Exposure metering - "duplex vs "Norwood" techniques

[Doug Kerr]

It appears that Don Norwood's work on exposure metering was primarily initially aimed at devising an exposure metering system such that, in such cases as illumination of a human subject by "key-fill" technique, a single measurement by an appropriate exposure meter would serve to suggest the "optimal"photographic exposure.

When he began that quest, metering of such situations by serious cinematographers was believed to most often be done with the "duplex metering" technique. In that, best as we can tell two measurements of the illuminance on the subject were made with an "incident light" exposure meter at the subject location, one with the meter facing the fill light and the the other with it facing the key light.

Those two illuminance readings were averaged (it being unclear whether the arithmetic or geometric average was normally used), and the resulting value entered into the meter's exposure calculator to develop the photographic exposure recommendation to be used for the shot. This was of course rather "labor intensive".

Norwood's system would improve on that, allowing the photographic exposure recommendation for this shot to be determined with a single measurement, done with an exposure meter having a hemispherical light collector, made with the meter at the subject location and "aimed" at the camera.

If we assume a lighting situation in which there was no fill light,* then it can be shown that both the "duplex metering" technique (if we assume the averaging there to be "arithmetic") and the "Norwood" technique will give the same results for the key light at any angular position, if the value of the incident light metering calibration constant, C, is the same for both techniques.

*Norwood himself had suggested that the role of the fill light on exposure was so slight for typically-used key-fill ratios that he essentially ignored the effect of the fill light altogether in much of his work.

That equivalence seems comforting, as far as it goes.

If we now assume a small but non-trivial fill light (perhaps with a key-fill ratio of 8:1), and still assume that the averaging in the duplex metering technique is arithmetic, then the two techniques do not give comparable results for any position of the key light away from 0° ("at the camera").

Best regards,

Doug

 

[Doug Kerr]

In considering this., we need to recognize that Norwood's quest was for an exposure metering system that would be more convenient to perform than duplex metering and would give a "good" photographic exposure recommendation in many cases. He did not seek for this to mimic the behavior of the duplex metering system.

In fact, Norwood's later famous series of subjective tests suggested an exposure technique that differed in its expected behavior in many cases from that of duplex metering. This "exposure metering model", fortunately, would be in theory very nearly be practiced by an exposure meter with a hemispherical light collector.

This served to nicely vindicate Norwood's original "vision", which was that an exposure meter with a hemispherical light collector would give a "good" photographic exposure recommendation for essentially all lighting setups for a human face.

Best regards,

Doug

 

[Doug Kerr]

Norwood's subjective tests suggested that (if one ignores the impact of the fill light), if we assume a consistent "strength" of the key light, the ideal photographic exposure would increase linearly with the angle of the key light from "at the camera". At 90°, the ideal exposure would be twice what it was with the key light at the camera.

This would then suggest a comparable "directivity curve" of the exposure meter, so it would inherently take this into account. On a polar plot, that would in fact be an "Archimedean spiral"

Norwood initially then said that, conveniently, that would the directivity curve we would expect of a meter with a hemispherical light collector.

But that is not true. The theoretical directivity curve of such a meter is a different classical curve, the "cardioid" curve.

But the difference between the two is not great, and in any case this whole matter of exposure metering does not involve a "correct" result.

Best regards,

Doug

 

[Doug Kerr]

Don Norwood seemingly was quite conscious of a guideline often followed by experienced photographers: if a subject is lit solely by a light at 90° (directly to the side) the photographic exposure should be one stop greater than if the subject were illuminated by that same light source located at the camera position.

And the original Norwood system exposure meters in theory tracked with that exactly: the theoretical directivity of the hemispherical light collector 90° was 0.5 (relative to the directivity at 0°).

And in fact, "duplex metering" of a lighting setup with the sole light at 90° would bee expected to yield a photographic exposure one stop greater than for the same metering technique with that same sole light at the camera (assuming that the duplex metering technique used the arithmetic average of the two readings as the premise for computing the phtometric exposure recommendation.

Norwood apparently put so much stock into the validity of this "rule of thumb" that in a later patent, he described it, then saying that in more recent times the rule of thumb in common use had changed to call for a photographic exposure, for a single light source at 90°, of less than one stop greater (perhaps only 2/3 stop) than for that same light source at 0°.

Thus, he said, in a "Norwood system" exposure meter, the ideal directionality of the meter at 90° should be greater than 0.5, and he went on to describe a modification of the basic hemispherical light collector that would give that directivity.

In fact, if we assume a single light source (with a variable angular position), then the duplex metering technique (arithmetic average basis) and Norwood technique (with a hemispherical light collector) would theoretically give the same photographic exposure recommendation for any angle of the light from 0 through 90°.

Best regards,

Doug

 

[Doug Kerr]

If we then assume a "key-fill" lighting technique (two light sources), with the key:fill ratio 8:1, then duplex metering and ideal Norwood metering do not produce exactly the same photographic exposure recommendation, but the difference is not much, 0.15 stop with the key light at 90°.

If we then assume a more potent fill light (key:fill ratio 4:1), then the discrepancy between the two metering systems grows to 0.26 stop at 90°, still not consequential.

If we then assume an even more potent fill light (key:fill ratio 2:1), then the discrepancy between the two metering systems grows to 0.42 stop at 90°, still not consequential.

So we can see why Norwood's metering system was well received by the cinematographic community.

Best regards,

Doug

 

[Doug Kerr]

Interestingly enough, as to the duplex metering technique, if we consider it to be done with arithmetic average of the two readings, for any key-fill ratio, the photographic exposure recommendation with the key light at 90° will be twice the photographic exposure recommendation with the key light at 0° (at the camera).

This was a bit of a surprise to me. but when I looked into the math involved, I see it was to be expected.

Best regards,

Doug