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