Doug Kerr
Well-known member
Introduction
In discussion of photographic photometrics (notably in the area of exposure metering), we encounter two important quantities:
• Luminance - that can be thought of (a bit imprecisely) as the indicator of the "brightness" of a surface element in the scene.
• Illuminance - this is an indicator of the impact of the illumination at a point on a subject surface.
Another quantity, rarely heard of (except in my writings) is:
• Luminous flux density - this is an indicator of the "potency" of a traveling "beam" of light.
I will not speak in further detail here about luminance.
Illuminance is defined as the amount of luminous flux (the "stuff" of light) landing per unit area of the affected surface. Thus its unit is lumens/meter squared (lm/m²). But that has a special name, the lux. The standard symbol for illuminance is E (think "Ee-luminance").
Luminous flux density is defined as the amount of luminous flux (the "stuff" of light) traveling per unit cross-sectional area of a light "beam". Thus its unit also lumens/meter squared (lm/m²). (But the synonym "lux" is not formally apt here - it is for the quantity illuminance.) There is no standard symbol for luminous flux density, I use "e", since there is an obvious parallel between luminous flux density and illuminance.
Simplistically, luminous flux density quantifies the ability of a beam to illuminate a surface (that is to cause luminance). But there is another factor involved.
The illuminance, E, caused on a surface by the "landing" of a beam of luminous flux density e is given by:
We rarely hear about luminous flux density, and probably think that we never measure it, even in sophisticated lighting planning work. But it turns out that we certainly do.
Measurement of illuminance
And in fact an instrument that measures illuminance has a response to luminous flux arriving from different angles that varies as cos A. Manufacturers of such instrument go to a lot of trouble to bring that about.
Note that we cannot say of a beam of arriving light, to describe its potency in an easily-understood way, "it will cause an illuminance on a surface it hits of E lux." That is because the illuminance created on a surface it hits depends on the orientation of the surface (which influences the angle of incidence of the beam).
Non-planar photographic subjects
Serious incident light exposure meters, in their "usual" mode do not actually measure the true illuminance of the ambient light (as it would be on a plane of some certain orientation). The reason is that in an actual three-dimensional subject (see, for example, Figure 1), the surface of interest is not planar, thus having a single orientation.
Figure 1. Decidedly non-planar subject
Thus, in the general case, the illuminance upon a subject surface depends on its orientation. Accordingly, no photographic exposure will deal with each surface area in accordance with the strict objective of incident light metering. And so no reading with any kind of meter will tell us how to get such an impossible result. And thus a studio photographer, faced with a subject such as that in Figure 1, may need to "tailor" the overall lighting setup light to achieve the artistic effect wanted. (I think this guy did well. Notice . . ..Well, never mind.)
Still, there seems to be a desire to use a single reading with an incident light meter to give a meaningful single "overall" value of the illumination on a subject.
A single value
Famed cinematographer Don Norwood, the father of the famous "Norwood" series of incident light exposure meters, concluded (without ever expressing it quite this way) that this useful reading would be the average (over area) luminance over those surfaces of the subject the camera could see.
To allow this to be done with a single meter, Norwood equipped the meter with a hemispherical photoreceptor receptor. He saw this as a proxy for the part of the surface of a subject that was visible from the camera.
It turns out that if we characterize the response of such a meter to arriving light of differing angles of arrival, it exhibits what can be called a cardioid response (from the shape of a polar plot of the response).
Is the indication of such a meter really "meaningful" in cases where the lighting is so "directional" that the pattern of the meter matters? Beats me. All I know is that a lot of people use meters operating on that principle.
It has certainty been meaningful to Norwood's estate.
Flat subjects
Now in some cases, we wish to use incident light metering for a subject that is indeed planar (perhaps a historical newspaper page being "copied"). In that case (if we allow certain assumptions about its surface), we need to know the actual luminance on the subject. To get that, as I discussed earlier, the meter ideally should exhibit a cosine response.
Accordingly, serious incident light exposure meters often have provision for switching their response from cardioid to cosine.
More complex lighting challenges
Now, in actually dealing with a shot such as figure 1, the skilled photographer will plan for a lighting setup involving different sources (perhaps one of them being natural light through a window). She will typically have developed guidelines for this that result in certain target ration between the "potency" of the different light source "beams" as they are about to arrive at the subject. Of course, by "potency" I actually meany the luminous flux density, e, of the various beams.
But with what instrument can we measure that, so that we can adjust the light sources to get the ratio our recipe stipulates?
Well, if we revisit this equation:
we see that if we use a meter that measures luminance (notably, an incident light exposure meter switched to its cosine mode), and "face it toward the source", angle A will be zero, cos A will be 1.00, and the reading of the meter (E), will in fact be the luminous flux density (e), just what we need. And we may write down the result in lux (even though that isn't really quite the proper unit for this quantity).
Now, we rarely describe this as "measuring the (relative) luminous flux density of the various component beams". If anything, we may speak of it as measuring "the relative illuminance from the various sources".
But by now we should realize that a beam of light does not have an illuminance. It can only cause an illuminance by landing on a surface, and that illuminance depends not only on the "potency" of the beam (its luminous flux density) but also on the angle at which the beam strikes (and thus on the orientation of the surface).
So yes, gang, many of you in fact from time to time measure luminous flux density, even if you thought you were measuring something else.
Best regards,
Doug
In discussion of photographic photometrics (notably in the area of exposure metering), we encounter two important quantities:
• Luminance - that can be thought of (a bit imprecisely) as the indicator of the "brightness" of a surface element in the scene.
• Illuminance - this is an indicator of the impact of the illumination at a point on a subject surface.
Another quantity, rarely heard of (except in my writings) is:
• Luminous flux density - this is an indicator of the "potency" of a traveling "beam" of light.
I will not speak in further detail here about luminance.
Illuminance is defined as the amount of luminous flux (the "stuff" of light) landing per unit area of the affected surface. Thus its unit is lumens/meter squared (lm/m²). But that has a special name, the lux. The standard symbol for illuminance is E (think "Ee-luminance").
Luminous flux density is defined as the amount of luminous flux (the "stuff" of light) traveling per unit cross-sectional area of a light "beam". Thus its unit also lumens/meter squared (lm/m²). (But the synonym "lux" is not formally apt here - it is for the quantity illuminance.) There is no standard symbol for luminous flux density, I use "e", since there is an obvious parallel between luminous flux density and illuminance.
Simplistically, luminous flux density quantifies the ability of a beam to illuminate a surface (that is to cause luminance). But there is another factor involved.
The illuminance, E, caused on a surface by the "landing" of a beam of luminous flux density e is given by:
E=e cos A
where A is the angle of incidence of the arriving beam. (I have frequently discussed how the "cos A" gets in there, and I will not bore with it here.)We rarely hear about luminous flux density, and probably think that we never measure it, even in sophisticated lighting planning work. But it turns out that we certainly do.
Measurement of illuminance
And in fact an instrument that measures illuminance has a response to luminous flux arriving from different angles that varies as cos A. Manufacturers of such instrument go to a lot of trouble to bring that about.
Note that we cannot say of a beam of arriving light, to describe its potency in an easily-understood way, "it will cause an illuminance on a surface it hits of E lux." That is because the illuminance created on a surface it hits depends on the orientation of the surface (which influences the angle of incidence of the beam).
Non-planar photographic subjects
Serious incident light exposure meters, in their "usual" mode do not actually measure the true illuminance of the ambient light (as it would be on a plane of some certain orientation). The reason is that in an actual three-dimensional subject (see, for example, Figure 1), the surface of interest is not planar, thus having a single orientation.
Figure 1. Decidedly non-planar subject
Thus, in the general case, the illuminance upon a subject surface depends on its orientation. Accordingly, no photographic exposure will deal with each surface area in accordance with the strict objective of incident light metering. And so no reading with any kind of meter will tell us how to get such an impossible result. And thus a studio photographer, faced with a subject such as that in Figure 1, may need to "tailor" the overall lighting setup light to achieve the artistic effect wanted. (I think this guy did well. Notice . . ..Well, never mind.)
Still, there seems to be a desire to use a single reading with an incident light meter to give a meaningful single "overall" value of the illumination on a subject.
A single value
Famed cinematographer Don Norwood, the father of the famous "Norwood" series of incident light exposure meters, concluded (without ever expressing it quite this way) that this useful reading would be the average (over area) luminance over those surfaces of the subject the camera could see.
To allow this to be done with a single meter, Norwood equipped the meter with a hemispherical photoreceptor receptor. He saw this as a proxy for the part of the surface of a subject that was visible from the camera.
This is probably realistic if the subject is a human head. It is probably less realistic for the entirety of the subject in Figure 1.
It turns out that if we characterize the response of such a meter to arriving light of differing angles of arrival, it exhibits what can be called a cardioid response (from the shape of a polar plot of the response).
Is the indication of such a meter really "meaningful" in cases where the lighting is so "directional" that the pattern of the meter matters? Beats me. All I know is that a lot of people use meters operating on that principle.
It has certainty been meaningful to Norwood's estate.
Flat subjects
Now in some cases, we wish to use incident light metering for a subject that is indeed planar (perhaps a historical newspaper page being "copied"). In that case (if we allow certain assumptions about its surface), we need to know the actual luminance on the subject. To get that, as I discussed earlier, the meter ideally should exhibit a cosine response.
Accordingly, serious incident light exposure meters often have provision for switching their response from cardioid to cosine.
More complex lighting challenges
Now, in actually dealing with a shot such as figure 1, the skilled photographer will plan for a lighting setup involving different sources (perhaps one of them being natural light through a window). She will typically have developed guidelines for this that result in certain target ration between the "potency" of the different light source "beams" as they are about to arrive at the subject. Of course, by "potency" I actually meany the luminous flux density, e, of the various beams.
But with what instrument can we measure that, so that we can adjust the light sources to get the ratio our recipe stipulates?
Well, if we revisit this equation:
E=e cos A
we see that if we use a meter that measures luminance (notably, an incident light exposure meter switched to its cosine mode), and "face it toward the source", angle A will be zero, cos A will be 1.00, and the reading of the meter (E), will in fact be the luminous flux density (e), just what we need. And we may write down the result in lux (even though that isn't really quite the proper unit for this quantity).
Now, we rarely describe this as "measuring the (relative) luminous flux density of the various component beams". If anything, we may speak of it as measuring "the relative illuminance from the various sources".
But by now we should realize that a beam of light does not have an illuminance. It can only cause an illuminance by landing on a surface, and that illuminance depends not only on the "potency" of the beam (its luminous flux density) but also on the angle at which the beam strikes (and thus on the orientation of the surface).
So yes, gang, many of you in fact from time to time measure luminous flux density, even if you thought you were measuring something else.
Best regards,
Doug