

Thus, this curious story has led to the "rehabilitation" of the 18% reflectance card!

Which cameras use ISO SOS?

To the best of my knowledge, the Canon EOS DSLRs use the ISO SOS basis for rating sensitivity.

Actually, Canon says that they use SOS REI, which means that they have chosen an arbitrary value that they think works well, with no technical definition, but then they tell us that the intent is that this be essentially the ISO SOS.


To the best of my knowledge, the Nikon DSLRs use the ISO speed basis for rating sensitivity.

Actually, Nikon says that they use SOS REI, which means that they have chosen an arbitrary value that they think works well, with no technical definition. But information from colleagues suggests that this is essentially the ISO speed.

But, there is also the issue of how the spot metering mode works compared to, for example, a center-weighted average mode. That could change the implications of the use of a metering card. I have no insight into this.

About "18% gray"

The gray card with a reflectance of 18% if very often called an "18% gray card". But in fact its color is not 18% gray. Its color is 82% gray. So to avoid misunderstanding, we should perhaps speak of an "18% reflectance gray card".

Best regards,

Doug

In the original note in this thread, I essentially said, regarding incident light metering technique:

A. We are interested in the illuminance upon the subject.

B. An incident light meter (or multi-mode meter in the incident light mode) measures that.

C. We can also measure that by using a reflected light meter (or our camera's exposure metering system) to regard a "gray card" exposed to the illuminance on the subject.

But in fact, in the general case, B is not actually true. I oversimplified the situation to get on with my real point. Here, I will deal with the reality.

Illuminance

If we have a beam of light with a certain luminous flux density (a quantity we do not hear much about; it is an un-noticed "intermediate result" of the chain that leads to luminance), then the illuminance it causes on a surface is proportional to the product of the luminous flux density of the beam and the cosine of the angle of arrival of the beam (measured from a direction perpendicular to the surface).

An illuminance meter

If we wanted to make a meter to measure illumination, we would need for the meter, when its photoreceptor is struck by a beam of light with a certain luminous flux density, to "recognize" the product of the luminous flux density and the cosine of the angle of arrival of the beam. Thus we say it must have a "cosine response".

Is that tricky to arrange? Fortunately, not at all. A flat photoreceptor essentially responds to the illuminance on it. That is just what we want. And of course we can then say that such a photoreceptor has a "cosine response".

The reality

Of course, for this process to work out, we must know the luminance on the subject. If the subject is a flat surface that is easy to measure. We need to have the flat photoreceptor of our hypothetical illuminance meter at the subject and parallel to its surface.

But in general our subject is not a flat surface. Suppose it is a human head. Will it receive the same illuminance on all parts? Not necessarily. It depends on the nature of the light source. If the light comes only from about the direction of the camera, the luminance at the ears will be much less than on the center of the forehead (those pesky cosines again).

So how can we determine the "proper exposure" by metering? If our intent is for all parts of the head to end up at the same place on the camera's tonal scale, there is no single exposure that will do that. And of course, we may with to set up our lighting to produce the luminance we want on different parts of the head to get the proper "modeling".

In cinematography

I am not wholly convinced of the rationale that leads to the exposure meter design I will discuss here. But I will proceed to tell the story as I understand it.

In cinematography, great emphasis was placed on determining the proper exposure before a take by metering.

Apparently, using actual measurement of the luminance on the subject (say based on a subject surface "facing" the camera), done with an incident light meter with cosine response, often "understated" the effective luminance, leading to the "recommendation" of a greater photographic exposure than was desirable.

Cinematographer Don Norwood, in his patent on the exposure meter design I will be discussing here, said, in effect, "That's because the light arriving from the side is 'discounted' (by the cosine response of the "flat photoreceptor" exposure meters of the time). So he suggested that the meter should "take greater account" of light from the side. We could describe that as the meter having a response pattern that declined more slowly with increasing angle than the cosine pattern of a "flat photoreceptor" meter.

Now of course light arriving "from the side" is also "discounted" in its effect on the illuminance upon a camera-facing subject surface. So for such a surface, the reading of a "flat photoreceptor" meter has the correct implications on exposure. (That's why we give the meter a cosine response.)

Of course light from the side is greatly effective on the luminance of a side-facing surface (let's say the model's cheek). It would only properly be recognized by a flat-receptor meter with the receptor parallel to the cheek.

And of course, in truly-scrupulous metering, measurements at various angles should probably be taken, and a decision made as to how to choose the photographic exposure to "place the different surfaces on the tonal scale" the way the cinematographer has in mind. And if that can't work out, then the lighting needs to be changed.

But Norwood's work was based on the presumption of a single measurement. In effect, he said, "Light from all directions should be equally recognized in the meter reading." And I don't follow the rationale of that.

For example, first suppose that the overall lighting comes "uniformly from all directions". Then an actual illuminance measurement for any meter orientation, will tell us what we need to know to choose the proper exposure.

And if the light does not come substantially uniformly from all directions, then the luminance on the differently-oriented parts of the subject will be different, and no single measurement is definitive as to exposure.

A dome of its own

In any case, Norwood's approach to making the response of the meter fall more slowly with increasing angle (in his initial patent) was to use a hemispherical photoreceptor (a translucent hemispherical dome with a hemispherical photoreceptor nestled just inside it

This was later replaced by a hemispherical translucent dome with a flat photoreceptor at its "mouth" (mush less costly to manufacture). This of course became the hallmark of meters following Norwood's design (such as the famous "Norwood Director" series).

Now, how did Norwood determine what the ideal response pattern is, what was it, and how did the translucent hemisphere attain it (or approximate it)?

Well, in Norwood's patent, he tells a story based on a hypothetical hemispherical subject (that being a proxy for the head of a subject - that is, the half of it that faces the camera, the rest being of no importance), and smoothly travels to the fact that the hemispherical dome of his device would thus receive light comparable to that received by the hemispherical "head" (which after all would seem to be want we would want to measure).

The problem with that model is this. Indeed the hemispherical dome would collect the same amount of light overall that landed on the hemispherical head (and deliver that to the photoreceptor for measurement).

But it is not the total amount of light that falls on the head that is of interest to us. We are interested in the luminance on various parts of the head. And if the light is not uniform in its direction of arrival (and if it is, this whole matter becomes trivial), that luminance will not be uniform for all portions of the head surface.

So is the total amount of light that hits the head at least an indication of the average luminance (let's say, as averaged over the field of view from the camera). Not necessarily. It if it were, is that the best indicator of the proper exposure? Probably not.

But, moving right along anyway.

The pattern of the Norwood system.

It turns out that in an ideal situation, with a hemispherical diffuse dome over the photoreceptor, the response pattern would be not be:

where A is the angle of incidence but rather this:

In fact, a polar plot of this pattern is the famous "cardioid" curve. And this indeed declines more slowly than the cosine pattern.

Is this an ideal pattern? There is no derivation of what an ideal pattern would be - only a story that proceeds from a hemispherical head. But we get it with a dome.

Based on Norwood's initial premise, wouldn't a uniform pattern be the best? Maybe. But that is a little less handy to implement. (You have to have a sphere collector, with only a wee hole for the collected light to be observed by the photoreceptor, so the photoreceptor has to be wee, and then the whole thing is less sensitive, etc. etc.)


In the international standard

In fact, the international standard for exposure meters (ISO 2720) provides for two approaches, one with a cosine pattern and one with a cardioid pattern. Why two? Well the standard speaks to that thus:

A. For the "flat receptor" pattern (cosine): to determine actual illuminance if that is what you want to know; to make measurements of individual sources in a multi-light studio situation for "light balancing" purposes.

B. For the "hemispherical receptor" pattern (cardioid): For general purpose photographic exposure determination.

Why is the cardioid pattern the second one? Because that's what Norwood's basic implementation used. And people seemed to like the results (his company and its successors sold a lot of meters).

According to the standard, a different value of C (the incident light metering calibration constant) is used for the "cosine" and cardioid" patterns. My guess is that this is to make the two kinds of meter give the same exposure recommendation for some defined arrangement of light sources (possibly uniform omnidirectional light).

For light that comes from "head on", the cardioid meter will call for a greater exposure (as if it assessed the light as "less").

Actual meters

In fact, for many serious exposure meters using a dome in their incident light mode, the dome can be removed, and the explanation of the purpose of that parallels the language of the standard as I quoted above.

That is, if we really want to measure illuminance (for some scientific purpose, or some complicated photographic planking purpose), including ascertaining the illuminance caused at a certain point by individual photographic lighting sources, we need an actual illuminance meter, with a cosine response (meaning with the dome off).

But if we are just going to shoot a subject, and want to make one measurement, we can partake of "Norwood's technique" and use an instrument with a cardioid pattern or thereabouts (that is, with the dome in place).

Now does a meter with a cardioid pattern (or thereabouts) actually give, by way of a single reading, "the best exposure guidance over a range of lighting situations and subject shapes"?

Beats the hell out of me.

And if so, why does that happen?

Beats the hell out of me.

Remember, I was never able to figure out how Drew Strickland's white balance measurement diffuser could work when aimed at the scene from the position the camera will have for the shot. And he says he sells plenty of those.

Best regards,

Doug