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Norwood's dome - what's with that?

Doug Kerr

Well-known member
Today, most incident light exposure meters (including meters offering both reflected and incident light modes, when in the incident light mode) employ a "light collector" of generally-hemispherical form. This design is directly traceable to an exposure meter design originated in the late 1930s by Don Norwood.

Just what does this hemispherical collector do, and why do we want to do that? The story is not at all simple. It includes the fascinating tale of how a valuable concept initially adopted by intuition was later given "cover" by a back-formed (and in some cases, rather questionable) "scientific" explanation.

My article, "Norwood’s dome: a revolution in incident light photographic exposure metering" discusses this at length, warts and all. It has just been reissued to include further background in several of the issues involved and to add a new appendix with a technical derivation that is germane to the story. It can be found indexed here:

Best regards,

Doug
 

Asher Kelman

OPF Owner/Editor-in-Chief
"The Norwood Dome Paradox"

Today, most incident light exposure meters (including meters offering both reflected and incident light modes, when in the incident light mode) employ a "light collector" of generally-hemispherical form. This design is directly traceable to an exposure meter design originated in the late 1930s by Don Norwood.

Just what does this hemispherical collector do, and why do we want to do that? The story is not at all simple. It includes the fascinating tale of how a valuable concept initially adopted by intuition was later given "cover" by a back-formed (and in some cases, rather questionable) "scientific" explanation.

My article, "Norwood’s dome: a revolution in incident light photographic exposure metering" discusses this at length, warts and all. It has just been reissued to include further background in several of the issues involved and to add a new appendix with a technical derivation that is germane to the story. It can be found indexed here:




Doug

"The Norwood Dome Paradox" is a great term for intuitively carved out concepts that have proved useful. In fact, when some ideas cannot, as yet be explained by rational means, we tend to think it's magical, just as in the puzzle of hour hummingbirds could fly at such fast rates of wing beats.

What other useful ideas, initially based on intuition, were subsequently explained by solid scientific logic, and were initially viewed by scholars as suspect?

Asher
 

Doug Kerr

Well-known member
Hi, Asher,

What other useful ideas, initially based on intuition, were subsequently explained by solid scientific logic, and were initially viewed by scholars as suspect?

A very important question. I'm sure there are many examples of just that.

But to avoid any misunderstanding, such is not the situation with regard to Norwood's dome. It was indeed based on intuition, and the intuition led to an empirically-useful solution to a problem that cannot be objectively defined.

It is always better to be lucky than good.​

And it was never subsequently explained by solid scientific logic (and in fact, there could be no such thing, given that the objective could not be "objectively" defined). There was just a substantially-flawed (and likely "back-formed") "explanation" published in a scientific journal.

Best regards,

Doug
 

Doug Kerr

Well-known member
I have probably attached too much importance to the fact that, with regard to photography of human subjects using "key-fill" lighting technique, there is no unique "best" exposure result.

In fact, in all photography, the matter of the exposure result is one of the important artistic choices made by the photographer/cinematographer. We may well look at a photo presented here and say, "Wow - that is really lovely", and part of the reason it makes such a positive impression on us is because of the way the photographer has "planted" the tonal range of the scene in the luminance range of the color space, even though we might not be able to say just what it is about that choice that we like so much.

Evidently, the result suggested by the use of a Norwood-principle incident light meter in cinematography very often gave a result that matched the cinematographer's vision - or at least, gave a good first cut at it.

And probably Norwood's great marketing skills fit into the picture.

And I don't have any problem with that reality.

What did disturb me, as I investigated this matter, was the way Norwood:

• First, after apparently being pressed for a while to explain the principle by which his meter often gave such "appropriate" results, conjured the facile explanation about the hemispherical receptor dome of the meter being an analog to the visible-to-the-camera part of the subject's head.

This is one of those things that makes one perhaps say at first, "Oh, of course - how clever". But upon further examination, it turns out that the most apt response is, "So what?".

• Later, after apparently being further pressed for a scientific explanation of the principle involved, Norwood reported on a series of empirical tests of different exposure levels for different "key-fill" setups, and showed that the behavior of his meter would comport almost exactly with the empirically-observed ideal exposure levels.

And I have no problem with that reality either.

What I do have a problem with is, in Norwood's paper following this trail, there are several "gaffes", errors in logic or algebra (accidental or otherwise), which conveniently serve to make exact the alignment between (a) the exposure suggested by the empirical testing to be "ideal" and (b) the exposure that would be recommended by a Norwood-principle meter. (This is discussed at length in one of the appendixes to my paper.)

So, Brother Norwood, you were on to a really good thing - but don't shine me on.

By the way, my favorite incident-light exposure meter is one that is the direct descendant of Norwood's original product. I in fact have a specimen of almost every meter model - made by a succession of manufacturers - in that line of descent. It is considered that this, the Sekonic Studio Deluxe III, Model L-398A, is the last of that "direct descent line":


IMG_232874.jpg


Sekonic L-398A exposure meter​

But the principle is followed in other, more modern, meters.

Best regards,

Doug
 

Asher Kelman

OPF Owner/Editor-in-Chief
Thanks for the interesting account of a better than average con man at work with a better than average invention!

It is really an apt metaphor for selecting a politician: you know they are lying since their lips are moving, but you want to know which one of them is most likely to steal one's best silverware, make it more embarrassing to be a tourist overseas or screw up the entire planet!

Asher
 

Doug Kerr

Well-known member
Hi, Asher,

Thanks for the interesting account of a better than average con man at work with a better than average invention!

An excellent précis!

It is really an apt metaphor for selecting a politician: you know they are lying since their lips are moving, but you want to know which one of them is most likely to steal one's best silverware, make it more embarrassing to be a tourist overseas or screw up the entire planet!

Also well said!

Best regards,

Doug
 

Doug Kerr

Well-known member
The subjective test upon which Norwood's seminal paper was based was very clever, and certainly telling.

The setup was a series of photographs taken of a series of human subjects. In each series, as near as I know, the subject was posed facing the camera. For each subject, shots were taken with different lighting setups, all using the "key-fill" principle.

For the different shots in a series, the key light was positioned at different locations, described in terms of angle from "straight on" (meaning from the camera position) (which would be "0°). The key light positions used for each series were in fact 0° ("head on"), 45°, 90° (exactly "to the side"), and 135° (a bit to the back).

The key light was always "straight on".

For all the shots in a series, the intensities of the key and fill lights were constant, with a key:fill ratio of 8:1.

For each subject, with the key light set "head on", the illuminance on the subject was measured with a traditional incident light exposure meter, and (based on some widely accepted "incident light metering calibration") a photographic exposure (combination of aperture and shutter speed) was chosen. This would be the "reference exposure" for the series.

Then, with the lighting setup still at "key light straight on" (0°), a shot was taken using that "reference exposure".

Then the key light was moved to the 45° position. Several shots were taken, with different exposures at 1/2-stop intervals, including above, at, and below the reference exposure.

Then the key light was moved to the 90° position, and again a series of shots were taken with different exposures, as described just above.

Finally, the key light was moved to the 135° position, and again a series of shots were taken with different exposures.

Now, all the shots were developed (consistently) and each printed, using identical print exposure times.

Now several observers were asked to view the multiple prints for each subject. For each subject, they were asked to first view the "key at 0°" print. Then, for each of the three other key light angles, they were asked to review the prints for the various different exposures, and choose the one that "looked like" the "head on" print.

Now here we run into one of the clinkers in this matter. "Looked like" in what regard? Obviously none of these prints from, for example, the "key light at 90°" set actually looked like the "key light at 0°" print. The shadowing of the subject's face would be much different. So perhaps in fact they were asked to choose the print where the "overall exposure impression" was most comparable of that for the 0° print. We just don't know.

But, moving on.

The reports for the different observers, over the different subjects, were analyzed. We have no information on the statistical properties of the data and how it was consolidated. In any case, it was reported that, "overall", the observers, considering the "runs" for the different subjects, concluded that, for each of the three "not head on" key light positions, a consistently greater exposure (compared to that used for the head-on shot) was needed to produce "the same appearance" as for the head-on shot.

That "needed exposure bump" was this, for those different angles (given here in "stops"):

0° 0 (by definition, as this was the reference condition)
45° 0.5 stop
90° 1 stop
135° 2 stop

How tidy.

Norwood then said that, for an exposure meter to "tell the cinematographer to use the appropriate exposure", its response to the light on it would have to vary, with angle of incidence (that is spoken of as its "directivity"), this way (in stops):

0° 0 (by definition)
45° -0.5 stop
90° -1 stop
135° -2 stop

How tidy.

Except that this is not so. The reason is that the meter "sees" both the light from the key light and from the fill light. If one goes through the photometrics involved, it can be shown that the needed directivity of the meter would have to be (I take the liberty of showing the result to two decimal places):

0° 0 (by definition)
45° -0.48 stop
90° -1.22 stop
135° -2.82 stop

Not a big difference (except at 135°, a situation that is not really of any great importance). But enough to throw shade on the candor of Norwood's "proof".

In any case, Norwood next presents what he says would be the theoretical directivity of a hemispherical-receptor meter:

0° 0 (by definition)
45° -0.5 stop
90° -1 stop
135° -2 stop

Well, fancy that! Exactly what he says (though incorrectly) would be needed to give the ideal exposure recommendation for the various key-fill lighting setups.

But in fact if we derive the theoretical directivity of a hemispherical receptor meter, we get this (again I take the liberty of showing the result to two decimal places):

0° 0 (by definition)
45° -0.23 stop
90° -1.00 stop
135° -2.78 stop

Well, that's correct for one of the non-zero conditions (90°). And, at 135°, while quite different from Norwood's reported value, it is close to the actually-needed value!

Now of course these discrepancies are not large numerically. So in fact Norwood's overall presentation suggests that, at least for the key-fill lighting situation, a hemispherical-receptor meter will in fact, if only by happy accident, give good exposure guidance.

On the other hand, with regard to Norwood's paper, I must grade it very low on "candor".

Best regards,

Doug
 

Doug Kerr

Well-known member
One of the "gaffes" to which I refer in Norwood's seminal paper on the hemispherical-receptor incident light exposure meter was in reckoning the needed "directivity" of the meter. By directivity we mean the relative response of the meter to light of a given intensity arriving from different angles. This is stated numerically relative to the meter's response to light arriving from 0° ("head on"), which is said to be 1.000.

In this discussion, I will state various ratios in normal numerical form, rather than in "stops", as the math works best that way.

I will consider here the case in which the key light it at an angle of 90° (exactly "from the side"). A similar demonstration can be made for the other angles appearing in Norwood's paper.

Norwood's subjective testing suggest that, in order for the exposure result with the key light at 90° to be "visually equivalent" to the exposure result with the key light at 0° (head on), the photographic exposure for the 90° setup will need to be 2.0 times the photographic exposure for the 0° setup.

For the exposure meter to "recommend" this exposure in the 90° case, its "reading" must be 0.5 times that for the 0° case. The reason is that the photographic exposure recommended by the meter is inversely proportional to its "reading" of the incident light. (For example, with a fixed lighting setup, if we were to cut the light in half, we would need twice the photographic exposure to get the same exposure result.)

Norwood then tells us that for this to be so, the meter directivity at 90° (for light arriving exactly from the meter's "side") must be 0.5.

But that is not so.

Consider that we have a meter whose directivity at 90° is in fact 0.5. Now, first consider the case of the key light being at 0° (and of course the fill light, as always, is at 0°). We consider this to be the "reference" illumination situation. And the relative response of the meter is 1.000 (as its directivity at 0° is, by definition, 1.000).

We will consider the totality of illumination here to be 1.00 unit. The ratio of key light illumination to fill light illumination is 8. Thus the illumination from the key light must be 0.888 unit (8/9 of the total), and from the fill light 0.111 unit (1/9 of the total). (I will work only to three decimal places here.)

Now, to get to the setup of interest, we move the key light to the 90° position. It still has its same intensity (0.888 unit). Because we assume this meter to have a directivity at 90° of 0.5, the meter's "relative response" to the key light is 0.444 unit (0.5 × 0.888).

The meter of course also receives the illumination from the fill light, with an intensity of 0.111 unit. It still strikes the meter at 0° (head on), and, by definition, the meter directivity at 0° is 1.000. Thus the meter response to the fill light illumination is 0.111.

Thus, the total relative response of the meter to the two light sources (the meter "reading") is 0.555 (0.444 + 0.111).

But, as we saw above, for the meter in this case to recommend the needed photographic exposure (2.0 times that for the "0°" setup), the relative meter reading must be 0.5.

Thus, 0.5 is not the needed directivity of the meter at 90°. (We can in fact with a little further algebra, which I will spare the reader, determine that the needed directivity at 90° is 0.438.)

Now, is the amount of this discrepancy enough to invalidate Norwood's demonstration of why a hemispherical-receptor meter produces a useful photographic exposure recommendation when using the key-fill lighting technique over a range of key light positions? Of course not. After all, that whole story revolves around a highly-subjective evaluation by test subjects, so we are not speaking here of a "theoretically exact" result (even though Norwood would like us to think that it is).

What this gaffe does is just cast cast some shade over Norwood's paper. Clearly, he knew the result he wanted, and in various places (including as discussed in this note) jumped to some unwarranted conclusion when that produced a delightful "alignment of the planets."

Time now for breakfast (breakfast A today).

Best regards,

Doug
 
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