Incident light metering - Norwood's dome, and noodle, revisted

I have written about this topic several times (including recently) but in fact was never really comfortable with my understanding about what was really going on in this matter. I think that I was "overthinking" it. Now I believe I have a better grasp of what is really going on.

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Incident light exposure metering

In incident light exposure metering, the meter measures the light incident on the subject, and from that measurement (combined with the sensitivity of the film or digital sensor, develops a recommended photographic exposure (combination of shutter speed and aperture).

Simplistically, the objective is to give each area of the scene an "exposure result" that is proportional to the reflectance of that area. In this way, a scene that comprises a white cat on a snowdrift will lead to an image that looks like a white cat on a snowdrift. Under basic reflected light metering, that image might look like a gray cat on an ash heap.

Two meter configurations

Most serious incident light exposure meters offer two configurations. In one, the receptor is covered by a roughly-hemispherical translucent dome. In the other, the receptor (nominally flat) is bare, or in some models, is covered by a filter-like disk put on in place of the dome. In any case, although in this configuration the receiving organ may not be microscopically flat, the intent is that it will respond as would a classical flat receptor (Bart describes it as "simulated flat").

Thus, in the "flat" configuration, we would expect the meter to measure for us the luminance of the incident light upon the plane of the receptor. In the "dome" configuration, the meter measures something else. Just what that something else is, and why we are interested in the meter knowing it, is the mystery that is the subject of this note.

The uses of the two configurations

Typically, the flat configuration (often, and aptly, called the "luminance measurement" configuration) is recommended for such uses as:

• Measuring the luminance of the illumination on a desktop.

• In photography, measuring the impact of the individual lighting sources when setting up a planned overall lighting setup.

The domed configuration is said to be used for "incident light exposure metering".

The realities of incident light metering

If all the surfaces of the important subjects in a scene face in the same direction (and of course they would all have to be flat for that)—not necessarily toward the camera—then measurement of the luminance of the incident light, with reference to the plane with which all the surfaces are parallel, will tell the meter what it needs to know. That illuminance, by the way, will be the same on all our surfaces (we assume none are "shadowed").

Note that it does not matter wither the ambient illumination all comes from one direction, or one source, or otherwise. The behavior of the flat receptor (what we speak of as a "cosine response") will inherently take account of that.

But of course we rarely have that situation. Suppose our subject is a human face. The forehead has essentially one orientation, the cheeks essentially two others.

Now, depending on the overall nature of the light sources, those three surface areas may receive different illuminance. That of course will disrupt any chance that they all will get exposure results proportional to their reflectance.

And of course we often "play" that to our advantage in getting a desired artistic result. We may intentionally arrange for a potent light source on the right side of the face and a far less potent one on the left, so the left side will appear "shadowed".

Now the matter of incident light exposure metering is not nearly so straightforward. No single measurement can simply lead to the "proper" photographic exposure. After all, the meter has no idea that we want the subject's left cheek to be "darker" than its reflectance would dictate.

Nevertheless, photographers, especially in less extreme situations, are anxious to get "the answer" from their incident light meter.

"The answer"

One approach can be unscientifically described as to try and measure the "average illuminance" on the variously-oriented surfaces of the subject.

One way to do that would be to have a meter whose receptor did not have a cosine response but was rather omnidirectional. That is, its reaction to a shaft of light of a certain potency was independent of the angle at which it arrived on the receptor. We could make a meter that did that by giving it a spherical receptor.

The work of Don Norwood

Famed cinematographer Don Norwood, the developer of the famed series of incident light exposure meters that bear his name, was one of the first to study this concept.

It seems to me as if he reasoned thus:


OK.

In other words, perhaps we wanted to have the meter have an omnidirectional pattern out to 90°, but be "dead" beyond that. And we would always face it toward the camera.

Now to continue my interpretation of Norwood's presumed thoughts:

But if we do that, then the response of the instrument turns out to follow very nearly the mathematical curve called the cardioid—not a uniform response out to 90° and none beyond.

Now does this follow the concept of "measuring the average luminance upon all surfaces not facing away from the camera"? No.

But in fact there is no theoretical basis for concluding that such a measurement would be the "ideal" one to guide photographic exposure, with a single measurement, over a wide range of different situations. It just "sounded reasonable".

Evidently, Norwood found that metering with a hemispherical receptor (to use my words) "gave a good result in many cases".

And so, the "cardioid" receptor response of an incident light exposure meter became enshrined in the armory of the industry. The international standard for the properties of freestanding exposure meters, ISO 12232, even prescribes a cardioid response for the "exposure measurement" mode of incident light exposure meters.

And of course meters based on Norwood's patents (by his firm and various successors-in-interest) became widely used, especially in the cinema industry.

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And to think of the hours I spent trying to develop a theoretical model for why the measurement taken with a meter with a cardioid response would be a good one to use for general.

So "domes up", soldiers.

I close with some images. Here is what is arguably the most beautiful exposure meter ever made, the Norwood Director Model B, as made by American Bolex (ca. 1948):


Here we see the noted Turkish cinematographer Erkan Umut making an incident light measurement for Sibel Can, the famous Turkish singer (1996). The meter is a Minolta Autometer IIIF.


Best regards,

Doug

I believe I have cracked another conundrum in the matter of the two responses ("cosine" and "cardioid") for incident light exposure meters.

The "calibration" of the meter is defined by the constant C. The international standard "allows" a wide range of values of C. But a separate range is specified for the "domed" (cardioid pattern) and "flat" (cosine pattern) form of such a meter.

Both ends of the range for the cardioid form are about 4/3 the values for the cosine form. Simplistically, that means that the cardioid form expected to be set up to be "less sensitive" than the cosine form. What's with that?

Well, first note that the "sensitivity" as described by the calibration equation (depending on the value of C), refers specifically to light striking the meter "head on" (that is, perpendicular to the plane of its receptor).

For both "patterns", the sensitivity declines as the angle of arrival of the light increasingly departs from "head on". In the case of the "cosine" pattern, this is needed so that the meter will in fact recognize the actual luminance of a possibly-complicated light source situation.

For the cardioid ("dome") pattern, this decline is slower than for the cosine pattern.

If we were for some reason interested in the two configurations having the same "average" sensitivity over all angles of arrival, then the "head on" sensitivity for the cardioid pattern would have to be less than for the cosine pattern (since the sensitivity of that pattern "declines less" with increasing angle)—more on the sides, thus less "head-on".

And in fact, the specified relative values of C for the two configurations fit very closely with that model.

A physical interpretation of that, likely the premise for the arrangement, is that if the manufacturer chose values of C for the two configurations that differed in the ratio of the specified ranges, then the meter in its two configurations would give essentially the same exposure recommendation when exposed to the same "omnidirectional" illumination—illumination where the light arrived uniformly from every direction.


Best regards,

Doug

By the way, to compare the two different receptor configurations, here is a Norwood-style meter (at the time branded by Sekonic) in its "cardioid" configuration (with the dome):


Here is a slightly different model equipped with the Lumidisc in place to adapt it to the cosine ("flat") mode:


Best regards,

Doug

This gem is from the "Q & A" section of a user manual for an early Norwood Director incident light exposure meter (ca. 1952):


Of course, we know that outlook is a bit fanciful, but this is the essence of the Norwood concept.

Best regards,

Doug

I was pleased to have cracked the conundrum of the differing values of the incident light exposure metering constant, C, for the cosine response ("flat receptor") and cardioid response ("hemispherical receptor") forms of the meter.

But I still remained uncomfortable with my understanding of the value of the cardioid response in determining the desirable exposure. Finally, it came to me. Here is the story as I now understand it.

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The underlying objective

Simplistically, the underlying objective of incident light exposure metering is to, in the image, have each element of the subject end up with a photometric exposure that is, as a fraction of the "saturation photometric exposure", equal to the reflectance of that element. (This is closely related to the underlying concept of the Zone System.)

Incident light metering

We basically seek to attain this objective by measuring the illuminance of the incident light and from that (along with the known or assumed sensitivity of the film or digital sensor) selecting a certain photographic exposure (combination of shutter speed and aperture), following a linear incident light exposure metering equation.

The catch

The complete success of this technique depends on all significant surfaces of the subject receiving the same illuminance. But often this is not so because:

• Different subject surfaces face in different directions (e.g., for a human face essentially every spot faces in a different direction), and

• The luminous flux density of the arriving incident light is not the same from every direction of arrival (certainly common for many "indoor" situations, including studio lighting setups).

This fact prevents full attainment of the underlying objective mentioned above. There is no single exposure that will fulfill that objective, and no metering scheme can overcome that.

But so it shouldn't be a total loss

But perhaps, all that being said, we should try and make the best of the situation by trying to determine the average luminance over all of the subject surfaces that can be seen by the camera*, and basing our exposure on that.
Then, "on average", we will attain the objective.

Is that the "best thing" to do? Maybe not. But it is easy to do, and thus is perhaps a good "default" technique.

But how do we do that?

We could conceptually imagine doing that that by an elaborate scan over the (visible to the camera) surface of the subject with a luminance meter, and combining those many readings mathematically to get the average. But that is hardly practical for ordinary photography.

But we can do it in one measurement with a clever trick. We use a meter whose receptor is a hemisphere, with its "peak" facing the camera. This is a proxy for the part of a human subject's head surface that it visible from the camera.

The average illuminance on that hemispherical surface is proportional to the total luminous flux that strikes it (which is to what the hemispherical receptor responds). Thus, the meter's determination is a good approximation of the average luminance on the portions of the surface of a human head that are visible to the camera.

The cardioid response pattern

Where does our interest come from in having the "directivity response" of the meter follow the cardioid mathematical function?

Well, if we have a hemispherical receptor, we find (as a simple matter of geometry) that the area it presents, seem from a point at some angle with respect to the axis of the hemisphere, in fact follows the definition of the cardioid function. The amount of luminous flux collected by the hemispherical receptor from a beam of a certain luminous flux density is just proportional to its projected area in the direction from which the beam comes. And the response of the meter follows that.

Thus a hemispherical receptor will exhibit a cardioid directivity response. It is not the cardioid response itself that makes this scheme work, but rather the behavior of the hemispherical receptor as a proxy for the subject. The cardioid response is just an unavoidable property of that scheme.

Generalizing the concept

But now, if we wanted to use some other implementation of this concept than a hemispherical receptor (perhaps we don't want to infringe Norwood's patents), so long as the directivity response of the meter follows the cardioid function, the result must be exactly the same as I described above.

Thus, for example, in the international standard for exposure meters, for the incident light type, for one form a cardioid directivity response function is specified. (For the other form a cosine response is specified.)

Best regards,

Doug