About luminous flux density

[Doug Kerr]

In technical articles, we commonly see the “potency” of a light beam at a certain place in its travels quantified as the illuminance of the beam there.
But that is not apt. Illuminance is not a property of a beam of light at some place in its travels. It is a measure of the illumination afforded by a beam of light on some surface, having a certain orientation, at such a place.

What does properly characterize the “potency” of a beam of light at a certain place is its luminous flux density. Yet we almost never see that quantity mentioned. Luminous flux density and illuminance have very similar definitions, and are closely related, so it is perhaps understandable that authors get them confused.

I sort this out (hopefully) in a new technical article on The Pumpkin, "Luminous flux density: the rarely mentioned photometric quantity".

This is a link to its listing on The Pumpkin index page:

The Pumpkin

Index page of Doug Kerr's The Pumpkin

dougkerr.net

Best regards,

Doug

 

[Jerome Marot]

Personally, I find all these definitions much simpler to understand when talking about energy. There is a light or, generally, electromagnetic source. It emits some energy in some directions of space. "Flux" is that energy in a particular direction. When talking about "illuminance" we simply need to multiply by the particular spectral sensitivity of the human eye.

But that is just me. Thanks for the paper.

 

[Ted Cousins]

Personally, I find all these definitions much simpler to understand when talking about energy. There is a light or, generally, electromagnetic source. It emits some energy in some directions of space. "Flux" is that energy in a particular direction. When talking about "illuminance" we simply need to multiply by the particular spectral sensitivity of the human eye.

But that is just me. Thanks for the paper.

Found this on-line, quite helpful:

https://luminusdevices.zendesk.com/...lux-Illuminance-Luminous-Intensity-Lux-Lumens

Does not illustrate flux density ... but one can see the inverse square law at work in the beam from the candlewick ...

 

[Doug Kerr]

Hi, Ted,

That is really pretty nice.

Indeed it misses the "step" in the phtometric chain that quantifies the "potency" of the beam when it is about to hit the target surface shown - that metric being the luminous flux density.

But, as I decry in my recent Pumpkin article, jumping the luminous flux density step in the "trail" in, say, some phtometric derivation is almost universal.

Best regards,

Doug

 

[Doug Kerr]

Often, some algorithm can most readily validated (or invalidated) by testing some special case. But this often goes awry, as when it leads to a division by zero some place in the trail.

In other case we recognize the algorithm as being empirical, and can accept that outside of some "usually-encountered" range its accuracy may severely degrade.

That having been said, it is entertaining to look into the behavior of the famous "duplex metering" scheme for a special case: where the sole light source is at the camera.

Suppose that light source affords at the subject, on a plane "facing" the light source, some illuminance Ev1. Our meter, facing that light source at the subject, indicates that illuminance. We set that into the meter's exposure calculator, and it returns a certain photographic exposure recommendation. Surely this is the "proper" exposure for this shot.

Now we place an imaginary light source at 90°, imaginary in that its potency is zero. But we press on with the duplex measurement. We aim the meter toward this imaginary light, and the meter indicates an illuminance of zero

The geometric average if two values, one of which is zero, is undefined. So I will use the arithmetic average. This is just half the illuminance indicated in the first measurement. We dutifully set this into the exposure calculator, which returns an exposure recommendation twice that of the earlier measurement (which we decared to be "proper" for this shot).

Yet nothing has actually changed, the 90° light being imaginary, with zero potency. How has the duplex measurement scheme failed so badly?

I suspect the answer is, "It is empirical, and is only fairly 'correct' for some reaonable ratio betwwen the two light sources."

******

I note that, in this contrived example, a "Norton" expsure meter would of course give the same exposure recommdeation with and without the imaginary, impotent second light source (since we do not "re-aim" the meter when we add thqt imaginary source). And assuming that this meter exhibited some resonable value of C, then that exposure recommendation would be "correct".

Interesting.

Best regards,

Doug

 

[Doug Kerr]

Sorry - I had meant to post the above essay in the thread on "Norwood's Dome".

Best regards,

Doug

 

[Doug Kerr]

This is not as "stylish" as the figure above, but I think is more complete.

I note that if the target surface is "Lambertian" (i.e., a perfect diffuse reflector), then the luminance will be the same from any angle of observation (in front of the surface, of course).

Best regards,

Doug

 

[Doug Kerr]

I do not at all mean to suggest that this illustration by itself explains the various quantities. For example, actually explaining the quantity luminous intensity typically requires (at least from me) a paragraph or so of text.

Best regards,

Doug

 

[Doug Kerr]

Here is one of my "canned" explanations of luminous intensity:

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Luminous intensity is the measure of the “potency” of a very small light source (ideally, a “point source”), in a certain direction.

It is defined as the amount of luminous flux per unit solid angle in the emission of light in that direction by that source.

Why “per unit solid angle”? Could we not just speak of the amount of luminous flux emitted in that direction? Well, the amount of space “in a certain direction” is just a line, and has zero cross‑sectional area at any distance. Thus it could not contain any flux at all.

So instead we report the amount of luminous flux per unit of solid angle in the direction of interest (generally thinking in terms of an infinitesimal solid angle).

******

Best regards,

Doug