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Norton's dome - the final (?) mystery solved

Doug Kerr

Well-known member
As I have studied the "Norwood concept" of incident light exposure metering (which is practiced today in almost all serious photographic incident light exposure meters - the hemispherical dome is its hallmark), I had remained baffled by one concept.

I became well familiar with the precise way such a meter would respond to incident light, and with many implications of that.

But what was missing for me is this: Why does the "reading" of such a meter lead to a photographic exposure that, in some way, is "very appropriate" over a range of lighting situations. This question of course leads to a nightmare web of underlying questions, such as "what about a certain photographic result makes us consider it 'very appropriate' from an exposure standpoint."

It turns out that my error was in fact to try to consider the "general case". I now realize that Norwood's work largely focused on a particular real situation he, as a cinematographer, regularly faced: the use of a "key plus fill" lighting setup.

In a 1950 paper, Norwood identifies this context, and (by way of describing the premise of a test program he described) essentially articulated the real issue in this matter, which I will state thus:

Consider studio light with a combination of a key light and fill lighting, and consider a range of specific setups where the key light (or a certain consistent potency) aims at the subject from different angles (head-on, from 45° to one side or the other, etc.)

What kind of exposure meter will, over all of those variations, recommend a photographic exposure that will lead to images that will be adjudged by a typical viewer as "equally appropriately exposed".​

Norwood reports a test series to investigate the relationship between the placement angle of the key light and the photographic exposure that would be needed to give an image that would be judged as "equally well exposed" as an image shot with a "head-on" key light and a certain reference exposure.

This in fact led to a function of angle that describes the "relative effectiveness" of a key light of a certain potency directed from a certain angle (amazingly, it is precisely linear with angle) [note 1]. Norwood then points out that if the response of an exposure meter followed that same function of the angle of incidence of the light, then the indication of that meter will, for any placement of the key light, recommend the exposure that will lead to an image that would be judged "as properly exposed as the reference image" (with a head-on key light).

He then goes on to point out that this is in fact exactly the sensitivity function of a hemispherical receptor meter. [note 2]

Thus we see that the use of a hemispherical receptor meter would be expected to give us exposure recommendations, for various key light positions, that lead to exposure results that typical viewers would judge as consistent in terms of "proper exposure".

Very nice.

What about other complex lighting situations? Who knows.

Notes

[1] It is very suspicious that the results of this highly subjective comparison study gives a function of effective influence of a key light versus angle of placement that is precisely linear.

[2] In fact what he cites for the sensitivity pattern of a hemispherical receptor meter is not quite what is typically considered to be the sensitivity pattern of a hemispherical receptor meter. (He cites a linear function for his meter design, whereas it is generally considered that a hemispherical receptor meter would have approximately a cardioid pattern.)

Comment

It is amazing that the peg here fits so precisely in the hole, and I see evidence that both the peg and the hole may have been shaved to make that so.

Thais is not to say that the concept I describe above is not valid. It makes sense to me. And the issue is not one that could have any "precise" conclusions.

I'm just always suspicious of studies that seek to show that a certain change to a telecom system will about double its user satisfaction, and in fact ends up with a measured improvement factor of 2.00000000.

Best regards,

Doug
 

Doug Kerr

Well-known member
In my note above, I point out that in his 1950 SMPTE paper, Don Norwood states a response curve (response vs. angle) for a hemispherical receptor meter that does not jibe with what is ordinarily derived for a hemispherical receptor meter.

The discrepancy, by the way, in not very great numerically. But the discrepancy is disconcerting. It is as if in a derivation we were expecting to see 1/pi but found the square root of 10 instead.​
I see now how that happened. In the text of his paper, Norwood seems to derive that response curve "on the fly", in this passage:

The hemispherical light-collector accomplishes this dual function in the following manner: With a 0° key-light, the illumination will fall on all parts of the hemisphere and a reading of 100% of the intensity value will be obtained. With a 90° key-light, only one-half of the hemisphere will be illuminated by the key-light. It follows that a correct 50% downward modification of the intensity value is obtained.

[So far so good, chief. When viewing the hemisphere from an angle of 90 °, we see 1/2 of its "frontal" area (50%)]

Similarly, with a 45° key-light, a 25% downward modification is achieved.

[No, that is based on the assumption that when viewing the hemisphere from an angle of 45 °, we see 3/4 of its "frontal" area (75%). But in fact we see 0.853 of its frontal area. Ah, those pesky cosines]

With a 135° key-light, a 75% downward modification is achieved.

[No, that is based on the assumption that when viewing the hemisphere from an angle of 45 °, we see 1/4 of its "frontal" area (25%). But in fact we see 0.147 of its frontal area. Ah, those pesky cosines.]

The lesson here: don't try and derive the properties of one of your inventions in your lap.

Of course the great thing about that erroneous response curve is that it is exactly the one that Norwood says is desirable to match the apparent impact of an off-axis key light.

Best regards,

Doug
 
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