inverse-square law and exposure

[John Chardine]

The inverse-square law suggests that as you get farther from your subject, the amount of light received from the subject declines. Roger mentioned this in a post the other day. This should affect the correct exposure of the subject. I tested this by putting up a white screen on my display, taking a spot meter reading from the centre of the display, then doubling my distance away and taking another reading. By doubling the distance I should get 1/4 the light, or two stops less. Here are the results:

ISO 400

1 meter away, 1/80s, f8
2 meters away, 1/80s, f8
4 meters away, 1/80s, f8

You get the picture!

So as I'm backing up, the spot meter is reading from a bigger area of the display and therefore taking in more light, so maybe that is what compensates for the distance. But how is what I did different from taking a spot meter reading of someone's face at say 5 meters, then backing up to 10 meters and taking another reading on just the face? Here's another example- say I was Buzz Aldrin on the moon making images of the surface. Would he have used the same exposure settings that I would use on Earth with my 500mm lens so long as ISO was equivalent?

[Alan Melle]

I don't think that is a correct interpretation of the Inverse Square rule. The Inverse Square applies to the distance of the light source to the subject, not the distance of the photographer to the subject....unless the photographer is also carrying the light source. In this case your subject is a backlighted display screen. The distance of the light source to the screen does not change when you change position so the exposure remains the same. Now if you use the backlighted screen to provide light on an object and you move the object away from the screen (the light source) then you will find the inverse square rule coming into play.

[John Chardine]

Hi Alan- the inverse-square law just describes how electromagnetic radiation, e.g., light, spreads out (falls off) with distance from source. The source can be reflected light or from a luminous object.

http://en.wikipedia.org/wiki/Inverse-square_law

Anyway, the thread I mentioned is here:

http://www.birdphotographers.net/forums/showthread.php/106648-Picture-size

and the quote from Roger is here (excerpt from pane 5):

"Now if you can change your distance to the subject to get closer, or use a larger lens, you gather more light. The full frame sensor has the advantage if one can get closer to fill the frame, or use a larger lens. For example a 1DX + 600 f/4 beats out a 1DIV + 500 f/4 because the 600 f/4 lens has a larger aperture and collects more light. A 1DX with a 500 would also beat out a 1D4+500 if the 1DX moved closer to fill the frame: closer means more light collected from the subject (the 1/squared distance law)."

[arash_hazeghi]

John, the law you are talking about is for spherically-symmetrical radiation from a point source, i.e when r_s << r_d . it does not apply to your examples above as you do not have a point source. your light meter is good.

for photography, especially avian we do not deal with point sources, the meter uses ambient light, i.e. light reflected from the sky, background etc. so the distance argument don't really apply i.e. it is not sensitive to subject distance. You can test this in the field next time you are shooting a bird...

if you want to see this effect try metering a candle in a really dark room from a few yards away, it's a better example.

[John Chardine]

Thanks Arash. So if the candle is a good example of this then maybe subjects small in the frame (focal length limited situations) would also be. Could you explain what r_s and r_d are. Also, still interested in knowing the answer to the moon example I gave.

[arash_hazeghi]

hey John,

It doesn't apply to that case because the point source has to be the sole source of the radiation. In small bird in the frame most of the light is actually from ambient not the bird (that's why I said really dark room). I can't think about any case that it would apply to bird photography. rs= light source radius, rd= working distance.

In the case of moon or a distant star you can see that it does act like a point source, however the distance to the source is fixed so it is the same for everyone looking from the earth.

best

[Roger Clark]

This is a confusing subject, so I'll try some clarifications. To put it in to perspective, I once made a question like this when I was teaching a graduate course on advanced reflectance spectroscopy when I was at the University of Hawaii, Most grad students stumbled a bit on the answer. But the solution is simple once one understands the concept.

1) Light from a point source shows the 1/square law.

1) Light from every spot on a subject, like a small detail in a feather on a bird, and the light reflects in multiple directions: such spots show the 1/square law from the source (e.g. the spot on the bird). This is diffuse reflection and the majority of what we observe and photograph in the natural world. The 1/square law applies.

2) light reflected from perfectly flat surface is directional reflection, and the 1/square law still applies, but the distance is to the source, not the reflecting mirror. If the mirror were perfectly flat, the distance to the source would be the sun (for terrestrial photography).

2a) partially directional (or partially diffuse) reflections have a virtual source in between #1 and #2.

Thus, the inverse square law applies to all subjects all the time. There are no exceptions but one must use the correct source distance.

Now the confusing part (but also the important part in photography and detail on a subject).

John in your experiment you used a uniform target that hid some of the effects of the inverse square law. As you backed up, the light from each spot on white screen gave you less light (e.g. each square mm, or each square micron on the screen). But by backing up, you changed the spatial field of view at the subject: the spatial size of what each pixel sees on the screen. That change in area perfectly balances the light fall-off. So back up 2x and the light fall-off from a spot is 4x, but the area imaged by the pixel increases area by 4x, thus balances.

OK, but that test was for a uniform subject. What about a real subject where we want to resolve detail on the subject? Say we want to resolve the feather detail in the feathers on a distant bird. By standing in one spot, we can increase focal length (add a TC), to make the pixel see a smaller area on the subject. Photographers (especially in today's digital world) seem fixated on the focal plane (the pixels) but should instead think about the subject. By increasing focal length (e.g. adding the TC), the pixels see smaller detail on the subject. But by adding the TC, photographers say there is less light so one needs a longer exposure time. Actually the light per detail is the same! You only way change the amount of light is by increasing the aperture (diameter of the lens) or moving closer (the 1/square law) (excluding lengthening the exposure time). If you sum the light over the same detail with and without the TC, the amount of light will be the same. If you want more light for the smaller detail on that spot on your subject, you need to do one of 3 things: 1) lengthen exposure time, 2) increase the diameter of the lens, or 3) move closer (1/square law).

Summary: inverse square law always applies to all photography and everything we see in everyday life, just gets hidden by changing detail (spatial resolution) on the subject.

Roger

[arash_hazeghi]

The arguments above is very misleading for a photographer as a bird is not a point source neither is it a uniform flat surface that fills the frame to argue fall-off is canceled by FOV. It reminds me of spherical cow in vacuum joke :w3



just go shoot a bird from 10 yards and then 20 yards and see for yourself.

[Roger Clark]

The arguments above is very misleading for a photographer as a bird is not a point source neither it is uniform flat surface that fills the frame to argue fall-off is cancels by FOV. It reminds me of spherical cow in vacuum jokes.

just go shoot a bird from 10 yards and then 20 yards and see for yourself. It doesn't apply and photographer don't need to worry about it.

And what happens when you back aff to 20 years? The pixels on subject reduces 4x (area), so you've collected 4x less light on the subject (thus inverse square law). One can also say the light per pixel is the same, but that is only because the area per pixel increased 4x.

This forum is about the science of photography and explanations of the effects going on. Understanding such effects allows one to make better decisions in the field. You can choose to understand and apply the knowledge or not.

Roger

[arash_hazeghi]

And what happens when you back aff to 20 years? The pixels on subject reduces 4x (area), so you've collected 4x less light on the subject (thus inverse square law). One can also say the light per pixel is the same, but that is only because the area per pixel increased 4x.

there are 2 misleading statements above

1) bird is not a sole point source, most of the light that the sensor collects is ambient light, from the BG, sky etc. it is uniform scattered light and doesn't fall off with distance.

2) you get 4X less pixels but each pixel is equally bright, so in terms of camera exposure it makes no difference. Any photographer can tell exposure does not change when they get closers to farther from a subject under the same lighting. The resolution/detail is a separate argument and should not be confused.




This forum is about the science of photography and explanations of the effects going on. Understanding such effects allows one to make better decisions in the field. You can choose to understand and apply the knowledge or not.

Roger


Not when something is explained using unrealistic assumptions that do not apply to the actual case, i.e. spherical cow in vacuum. (http://en.wikipedia.org/wiki/Spherical_cow)
It does not relate to field photography and it does not help photographers make better decisions, it confuses them rather.

Too much abstraction with theory often results to misleading results.

[Roger Clark]

there are 2 misleading statements above

1) bird is not a sole point source, most of the light that the sensor collects is ambient light, from the BG, sky etc. it is uniform scattered light and doesn't fall off with distance.

The bird is not a SOLE point source; it is the SUM of a bunch of point sources. Each point source displays the 1/square rule. Here is a way to prove that a "large" diffusely reflecting target obeys the 1/square law. In a dark room or perhaps outside at night, place a light (e.g. a spot light) so only the paper is illuminated. Do John's experiment and get the same results. Now get a second sheet of paper and place it at 1 meter, two meters, 3, 4, etc. Now image the SECOND piece of paper and measure the exposure. The exposure will drop with distance from the first paper, proving the "large" diffuse source obeys the 1/square law (note in a small room, there could light reflected from the walls making the second paper a little brighter).



2) you get 4X less pixels but each pixel is equally bright, so in terms of camera exposure it makes no difference. Any photographer can tell exposure does not change when they get closers to farther from a subject under the same lighting. The resolution/detail is a separate argument and should not be confused.

While exposure (light) per pixel, one gets the same exposure. it is entirely due to the change in spatial detail on the subject, compensating for the inverse square law, not that the inverse square law does not apply.




Not when something is explained using unrealistic assumptions that do not apply to the actual case, i.e. spherical cow in vacuum.
It does not relate to field photography and it does not help photographers make better decisions, it confuses them rather.

How ironic. Again, this forum is about the SCIENCE of photography and how things actually work, not one's impression. I gave the correct explanation of why one observes the exposure in John's experiment to be the same. It has nothing to do with cows in a vacuum. It does relate to field photography if one wants to record a given detail on a given subject and understand what is going on. If not then simply press the shutter button and don't read this forum.

If you want more detail and the gory equations, see:
Clark, R. N., 1979, Planetary reflectance measurements in the region of planetary thermal emission: Icarus, 40, p. 94-103.
where I give the equations for both reflected and emitted light from planetary surfaces. Note, for example, there are 1/distance squared terms for both the illuminating source (e.g. sun-earth distance) and from the reflecting surface (e.g. a bird or a landscape to the observer).

Note too that the sun and moon are not point sources, yet the light we receive from them obeys the inverse square law.

Roger

[arash_hazeghi]

It has nothing to do with cows in a vacuum. It does relate to field photography if one wants to record a given detail on a given subject and understand what is going on. If not then simply press the shutter button and don't read this forum.



One cannot establish something by getting into circular arguments and irrelevant examples.

The bottom line is that camera exposure DOES NOT change with distance for an avian subject, per John's simple question, period. One can argue and theorize till the cow comes home but that doesn't change the simple fact that every experienced photographer knows. The assumptions are incorrect and the conclusion is misleading.

I wasn't literally talking about cows in vacuum, I thought that one was easy to get :bg3::w3

I do agree that this forum is not useful for photographers. And photographs are made by pressing the shutter not by pseudo-theoretical arguments IMO. Maybe a better name for this forum was "theoretical photography".

Have a good weekend everyone.

[Ed Cordes]

I like the title of this forum as is. I like reading about the more theoretical aspects of photography and enjoy professional give and take in an academic vein. We have all learned a lot here. Heated discussion and argument detracts from the experience we all are looking for. Just my $0.02.

[Roger Clark]

I like the title of this forum as is. I like reading about the more theoretical aspects of photography and enjoy professional give and take in an academic vein. We have all learned a lot here. Heated discussion and argument detracts from the experience we all are looking for. Just my $0.02.

I too see little point in arguing like this. I have resigned as moderator on BPN.
Roger

[Chris Warren]

I like this forum as well, as is. Thanks for sharing your reference, Roger, as I intend to check it out at my earliest convienence.

Chris

[Gary Kinard]

Wow, I just read this. I sure liked your views Roger. I always found them sound and logical. Hummmm

[Grady Weed]

I too see little point in arguing like this. I have resigned as moderator on BPN.
Roger

BPN has lost a good, competent and highly valued moderator. Arguing pushes people away. Way too many sites start out fantastic, then go south due to stuff like this. Sorry to see you go Roger. Thanks for your support!

[Ed Cordes]

I too see little point in arguing like this. I have resigned as moderator on BPN.
Roger
Oh Man! I hope my post didn't lead to this. Roger, I have kept coming back to BPN many times for your scientific explanations of the physics of photography. I have truly learned a lot from you. BPN and its subscribers have lost a valuable resource with your resignation. I would hope you would reconsider.

[Tom Graham]

I am also sad to see you leave Roger. I always watched for your contributions to any forum here.
Your comments and advice were/are based on sound science, total understanding, and exacting research. And your explanations/presentations always lucid. Please continue to contribute as a member if not moderator.
I'll l have to visit your web site much more often. http://www.clarkvision.com/ . Your current site lead in photo of two sandhill cranes is wonderful.
And continuing great scientific work, recognized world wide, with the USGS.

Tom

[adrian dancy]

I can only echoe the comment made by Tom

Thanks Roger
AD

[BillTyler]

The original posting showed a simple misconception, and much of the subsequent discussion seems to have wandered off that point. Let's suppose I'm taking a picture of your face. You're standing in bright sunlight (ouch, squint) and I'm 10 feet away, set at ISO 400. My spot meter tells me the exposure is 1/400 at f/16. Now I back off to 20 feet, doubling the distance. It's true that my lens now receives only 1/4 as much light from your face, but, crucially, that light now needs to cover only 1/4 as much area on the sensor, so each pixel involved in imaging your face receives the same amount of light as before. 1/4 the total light, 1/4 the total number of pixels, no change in camera settings except focus is needed.

Where the inverse square law comes into play more importantly is in the ability of a light source to illuminate a subject. Start with a point source (or something that's very small) such as a small light bulb, or a flash. The light from the flash falls off as the square of the distance, so moving the flash twice as far from the subject results in the subject getting 1/4 the amount of light. Let's use the face example again. Since the face is now getting 1/4 as much light, the exposure has to be upped by 4x, or two stops, to get the same amount of light onto the sensor. This has to do with light source-to-subject distance, and is not at all related to camera-to-subject distance, unless you happen to have the flash mounted on the camera instead of on a stand.

What happens if the light source is larger than a point? All real sources are, of course. Let's go to the other extreme and have an infinitely wide and high light source, emitting light uniformly from all parts of the surface. It turns out that this light source gives the same amount of light to the subject no matter what the source-to-subject distance is. Such a source can be approximated with light modifiers like softboxes, umbrellas, etc. to some extent. The key is to have the source relatively a lot bigger than the subject.

For sources somewhere between a point and an infinite surface, the falloff is somewhere between inverse-square and none at all.

Bill

[John Chardine]

Old thread now but always good to come back to things. Thanks Bill, but see Roger's pane 7, paragraph 8 starting "John in your experiment..." which I think says exactly what you are saying.

[BillTyler]

John,

You're right, of course. I'm in violent agreement with Roger. After the first few posts, which seemed to me to obfuscate the issue, I stopped doing more than skimming. My fault.

Bill