The "potency" of light

Today I would like to talk about the "potency" of light (to use a term that embraces several different concepts, which is the point of the discussion).


When we speak of light, we may be interested in any one of several distinct measures of "potency". These differ in much they same way that miles differs from miles per hour, or that watts differs from watt-hours; they refer to different physical phenomena.

For each of these measures, there are several units that can be used. Here, I will only speak of the preferred unit in modern technical work, that prescribed by the "SI" (the International System of Units); that is, the "metric" unit.

Luminous flux

Luminous flux is, in photometry, directly equivalent to power in radio engineering. The difference is that luminous flux takes into account the varying sensitivity of the eye to light of different wavelengths. A certain amount of luminous flux represents a certain amount of power, but the relationship varies with the wavelength of the light under consideration.

The SI unit of luminous flux is the lumen.

If we have a steady, continuously lit lamp, its total visible emission is characterized in terms of the value of luminous flux.

Luminous intensity

We may well be interested in the "potency" of emission of light from a source in some particular direction. If we consider a "point source" (that is, one whose cross-sectional area is small compared to the distance at which we will be concerned with its impact), then the pertinent quantity is luminous intensity.

Luminous intensity is defined as luminous flux per unit solid angle. Solid angle is a way to describe "the amount of 'space' embraced by a conical boundary". It is measured in the unit steradian.

Why does solid angle get into the picture? Couldn't we just speak of the amount of luminous flux emitted by our source in the direction of interest?

The problem is that zero luminous flux is emitted in any given direction. That is because "in a direction" implies "along a line". A line has zero cross-sectional area, and thus cannot serve as a conduit for any luminous flux.

If we imagine however a very tiny cone (with a very small solid angle), we can imagine some luminous flux being emitted within it. If we divide that amount of luminous flux by that solid angle, the result will be the luminous intensity in the direction of the cone.

Luminous intensity is a property of the emitter, not of its impact on a surface at some particular distance (although it of course influences that).

The unit of luminous intensity is the lumen per steradian. It has its own name: candela.

Luminous flux density

If we go out some distance from our emitter and imagine the light crossing a plane (perpendicular to the line from the emitter to the point, and consider a "window" of some small area on the plane, a certain amount of luminous flux will pass through that window. If we divide that amount of luminous flux by the area of the window, we get the luminous flux density at that point in space (from our emitter).

The unit of luminous flux density is the lumen per square meter.

We can think of the luminous flux density as describing the "potency of the beam" at a certain distance from the emitter in a certain direction.

The luminous flux density is proportional to the luminous intensity of the beam in the direction of interest divided by the square of the distance from the emitter to the point of observation - the famous "inverse square law".

Illuminance

If we put an actual physical "screen" at the location described above, again perpendicular to the line from the emitter, consider a circular patch of small area on it, and consider the amount of luminous flux landing on the spot, and take the ratio of that amount of luminous flux to the area of the spot, we get the illuminance on that spot (from our emitted beam).

The unit of illuminance is the lumen per square meter, just as for luminous flux density.

In our example, the values of illuminance and luminous flux density are identical. The difference (for now) is that the luminous flux density describes the potency of the beam (its potential to illuminate), whereas illuminance is the actual result (the amount of "illuminating" that is actually done).

But now, let's look at a more general case, where the object illuminated is not perpendicular to the line from the emitter.

Consider just the flux that landed on our little circular patch in the previous example. It is contained within a cone of small solid angle. Now imagine tilting our receiving screen by an angle of 60°. Now, the flux in the small cone lands on an elliptical spot, having an area twice that of the earlier circular spot (I picked the angle to make to some out that way). If we now reckon the ratio of luminous flux to area, we get half the previous value. In fact, now the illuminance is half what it was before - half the luminous flux density of the beam.

Thus, the illuminance on a surface depends not only on the luminous flux density of the beam but also to the angle of incidence. The illuminance is proportional to the luminous flux density of the beam times the cosine of the angle by which the beam's "angle of arrival" differs from "perpendicular".

Getting away from the "point source" - luminance

Often, we are concerned with the "emission" (or reflection) of light from what cannot be considered a point source - a surface whose dimensions are substantial. This is of course the case when photographing a a "scene".

How can we characterize the emission from such a surface? We can consider any small patch of the surface to be populated with a large number of point sources, all having the same luminous intensity. If we add up the luminous intensities of all the assumed little points sources, and then divide by the area of the patch, we get the quantity luminance. (It is often said to be "brightness", although in some cases that term is used technically with a slightly different meaning.)

The unit of luminance is the candela per square meter.

Note that the quantity luminance is a property of the emission from a surface, not of its effect at some distance. And in fact, perceptually, the perceived luminance of a surface is the same regardless of the distance from which the surface is observed. (The surface might or might not exhibit the same luminance when viewed from different angles of observation.)

The effect of time

The basic physical phenomenon to which photographic film or a digital sensor responds at a point is the product of the illuminance at the point and the time for which it persists (the exposure time), the illuminance-time product. In photography, we often call this quantity the photometric exposure. It is the "E" of the famous "D log E" curve of photographic film response, although the modern symbol for the quantity is H.

There are corresponding time-based versions of all the other measures: the luminous flux-time product (sometimes called photometric energy), the luminous density-time product, the luminance-time product, and so forth.

Flash photography

Since, in flash photography, the overall "output" of the flash unit lasts a finite time, in making photometric "calculations" we need to think of such measures of flash impact as the illuminance-time product on the subject. (Its unit is the lumen-second per square meter.)

In fact, the total "output" of a flash unit (in one "burst") is its luminous flux-time product. (The unit is the lumen-second.) Its total output in a particular direction is its luminous intensity-time product in that direction (the unit is the candela-second).

Note that the flash unit property Guide Number is directly relatable to the luminous intensity-time product (it is in a special form to allow us to solve the "standard flash exposure equation" in our laps).

Often, the output of flash units is stated in watt-seconds (the preferred SI unit is the joule, numerically identical). That is not a photometric unit, nor does it tell us any of the photometric quantities of interest. It tells us the electrical energy stored in the storage capacitor of the flash unit.

On any given flash unit, various watt-second settings generally produce proportional values of the quantity total luminous flux-time product (in lumen-seconds). However, the constant of proportionality varies substantially between flash unit models.


Aren't you glad you asked!

Best regards,

Doug

Did you use the link in Alex Krenvalk's reply to Doug's post?

If you clicked on the link in Alex Kenvalk's, (since deleted) "reply" to Doug's separate recent thread on Fourier Transforms (now mysteriously disappeared), or you want to know why Alex was banned, then read my new thread here. It explains why "Alex" was banned. Of course, I could have banned an innocent person. If so, and Alex, you are indeed a real person, my apologies.

Asher

Doug, this is a very clear explanation, as is your wont, of important concepts in how we can consider the relative power of light sources and their effect in lighting up a subject for photography.

Could you also add your thoughts on the effect of the type of light modifier. How about focused light or the use of a parabolic reflector? Perfectly collimated light or a focused light source may not seem to follow the inverse square law.

Asher

Asher Kelman said:

Doug, this is a very clear explanation, as is your wont, of important concepts in how we can consider the relative power of light sources and their effect in lighting up a subject for photography.

Could you also add your thoughts on the effect of the type of light modifier. How about focused light or the use of a parabolic reflector? Perfectly collimated light or a focused light source may not seem to follow the inverse square law.

Click to expand...

Yes, let me try to add some further thoughts on that.

Regarding the inverse square law, it obtains invariably if the source is of negligible dimensions (compared to the distance to the subject). But we rarely have that in our work. (The closest I come to it is firing my 580EX II to the far end of a stadium - and I need to buy a Better Beamer for that!).

But in fact when we have, for example, a big soft box, then the "inverse square law" doesn't really apply (such a setup does not even approximate a "point source").

Let me see if I can work up something in this regard that can be useful. The matter is actually very complicated. But I can show what the relationships are for a hypothetical emitter with certain idealized properties. Sadly, any real system will probably not even come close to that.

Best regards,

Doug

Doug Kerr said:

Yes, let me try to add some further thoughts on that.

Regarding the inverse square law, it obtains invariably if the source is of negligible dimensions (compared to the distance to the subject). But we rarely have that in our work. (The closest I come to it is firing my 580EX II to the far end of a stadium - and I need to buy a Better Beamer for that!).

But in fact when we have, for example, a big soft box, then the "inverse square law" doesn't really apply (such a setup does not even approximate a "point source").

Click to expand...

Doug,

Thanks for taking this on! It's really about us being taught the relationship to distance of the light from the subject. The rule is, according to the inverse square law, doubling the distance from the source reduces the power at the subject to 1/4. What is left out, of course, is that this relationship holds true for light arriving at any area distant from a tiny light source and at relatively short distances. You of course, know everything I'd write, but for completeness, my take on this:

Where the inverse square law doesn't seem to fit!


So then we need, as I have said previously, maps of light distribution according to the distance from a particular light reflector/light box, bare reflector or any other light modifier.

How you can make this easier to understand without the MFRS supplying maps, is, on a practical level, a major challenge!

Asher

Hi, Asher,

The inverse square law doesn't apply to an "extended" source primarily for this reason:

Indeed, we can consider an extended emitter to be a collection of many point sources.

If we could isolate any one of those myriad hypothetical point sources, then at some point on our subject (which would be along a line from that point source at a certain angle, and would be a certain distance from that point source), the contribution to the illuminance on that subject at that point would indeed follow the inverse square law. To be very precise, we would have to reckon the distance along that line, not from the center of the "soft box", although that distinction is not usually a big deal.

But now as we consider all the other hypothetical point sources, we find that for each one, the point of interest on the subject lies along a different angle from that point source, and so (even if the point sources have identical "emission patterns"), the luminous intensity toward the point on the subject is different for each one. And of course across the face of the soft box the patterns are not liklely identical anyway.

Now, if we move the subject to, say, twice the distance from the soft box, all those angles change, and so all the luminous intensities (from the individual hypothetical point sources) change - as well as the distance from them.

As a result, the net illuminance on the point on the subject does not (necessarily, or even likely) change as the inverse of the square of the distance from the center of the face of the soft box.

Best regards,

Doug

Hi, Asher,

Sorry I didn't have a chance to comment on your detailed presentation before - we were rushing out the door to the preparations for a big social event tomorrow.

Asher Kelman said:

Thanks for taking this on! It's really about us being taught the relationship to distance of the light from the subject. The rule is, according to the inverse square law, doubling the distance from the source reduces the power at the subject to 1/4. What is left out, of course, is that this relationship holds true for light arriving at any area distant from a tiny light source and at relatively short distances.

Click to expand...

Good so far. I'll accept your use of "power" as a colloquialism for the actual property of interest (which is luminous flux density).

Where the inverse square law doesn't seem to fit!

1. The sun: So for a point light source, the sun, which occupies a tiny part of the sky, the inverse square law applies but the distance of 5, 10 or 50 feet are insignificant as an addition to the distance from the sun and so as far as we're concerned the light is constant and the inverse square law doesn't apply.[/quote]
It applies - it's just that the effect is insignficant, for the reasons you mention.

For [a] large source relatively close to the subject, again the inverse square law seems to only partially apply, but why?

Click to expand...

I think I may have covered this in my "interim" message. There are three considerations . One has to do with the "target" being at a different angle "off the boresight" of all those little emitters except the ones right on axis. The second subtle factor is that the distance from the emitter to the target doesn't change exactly the same as the distance to the target from the center of the source (since it is oblique - Pythagoras, you know). The third is that the light arriving from each of the little emitters "off axis" arrives obliquely at the target point. Altogether, we have four of those pesky cosines at work there.

In fact, if we assume a circular "extended" emitter which is "Lambertian" across its whole surface (this tells us how the luminous intensity varies with "angle of observation"), and we start with a target at such a distance that the emitter is "40° wide" as seen from a point on the target, and we double the distance to the target, the illuminance on that point will be 0.27 times what it was in the first case (not 0.25 times, as the inverse square law would predict).

Departures of the "pattern" of emission from the "Lambertian" ideal can enlarge this discrepancy. The typical rag front of a soft box does not exhibit a Lambertian pattern.

You can observe this by observing your lit softbox (with, say, the modeling lamp on) from straight ahead and from a substantial angle. If the emission were Lambertian, you would see the same perceived brightness in either observation.

Best regards,

Doug

There's another issue, (but so esoteric to seem almost off topic), where we consider a single photon that does not hit any molecules of matter on the way to the person one is photographing. That photon, AFAIK, will not lose any light intensity on its path. What really is happening with that? Well it doers not diverge! A single photon will not give up it's energy no matter how fat it travels as long as gravity and other major forces do not alter its path.

So a point source really is source of light diverging in every direction unless blocked. Photons moving at angle will not lose power as long as the energy is not lost to some molecule in the intervening air or other medium. However, in practice, since all light from most light sources diverges as if from multiple point sources, then any given surface will receive less photons per square cm as distance increases, as long as a focusing reflector is not used. So therefore it seems that light in any line decreases, but really, it's light per unit area that has less light not the solid angle or the single photon.

Asher