Norwood's dome pondered again

As you may know, I have lately been concerned with understanding the real objective of the use of a "hemispherical receptor" incident light exposure meter, as pioneered by Don Norwood.

Norwood tells us that its real point is to have the meter recognize "all the light falling on a subject that would result in reflected light toward the camera." But just what does that mean, photometrically?

A major step forward for me was when I realized that the reading of a "hemispherical receptor" meter was just the average illuminance on the receptor (by area of the receptor).

In light of the fact that we consider the hemispherical receptor a proxy for the surface of our subject that can be seen from the camera, this then means that the meter reading gives us an approximation of the average illuminance on the camera-visible subject surface (by area of that surface).

But why should that be our best single determinant of the desirable photographic exposure? It is not even, for subject elements of some given reflectance, the average luminance they have as seen from the camera. (This has to to with the projected area toward the camera of elements of different orientations.)

But now I think as follows. We are not really interested in the average illuminance on the visible subject surface. We really would like to know the midpoint of the range of illuminance on that surface.

That way, for subject elements of any given reflectance, the range of luminance toward the camera (and thus the range of photometric exposure on the sensor) would be symmetrically disposed about the ideal value - probably our best bet.

But we cannot with any simple "one-shot" meter measurement determine the midpoint of the illuminance.

But the photometric geometry is such that the midpoint does not depart much from the average.

Thus by measuring the average illuminance (which the hemispherical receptor meter does for us handily) we get a value that is highly useful in determining the desirable photographic exposure.

Best regards,

Doug

The scary thing for me in reading your hypotheses is that on one level I have no clue what you're talking about because I was a total math failure - too right brained, I guess - but today, I read your rationale and I don't just understand it, I begin thinking of ways to test these parameters. I don't think in equations as much as I think in concepts and outcomes. Thank you for stimulating the old gray matter.

Hi, Chris,

Chris Calohan said:

The scary thing for me in reading your hypotheses is that on one level I have no clue what you're talking about because I was a total math failure - too right brained, I guess - but today, I read your rationale and I don't just understand it, I begin thinking of ways to test these parameters.

Click to expand...

This is a very difficult area to actually grasp the significance of the hypotheses.

I don't think in equations as much as I think in concepts and outcomes.

Click to expand...

And of course that is really what is important. My interest is in finding out why we get those outcomes - partially just for intellectual satisfaction, but of course also because by understanding that we may see ways in which the outcome could be improved in certain situations.

Thank you for stimulating the old gray matter.

Click to expand...

And thanks for your support.

Best regards,

Doug

I did some analytical work to see if in fact the meter reading from a "domed" meter would, for various angles of arrival of a component of the incident illumination, track fairly well with the midpoint of the illuminance (as I had conjectured in my opening report in this thread).

In fact, it does not come even close.

For a certain assumed luminous flux density of the component "beam", for four illustrative angles of arrival, this table compares the relative meter indication to the relative midpoint of the illuminance upon the subject (or its hemispherical proxy) (both arbitrarily made 1.00 at 0°):


So I think my (contrived) conjecture as to the real relevance of the indication of a hemispherical receptor incident light exposure meter does not hold up.

Best regards,

Doug

Preface

It is often said that lawyers often say "Hard cases make bad law."

Like many things lawyers say, I don't necessarily believe that.

In science, we often try to determine analytically what performance we might expect of some system and test it against what we think we want it to do. In doing that, we often need to determine what "cases" we will use for the analytical tests.

Often the "extreme" cases are the simplest to analyze, so we may be attracted to them. But, realizing that often the system being analyzed cannot possibly "perfectly" meet our aspirations, perhaps an assessment of it based on extreme cases is not the most useful to us.

On the other hand, often it is the analysis of the extreme cases that gives us the most easily-grasped insight into how the system falls short.

Background

An exposure strategy

We look to exposure metering systems to choose for us a photographic exposure that will fulfill, to the degree practical, some particular "exposure strategy".

One strategy we might adopt is that the elements of the scene having different reflectance will be captured with an exposure result that is the same fraction of the "maximum result" as the reflectance of the element. As we will see shortly, sometimes it is just not possible to attain that, and in fact in many cases that isn't really what we want anyway.

Under conditions where this is attainable, the incident light exposure metering technique can be very useful in determining the photographic exposure that will fulfill that strategy.

In real life

But suppose we have a situation on which the illuminance is not the same on the different elements of the subject (as a consequence of the lighting source situation). Then the exposure strategy I mentioned is unattainable. And of course we might not want it anyway.

For example, consider the moon in a quarter phase. It has basically (macroscopically) a uniform reflectance. But the illuminance on its surface, from the Sun, varies with the location on the surface (because of the difference in angle of incidence - those pesky cosines again).

It might look like this:


We probably wouldn't like all portions of it to have the same exposure result.

So there are various conundrums to deal with in the area of exposure strategy and exposure metering.

The Norton concept

Incident light exposure meters often exit a behavior that was initially devised by noted cinematographer Donald W. Norwood in the late 1930s. Meters with a prominent hemispherical dome in their incident light mode usually attempt to follow that concept.

If we analyze the behavior of such a "hemispherical receptor" meter, we find that it can be described this way:


"Mechanically", the meter does this by using its hemispherical dome as a proxy for the camera-facing portions of the surface of the subject. It actually determines the average illuminance (by surface area) on the dome, and we expect that the same will be approximately true for the subject itself.

The question is, how does the exposure recommendation developed by the meter this way work out as a guide to attaining our exposure strategy?

A hemispherical subject

By way of playing the game, we will consider an actual hemispherical subject. Suppose its reflectance is 57%.

Omnidirectional illumination

First, we will contemplate it illuminated by light arriving uniformly from every direction. From the camera, it would look about like this:


I have assumed that, given the illuminance on the object, I have chosen a photographic exposure that will in fact fulfill our famous exposure strategy. Thus in this image, the relative reflectance of the object is about 57%.

It is of course not very interesting.

Illumination from the camera

Now we will illuminate the object "from the camera" with a a beam that produces that same illuminance on the near face of the object as did the "omnidirectional" illumination. (I assume the same photographic exposure as before.) To the camera, it might look like this::


In the image, the luminance at the center is the same as for the entire object in the prior image. At the limbs, the luminance approaches zero.

Of course, this image does not fulfill our exposure strategy; under it, this uniform reflectance object would have, in the image, a uniform luminance.

Note that the reason that the far limbs of the object are dark is not because we observe them obliquely. It is because they are illuminated obliquely. (Recall that in the earlier figure the limbs of the object, although viewed obliquely, we not dark.)

Illumination from the right side

Now we will illuminate the object "from the right side" with a beam of the same potency as in the previous case. It produces that same illuminance on the right hand face of the object. (I assume the same photographic exposure as before.) To the camera, the object now might look like this (I assume the same photographic exposure as before):


In this image, the luminance at the right is the same as for the entire object in the first image. At the center, the luminance approaches zero.

So, how are those?

Results B and C do not fulfill our exposure strategy; under it, this uniform reflectance object would have, in the image, a uniform luminance. And it just doesn't - it can't, given that it is not uniformly illuminated.

But are each of these what we would think of as a "suitable" exposure result? I leave that up to the individual reader.

What about metering

My assumed exposures

Recall that in cases A, B, and C, I assumed the same photographic exposure, one that produced a match to the "exposure strategy" for the "brightest" portion of the object.

Metered exposures

Now we will assume that, for each of the setups, A, B, and C, we use a "Norton concept" incident light exposure meter to "recommend" a photographic exposure. We will look at these recommendations on a relative basis; the exposure recommended for case A (omnidirectional illumination) will be arbitrarily considered 1.00.

Case A: 1.00

Case B: 1.28 (+0.36 stop)

Case C: 0.5 (-0.64 stop)

Thus we see that the exposure recommendation of the "hemispherical receptor" meter for case B (illumination from the camera) would produce a result 0.36 stop "hotter" than I showed; for case C (illumination from the right), the meter recommendation would produce a result 0.64 stop less than I showed.

Would any of those be "wrong? Who knows.

So what does this tell us?

• If we have non uniform illumination, there is no obvious "correct exposure strategy".

• That being the case, we cannot say whether the exposure metering strategy performed by a "Norwood concept" incident light exposure meter is really somehow "the best we can do".

Best regards,

Doug