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

 

[Ted Cousins]

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

Goddit, thanks.

all the best,

Ted

 

[Doug Kerr]

Norwood and the "rule of thumb"

Don Norwood, in his 1950 paper before the SMPTE, "justified" his dome exposure meter concept through a very interesting series of subjective experiments.

The subjects were the faces of a series of human models. For each subject, Norwood first took a photo (on B&W film) with a single light source located at essentially the camera position. The photographic exposure used was, we believe, based on incident light metering (presumably using some well-accepted "exposure equation"). This was called the "reference image" for that subject.

Then, for the same subject, Norwood moved the same light, at the same distance from the subject, to different angles compared to "at the camera position". Angles of 45°, 90°, and 135° were used.

With the light at each of these positions Norwood took several shots with varying photographic exposures.

All the negatives were developed with scrupulously consistent processing, and print made from each with a consistent enlarger exposure.

Then, a number of observers were asked to review those prints, and for each subject, for the shots at each angle away from the camera position, to choose which shot they felt was the same in "exposure result" (my term) to the shot made with the light at the camera position.

Norwood then analyzed these responses. This showed that, for each angle of the light position (away from at the camera), the shots that were judged as having the same exposure result as the shot with the light at the camera position had an photographic exposure greater than for the "reference shot" by a rather consistent amount. This needed exposure increased very nearly linearly with the angle of the light, reaching about 2X (one stop) greater at 90°

Norwood characterizes this by saying that the "effectivity" of a certain light source decreased linearly with the angle of the source (falling to 1/2 at 90°).

Norwood them went on to say that, since the theoretical sensitivity of a hemispherical light receptor decreased linearly with the angle of the light striking it (not so), reaching 1/2 at 90° (true), an exposure meter with a hemispherical receptor would inherently "discount" each component of the light striking it consistent with the "effectivity" of light from that angle in image exposure (thus leading to the appropriate photographic exposure recommendation).

One light position of special interest was with the light at 90° from the camera. There, Norwood found, the required exposure for the same subjective "exposure result" as for the reference shot was consistently about one stop greater than for the reference shot.

We note (and Norwood noted) that this is fully consistent with the infamous "rule of thumb", which suggested that for a shot taken with the light located exactly to the side (i.e., at 90°) the proper exposure would be one stop greater than would have been used were that light at the camera position. To bring this about, the sensitivity of the exposure meter for light arriving at an angle of 90° compared to its sensitivity for "0°" light (its "directivity" for 90°) should be 1/2 ("one stop down"). And the directivity should be linear with angle.

Norwood apparently took great stock in that correspondence. In a later patent, he mentions that, as time had gone by (and photographers' standards of proper exposure had evolved), the rule of thumb had become to use an exposure, for the light source at 90°, of only perhaps 1/2 to 2/3 stop greater than with the same light at the camera position (rather than one stop greater, as had been earlier suggested).

Accordingly, Norwood said, the proper directivity for the receptor of a Norwood-type exposure meter at the 90° angle would be "1/2 to 2/3 stop" less than at 0°.

In the patent, he went on to show how certain modifications of the light collector would in fact give this modified directivity.

It is a fascinating "trail".

Best regards,

Doug

 

[Doug Kerr]

This is what Norwood said in that patent, verbatim (other than that I have changed the paragraphing a little in the interest of readability)

******
At the time that the device disclosed in my prior patent was designed, it was considered desirable by most photographers that the camera lens settings used under front and side lighting conditions differ from one another by one full f-stop, assuming that the intensity of the light source remained the same.

That is, if a particular f-stop setting were determined to be proper under a certain front lighting condition, then the camera lens aperture should be opened up one full f-stop more if the same light source were located at a side lighting position. With the same light source in a backlighting position, it was considered that the lens aperture should be opened up another full f-stop.

The hemispherical light collector dome of my prior patent was so designed as to inherently and automatically give this desired one full f-stop differential in reading between front and side lighting conditions, and between side and back lighting conditions. Since the issuance of that patent, however, the characteristics of films have changed considerably, and the opinions of photographers as to what lighting effects are aesthetically most desirable have also changed.

With particular reference to the relationship between front, side and back lighting, the film manufacturing companies are now suggesting a differential of only one-half f-stop in camera setting as between front light and side lighting, and between side lighting and back lighting. Many expert photographers feel that the proper differential is two-thirds of an f-stop between these various steps, but at any rate it is clear that the full f-stop differential previously recommended should no longer be used.

******

Later in that patent he suggests that the ideal meter directivity at 90° is down 2/3 stop from the sensitivity at 0°. (Earlier he had recommended down one stop.)

I do not have authoritative directivity curves for any "modern" exposure meters to see whether their manufacturers have hewed to that recommendation.

Best regards,

Doug

 

[Ted Cousins]

This is what Norwood said in that patent, verbatim (other than that I have changed the paragraphing a little in the interest of readability)

******
At the time that the device disclosed in my prior patent was designed, it was considered desirable by most photographers that the camera lens settings used under front and side lighting conditions differ from one another by one full f-stop, assuming that the intensity of the light source remained the same.

That is, if a particular f-stop setting were determined to be proper under a certain front lighting condition, then the camera lens aperture should be opened up one full f-stop more if the same light source were located at a side lighting position. With the same light source in a backlighting position, it was considered that the lens aperture should be opened up another full f-stop.

The hemispherical light collector dome of my prior patent was so designed as to inherently and automatically give this desired one full f-stop differential in reading between front and side lighting conditions, and between side and back lighting conditions. Since the issuance of that patent, however, the characteristics of films have changed considerably, and the opinions of photographers as to what lighting effects are aesthetically most desirable have also changed.

With particular reference to the relationship between front, side and back lighting, the film manufacturing companies are now suggesting a differential of only one-half f-stop in camera setting as between front light and side lighting, and between side lighting and back lighting. Many expert photographers feel that the proper differential is two-thirds of an f-stop between these various steps, but at any rate it is clear that the full f-stop differential previously recommended should no longer be used.

******

Later in that patent he suggests that the ideal meter directivity at 90° is down 2/3 stop from the sensitivity at 0°. (Earlier he had recommended down one stop.)

I do not have authoritative directivity curves for any "modern" exposure meters to see whether their manufacturers have hewed to that recommendation.

Best regards,

Doug

 

[Ted Cousins]

Interesting that Sekonic's L-398A dome illustration shows these angles

Fill and "back" lights apparently at 45 deg to the main light.

And page 11 for the 398A shows a 'contrast ratio' of 1EV, not 2/3 EV:

https://images.salsify.com/image/upload/s--4IXyBA16--/zv7etx1awyn1y8bjg2gg.pdf

Sekonic ... Consistency 'R' us ...

 

[Doug Kerr]

A few years ago I ran directivity curves on several incident light exposure meters from our collection. The setup was primitive, and I have no idea how close any of these meters were to "factory" performance, so I cannot express a very high degree of confidence in the results.

That having been said, for our Sekonic L-398M meter, the directivity at 90° measured at 0.41 (-1.28 stops).

That compares to:

0.5 (-1.0 stop) the value suggested by Norwood's original work.
0.5 (-1.0 stop), the theoretical value for a hemispherical light collector
0.63 (-2/3 stop) the value suggested by Norwood in his later patent.

Interesting.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

Interesting that Sekonic's L-398A dome illustration shows these angles

View attachment 14175

Fill and back lights apparently at 45 deg to the main light.

That illustration is very bad. Almost certainly the intent is for the "back light" (one general location of the "key light") coming from an angle of 135° and the "fill light" from an angle of 0. The arrows only suggest that each of the lights hit the dome (and of course they all actually hit all of the dome that they can geometrically).

And page 11 for the 398A shows a 'contrast ratio' of 1EV, not 2/3 EV:

https://images.salsify.com/image/upload/s--4IXyBA16--/zv7etx1awyn1y8bjg2gg.pdf

That speaks of some illustrative ratio between the measured "potency" of two light sources, and has nothing to do with the directivity of the meter.

Neither does that suggest what photographic exposure should be used for a light at 90° only (compared to with the same light at 0).

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

That illustration is very bad. Almost certainly the intent is for the "back light" (one general location of the "key light") coming from an angle of 135° and the "fill light" from an angle of 0. The arrows only suggest that each of the lights hit the dome (and of course they all actually hit all of the dome that they can geometrically).

That speaks of some illustrative ratio between the "potency" of two light sources, and has nothing to do with the directivity of the meter.

Neither does that suggest what photographic exposure should be used for a light at 90° only (compared to with the same light at 90°).

Best regards,

Doug

As Alice in Wonderland said "Curioser and Curioser" ...

Best,

Ted.

 

[Doug Kerr]

The famous Weston "Master" series of exposure meter are natively reflected light meters, but there was for them available an accessory light collector (two different types, in fact) to equip them for incident light metering.

These had the name "Invercone". They were not hemispherical but rather had a inverted cone surrounded by a frustum of a hemisphere. It is suggested in the literature that this structure was not necessarily developed to gave a more appropriate directive curve than a hemisphere, but rather had been developed to avoid the use of Norton's patents.

Again many years ago I did test on the directivity of a sample meter of this family from our collection, and again I warn that this was not necessarily very precise.

That having been said, the measured directivity of this meter (in the horizontal plane), with the "newer" type of Invercone collector, at 90° was very near to 0.5 (1.0 stop down).

The measured directivity of this meter (in the horizontal plane), with the "older" type of Invercone collector, at 90° was very near to 0.2 (2.3 stops down).

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

The underlying clinker in all this is that there cannot be any exposure metering process based on a single measurement (or even on two measurements) that will fulfill the various (and differing between individual photographers' "objective" of the exposure process, especially when we wish to encompass a range of lighting situation.

And indeed today that we realize that the "best" system of determine appropriate photographic exposure is to determine the luminance of many regions in the imaged scene (easily done in modern digital cameras) and than, with some algorithm that embodies a desirable "exposure result strategy", recommend (and typically automatically set) the resulting photographic exposure.

Best regards,

Doug