Norwood's dome in incident light exposure meters

[Doug Kerr]

First I note that there is not, to my knowledge, any "theoretical model" that gives rise to the "duplex metering" photographic exposure metering technique or that might "justify" it.

Thus we cannot "on paper' determine whether averaging the two readings on an "arithmetic" or "geeometric" baiss would be the most appropriate.

Many examples of the use of "duplex metering" found on the Internet (including in some YouTube videos) mention the "averaging" of the two meter readings, but almost never say how to do that (and thus what kind of average is involved, arithmetic or geometric).

But in some cases a numerical example is given, and those mostly suggest that geometric averaging was used.

This is relatable to a reckoning using the dials on an exposure meter's exposure calculator. We recall that the scales on these dials are logarithmic with respect to the quantity involved.

Choose some arbitrary aperture. For each of the two measurements, note the recommended shutter speed at that aperture. Now note the shutter speed that, on the calculator scale, is halfway between those. That shutter speed, with that same aperture, is the exposure recommendation based on this form of duplex metering.

This works because "geometric average" and "logarithmic average" are exactly the same thing.

One can then set that arbitrary aperture against this "midway" shutter speed, and then the exposure recommendation can be read as any of many combinations of aperture and shutter speed.

Another way can be used if the exposure calculator shows the exposure recommendation in terms of Ev (uslally marked "EV".)

For each of the two measurements, note the Ev shown on the calculator. Take the arithmetic average of those two Ev values. Set that as the "Ev" value. The exposure recommendation can then be read as any of many combinations of aptrure and shutter speed.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

It seems that when Norwood stated his work on exposure metering, the widely-used (and seemingly well-accepted) metering method for closeup shots of an actor's face in cinematography was the so-called "duplex metering" technique. (Just exactly what that means will discuss shortly.) This technique was burdensome in that it required two measurements to be taken for each shot.

Norwood's quest was for an instrument that could, with a single measurement, give a photographic exposure recommendation that was "as appropriate" as the one given by the duplex metering technique.

Now the matter of an "appropriate" photographic exposure is complex and subjective. But I think we can stipulate that if, for various specific well-defined lighting examples, two metering techniques yielded essentially the same photographic exposure recommendation, we could consider them to give essentially "equally appropriate" results.

Next we will have to adopt a complete definition of the "duplex measurement' scheme to be assumed. Considering the overall context of cinematography at the time, I think the most reasonable one is this:

• Using an "incident light" exposure meter that truly responded to the illuminance on its receptor, with both key and fill lights active, we make two illuminance measurements, both with the meter at essentially the subject's location:

1. With the meter axis toward the fill light

2. With the meter axis toward the key light

Those two illuminance readins are avaerged (I will assume for the moment arithmeticlly) and the result "fed into" the meter's exposure calculator to yield the exposure rcommendation.

So lets take a specific case and compare the two. I will assume the fill light at the camera position and the key ight at 90° to one side. And I will assume that the iluminance of the fill light is 0.125 of the illuninace of the key light. (That;s a pretty "hot" fill light, but I use this case to make the result stand out better.)

Fisrt I consider the duplex metering case. For the first meaurement, the fill light (head on) contriutes 0.125 units to the overall illumninance reading; the key light contributes nothing (since it at 90° to the meter axis, and the meter is assumed to have cosine directivty, the directivity corefficient wouold be the cosine of 90°, which is zero.) So that overall illuminance reading would be about 0.125 unit)

For the second meaurement, the fill light contriutes nothing (since it at 90° to the meter axis); the key light contributes 1.0 unit. So the second illuminance reading would be 1.0 unit.

We average those two illunminance radings (arithmetically) and get about 0.56 units. The "duplex metering" exposre recommendation would be based on that value.

Now we consider the use of a Norton meter. I will assume that it is calibrated so that for "head on" light, its exposure recommendation would be that same as given by a basic incident light meter for "head on" light.

But now we use it to meanure our key-fill lit actor. The meter is placed at the actor's position with its axis toard the camera (and fill light),

The fill light contributes about 0.063 units to the overall excitation of the meter. (Its luminance is 0.125 unit, It is at an angle of 90 to the meter axis. For a classical Norwood meter, the diectivity coefficient at 90° is 0.5. So 0.125 x 0.5 = 0.063.)

The key light contributes 1.0 unit to the overall excitation of the meter. Its luminance at the actor's postion is 1.0 unit, and the directivity of a Norwood meter at 0° ("head on") is 1.0.

Thus the total excitation of the meter is 1.063 unit. Accordingly, the exposure recommendation that the Norton meter would issue would be about 0.92 stops greater than we would expect to be issued by the duplex metering technique.

If in fact the actual practice "in the day" for duplex metering was to use the geometric average of the two illuminance readings, then the result of the duplex measurement would have been 0.35 unit.Then the exposure recommendation with the Norwood meter would have been about 1.60 stops greater than we would expect to be issued by the duplex metering
technique.

Interesting.

Best regards,

Doug

Interesting indeed Doug when applied to these two clearly explained instances of duplex metering (arithmetic and geometric means). Thank you for taking the time!

best,

Ted

 

[Doug Kerr]

A "rule of thumb", apparently widely followed at one time, tells that for the (sole) light source being at about an angle of 90° from the camera, the appropriate exposure would be about one stop greater than if the same light source were at the camera position.

It is interesting to compare this with the "duplex metering" approach also widely followed 'in the day" for that lighting situation.

I assume that, as generally recommended, we configure the exposure meter to make a "true illuminance" measurement (that is, typically, with the "flat", rather than "dome", light collector in place.

Suppose that, following the duplex metering protocol, we take a first reading with the incident light exposure meter at the subject position aimed toward the camera. We would expect that reading to be zero (the directivity of the meter being zero at 90° to its axis).

We then take the second reading with the meter at the subject position aimed toward the single light source. We would expect that to be the same as if we had this same light source at the camera, and metered with the meter aimed toward it. That is, the exposure recommendation from our second measurement alone would be the same as the "reference exposure".

Now, when we average the two readings, we would get (I will express these results as relative to the "reference exposure);

a. If the averaging were arithmetic, an "average" illuminance of 0.5 (and thus an exposure of 2.0 times the reference exposure).

b. If the averaging were geometric, an "average" illuminance of zero (and thus theoretically infinite exposure.

I note that result a is consistent with the result of the "rule of thumb" for this situation. Result b is of course absurd.

******

It is then interesting to compare these results with what we would expect of a "Norwood" exposure meter (according to his first generation plan) for this same lighting situation.

I will not go through all the numbers, but it turns out that we should expect the exposure recommendation from the Norton meter to be half that if the sole light were at the camera position. This is of course the same as I show above for duplex metering (for this lighting setup).

(We would not necessarily have that agreement for more complex lighting setups, such as when we have a key light and a consequential fill light.)

Just sayin'.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

It is not at all unlikely that the use of the geometric mean may be a misunderstanding, perhaps brought about by the matter I discussed above about the geometric average between, say, two shutter speeds being halfway between their positions on the exposure calculator dial.

Would this not have been discovered? Sure, but remember none of these techniques produces a "definitive" exposure recommendation. So if some photographer uses the "geometric mean" calculation, and finds the result too greatlkyb exposed for his liking, he will just in that same situaion later offset the recommendation to taste.

Maybe.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

We often encounter a similar misunderstanding with regard to "average" shutter speeds, owing to our habit of thinking of the denominator of the speed.

For example, if for some reason one wished to take the (arithmetic) average of the two shutter speeds 1/60 s and 1/120 s, it is tempting to some to think that the average is 1/90 s. Of course the arithmetic average of those two speeds is 1/80 s.

Best regards,

Doug