light meter measurement: incident light and the inverse square law

Tim Gray said:

You treat the line source as a line or a collection of points, there's no real difference. Actually the math is quite easy. I'm not sure what you are trying to prove with this kind of statement.

If you really insist on calling a line a collection of points, then go right ahead. Most of us, casually and mathematically, have a name for a collection of points: a line. As was stated before, inverse square law stems from essentially geometric arguments.

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What that statement is trying to show (if it is trying to show anything) is that this inverse square thing is not such a strange and exotic thing.
There's no real difference indeed, whether point or line, except that you don't calculate the effect of a change in distance from subject to one point light source, but to many. Each behaving in the 'inverse square way'.

Why make it clear that this is not an exotic phenomenon, but on the contrary quite 'the norm'?
Because despite it being so obvious that the OP's hunch about the light fall off was spot on, it gave rise to some serious doubt, and hard work explaining that there is nothing strange going on.

Q.G. said:

There's no real difference indeed, whether point or line, except that you don't calculate the effect of a change in distance from subject to one point light source, but to many. Each behaving in the 'inverse square way'.

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All I can say it's much easier to think of a line source as a line mathematically in this case and not as a collection of points. One can do that problem, but it's a heck of a lot easier to look for the symmetry in the problem.

Tim Gray said:

All I can say it's much easier to think of a line source as a line mathematically in this case and not as a collection of points. One can do that problem, but it's a heck of a lot easier to look for the symmetry in the problem.

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It hides the fact that this inverse square thing is at work then too.

And i'm not going to do the math.

Alright you win. Look at a big line source and think, "That's a collection of points, all behaving the inverse square law." What does that tell you about how the light falls off with respect to distance? I'd rather look at it and say it's a line source and it falls off as 1/r.

It's geometry. That's it. Inverse square law is for a point source (hint - it's not just for light). A collection of points is a line. It doesn't hide anything about that the 'inverse square thing is at work'. It's not a point source. A collection of points is not a point.

Again, the math is pretty dang easy. If you can write a fraction, you've done the math. I'm out. Hope I didn't annoy anyone being too pedantic.

You're not one for representing things the way that makes most sense in a given context then?

Q.G. said:

There's no real difference indeed, whether point or line, except that you don't calculate the effect of a change in distance from subject to one point light source, but to many. Each behaving in the 'inverse square way'.

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Not in any radiometric sense. As Tim stated, a point source, a line source, and an extended source are all different. The inverse square law is for point sources only. An area is not a collection of point sources not does it behave the same. This is well recognized in astrophotography where extended objects and stars are effected differently based on f-number and entrance pupil.

As stated before and from the Focal Encyclopedia of Photography:

Point source E = I/d squared
Line source E = I/d
Extended source E is invariant with d

Hikari said:

Not in any radiometric sense. As Tim stated, a point source, a line source, and an extended source are all different.

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Of course they are.
Where did you get the idea that only Tim thinks or says so?

Hikari said:

The inverse square law is for point sources only. An area is not a collection of point sources not does it behave the same.

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Why does this happen all the time..?!

Yes, it is, and it does.

I'm not going to tackle the, judging by how hard it has turned out to be to explain something very simple, no doubt unsurmountable problems that would be encountered explaining that to you.
So read a good book about photometry.

Q.G. said:

Of course they are.
Where did you get the idea that only Tim thinks or says so?



Why does this happen all the time..?!

Yes, it is, and it does.

I'm not going to tackle the, judging by how hard it has turned out to be to explain something very simple, no doubt unsurmountable problems that would be encountered explaining that to you.
So read a good book about photometry.

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Thank you. I have radiometry and photometry books. And I have read them. You do not need to explain anything to me because I understand how light works and behaves in this context. It is well documented.

Hikari said:

Thank you. I have radiometry and photometry books. And I have read them. You do not need to explain anything to me because I understand how light works and behaves in this context. It is well documented.

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Good.

My earlier comments applied to the great outdoors.

On the other hand, if using incident light metering indoors (e.g., light source is a window, lamp or flashgun) then distance from light source does matter and the inverse square law (subject to light source, but not subject to camera) does apply and readings should be taken as close as possible to the subject, meter pointing towards the camera.

Folks, incident light metering (like the tides) does work in a predictable fashion. If you want to explain just how it is that it works, there may be a PhD. thesis in it for you.

Incidentally, (pun intended) for those who agonize about metering a 3-dimensional subject half in the light and half in its own shade (say, a subject's face), that is exactly why the meter has a dome (some domes being more sophisticated than others) which, if the meter is pointed correctly, results in an in-meter averaging of the required exposure with a single reading (the dome being a model for the face).

In fact, this is what makes incident light metering so convenient: this relatively simple device -with a single reading- results in the same exposure outcomes as is generated by the averaging of a number of spot metered readings, shade and light averagings taken by reflected light metering, and any number of "you beaut" "matrix" and "honeycomb" metering contraptions.

There's a nice example in Photographic Materials and Processes that might help to clear things up. "If a hand held meter with a 50 degree angle of view is used to measure the reflected light from a given surface, the luminance obtained will be identical to that which will be given by a spot meter reading on the same area at the camera position. The reason for this independence is the fact that as the amount of light being measured from the original area decreases with increasing distance, the projected surface area included in the angle of view increases in direct proportion."

I skimmed through part of this thread, though I did not read the whole thing. If I repeat anything said by others without acknowledging your post please forgive me, and feel free to point it out if you want.

Now let me make a few comments. First of all, the inverse square law is correct and applies to essentially all cases, though it may seem to be hiding in some cases.

If you consider a small fraction of an emitting or diffusely reflecting body then the intensity of the light from that body is proportional to 1/r^2. The relationship applies when the size of the little chunk of emitting (or diffusely reflecting) body under consideration is small compared to the distance from the body.

A neighboring chunk of the emitting (or diffusely reflecting) body behaves the same way, namely when you are far away from the chunk the intensity of light from that chunk is proportional to 1/r^2.

The total amount of light being emitted is independent of the distance from the light emitting body. In other words, if I draw a small sphere around the body and measure the falling on the inner surface of the sphere then the total light is independent of the distance from the emitting body, or in other words it is independent of the radius of the sphere. Let me coin a term for this. I will call it the law of conservation of radiative flux. This law of conservation of radiative flux can be thought of as the origin of the 1/r^2 law, or alternatively the the law of conservation of radiative flux can be considered a consequence of the 1/r^2 law. It really doesn't matter which you consider to be the fundamental relation and which you consider to be the derived relation. It all amounts to the same thing.

Now, I believe the basic question in the thread revolved around the question of why you don't have to change the exposure setting as you place the camera at various distances from the object, given that the light intensity falls off as 1/r^2. The reason is that the image size (in terms of area) of the object on the film is also proportional to 1/r^2. Thus, the radiative flux per unit area on the image of the object on the film plane, being the ratio of the light intensity to the image size, is independent of the distance from the object to the camera lens, and you don't have to change the exposure.

There is a special exception to the description above. It is not an exception to the laws of optics, but rather relates to the consequences of how the laws apply to certain cases. If the object is essentially a point source then something else happens. When I say "point source" I don't actucally mean that the light originates from a point object, but rather that the ideal image of the object as it is projected on the film plane is smaller than the spot size of the lens. The spot size is determined by a combination of lens aberrations and diffraction, and these cause a point source to be imaged as a small spot of finite area on the film. In the case of a point source the area of the image is independent of the intensity of the light source. However amount of light focused in the image (a fuzzy point of finite size) is proportional to 1/r^2. Thus a star gets dimmer on the film plane as the distance gets greater, and you may need to adjust the exposure to record an image of a distant star.

I have left out some parts of the explanation and a few of the fine points, but I hope there is enough there to be understandable.

alanrockwood said:

...I have left out some parts of the explanation and a few of the fine points, but I hope there is enough there to be understandable.

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Great explanation.

Thanks

Uhh...what was the middle part, again?



JK. Thanks Alan. Very lucid.

Incidental metering for most subjects in my experience produces a much larger proportion of correct exposure than general reflected readings without a lot of f***ing about, it surprises me that more photographers don't use it.

I might need to try this incident reading thing-a-ma-jig. I've been using a spot forever and would be curious to see how my correct exposures per roll either fall or increase. Right now, I'm batting around 50-75%.

Klainmeister said:

I might need to try this incident reading thing-a-ma-jig. I've been using a spot forever and would be curious to see how my correct exposures per roll either fall or increase. Right now, I'm batting around 50-75%.

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I am surprised by your batting average (it should be far higher).

I too often use a spot meter, but I find it very successful.

In my case, I pick on an easily metered patch in the scene, decide what zone (as per Ansel Adams), adjust the exposure to place that patch in the selected zone and blast away. (A single -"key tone"- reading is usually all I need)

This "key tone" method seems to work practically every time, and can be done (if the patch is big enough) even using a normal reflected light meter (even using the TTL metering, in manual mode). It produces great "contra jour" results (my favourite), and even works in heavily shaded situations (under trees, inside buildings).

alanrockwood said:

...
I have left out some parts of the explanation and a few of the fine points, but I hope there is enough there to be understandable.

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I read through you splendid explanation again, and -again- found myself to be impressed.

I guess it has often been noted before but is worth saying again: a thing may be so, but it takes a "philosopher" to prove that it is indeed so.

(Similar to: anyone can build a bridge that stays up, but it takes an engineer to build one that only just stays up!)

Galah said:

I am surprised by your batting average (it should be far higher).

I too often use a spot meter, but I find it very successful.

In my case, I pick on an easily metered patch in the scene, decide what zone (as per Ansel Adams), adjust the exposure to place that patch in the selected zone and blast away. (A single -"key tone"- reading is usually all I need)

This "key tone" method seems to work practically every time, and can be done (if the patch is big enough) even using a normal reflected light meter (even using the TTL metering, in manual mode). It produces great "contra jour" results (my favourite), and even works in heavily shaded situations (under trees, inside buildings).

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Well, I often find myself chasing that last bit of sunlight and doing hasty metering. I'm also pretty picky with my negs, but ultimately my judgement can be off in finding something medium gray. That, and then trying/learning the BTZS has caused some interesting results. I'm guessing my development had more to do with some of that batting average than metering come to think of it. All is well though with Pyrocat HD now.