Those pesky cosines
Hi, Drew,
Actually, come to think of it. If I used your method of standing where the subject is and I have to choose a dominant light source from two or three different temperature light sources then having a more targeted angle of coverage would also be beneficial, as I would be taking in less of the other two "extraneous" light sources. I'll have to look into that.
I hate to keep singing this tune (you know, we Episcopalians always sing all the verses), but the concept of, in "incident light" measurement of incident light (!), aiming the instrument at the "principal light source" is just plain wrong. It is a notion that emerges from failure to realize that the "correct" solution is just as easily available. It is a wrong as doing one's bookkeeping only including the revenue from the largest customer.
Let's review this, starting from basic principles. I know that you understand all the principles involved, but I just want to make sure you know where I'm coming from.
Our real mission here comes from the fact that, if the subject is not illuminated by light having the chromaticity of the reference white of our color space, the rendition of the subject in a delivered image will not be perceived as having "the right color".
To overcome this, we (a) can determine the chromaticity of the light that actually illuminates the subject, (b) determine how this differs from the chromaticity of the pertinent reference white, and (c)use that difference to direct a "color transform" that results in the image of the subject, when viewed as a delivered image, having the "appropriate" appearance.
Let's imagine that we wish to "determine the chromaticity of the light that illuminates the subject" by measurement. We can do this (as is done in much professional work) with an incident light colorimeter. But we don;t all have those.
But we can also do it by fitting our camera with an "acceptance adapter" (a "white balance diffuser)" that allows the camera to be used to make the measurement. That way, for one thing, then result is already where it needs to be (inside the camera!). Otherwise, we would have to enter the meter reading into the camera, and guess what: it doesn't have a way to enter it!
Now I will start wioth an "idealized" case to allow the principles to be best visualized.
Suppose have a subject whose surface of interest is flat (and oriented in some arbitrary direction) and all the incident light comes from a single source. We put our "instrument" (camera with diffuser in place) at the subject location, facing in some arbitrary direction (presumably something like toward the camera position for the shot). The diffuser collects light from the single source, "homogenizes" it, and passes "a sample of the mix" through the lens to the camera sensor for determination of its chromaticity. That's easy.
Now, let's raise the ante., We still have our flat subject, but now the illumination comes (only) from two sources, a reddish one from in front, stage right, and a bluish one from in front, stage left.
The
illuminance on the subject (thats a specific photometric quantity, not just the concept of "illumination") from each of these sources is proportional to the luminous flux density of the beam at its "destination" and to the cosine of its angle of incidence. (This is a result of the surface being "Lambertian", which we must assume for the moment.) Suppose that all the factors involved mean that the illuminance provided by both sources is the same.
Then, the chromaticity of the "illumination" (which is what affects the color of the light reflected from the subject and captured by the camera in the actual image) can be thought of as the "average" of the chromaticities of the two light "beams".
How is the camera going to know what
that is? Well, suppose that the way the diffuser "combines" the light striking its surface from different directions of incidence (different illumination "beams") is such that contribution of each to the "mélange" delivered to the camera sensor is weighted by the cosine of the angle of incidence of that "beam". (I have a couple of diffusers that do very nearly that.)
Then, we orient the face of the diffuser the same way the subject's (flat) surface is oriented. Thus, for any "beam" of light, the cosine of its angle of incidence on the
subject will be the same as the cosine of its angle of incidence on the
diffuser.
In other words, that kind of diffuser makes the camera respond to the different light sources exactly the same way that the subject surface does.
Thus, the chromaticity determined by the camera (by measuring what has been collected by the diffuser) is precisely the one that it needs to know.
Note that this involved no notion of "facing the diffuser toward the principal light source."
Now suppose that, in a specific version of this case, one of the two light sources "twice as potent" as the other (with respect to the illuminance it creates on our subject. Suppose we then said, "Great! Now I can easily tell which one is the 'principal' light source and aim my diffuser toward it - I read someplace that is what I should do.", and we did that.
Now, the light from the so-called "principal" light source is weighted, in the combination being collected by the difuser for presentation to the camera, by the factor 1 (the cosine of 0°), while the other by a smaller factor (the cosine its angle of incidence on our diffuser, a larger angle than its angle of incidence on the subject, since we have the diffuser "aimed" at the other light source.)
The result will be that, even though this light source contributes 1/3 of the total illumination on the subject, and its chromaticity will actually be weighted by a factor of 2 greater than that of the other source in affecting the observed color of surface, we will weight it much more heavily in our measurement. Thus, the determination of the incident liught chromaticity will not represent the illumination on the subject, and the color correction will be "wrong".
(If the "principal" source were the red one, then our determination of the incident light chromaticity this way would be "too red", and the corrected image would be "too blue".)
And this is why (at least under this "ideal" model, "aiming at the principal light source" is just the wrong procedure.
Now lets leave the blackboard and go into the studio. Suppose that one or more of our premises here were not so. suppose the subject surface were not flat; suppose its behavior were not Lambertian. Then what?
Then my model of "ideal chromaticity determination" doesn't exactly work. Would aiming the diffuser "at the principal light source", however, work "most nearly correctly"? No reason to believe that. It might. It might be best to aim the diffuser toward the camera trailer, or the model's agent. We have absolutely no way to generalize.
And of course, of we have the "serious" mixed light mess I described, and the subject were a human face, there would be no color correction that would produce a "natural" rendering of the whole face. If we made our measurement with the diffuser facing the same way as the model's nose (and lets suppose that were toward the camera), then the right side of the models face would look decidedly reddish, and the left side decidedly bluish.
Now suppose that the red light source was known to be the more potent. The, if we had made the measurement with the diffuser "facing the camera", we would end up with the center of the model's face still being corrected "properly" (ah, the power of those little cosines - they work for us even if we don't understand them!), the right side a bit reddish, the the left side a little bluish. (And the right side would have been "brighter" than the left side.)
Now suppose we decided to hark to the "common rule" and aimed the diffuser at the red light.
Now, in the corrected image, the model's right side would have been about "properly balanced", the center of the face would have looked a bit bluish, and the left side a lot bluish.
Is that the result we want? (Elvira's agent says, "Great - just what she wanted!") And if so, then the "rule" worked fine. Good for us. But it might not be what Red Fox, the famed Cherokee author, would prefer.
In any case, the argument of the practical weakness of "incident light" measurement of the incident light is that it might be hard to figure out which is the "principal" light source doesn't hold, since that is not a matter of actual importance.
This is not to say that "incident light" measurement is always doable, or handy, nor to say that there is no useful alternative. That's another story altogether. It's just that when we are speaking of something, for better or worse, I like to speak of it in a way that matches the reality.
The notion of "facing the principal light source" is just a misconception. It doesn't match the "ideal case", and is not predictably the best in various "realistic cases".
Best regards,
Doug