## Saturday, June 12, 2010

### Fall-Off

The brightness of any point-source illumination diminishes rapidly with distance. This weakening of light is called fall-off.

It diminishes according to the inverse square law, which states that the effect of a light shining on a surface weakens at a rate comparable to the square of the distance between source and surface.

As the diagram above demonstrates, at twice the distance, the light is only one fourth as bright because the same rays must cover four times the area. At three times the distance, it drops to one ninth as bright.

Les said...

Okay, this is one thing that has bothered me -- if the light comes from the sun, how could the distance between one object and another on this earth affect the light on them? It does, obviously, and I've assumed it to be related to atmospheric interference, but is that all? Would the rule still hold if you compared equal distances in humid Washington State versus dry Arizona? It apparently doesn't hold true in space.

I think it's related to "rays of glory" effect. Poke a few holes in the clouds in front of the Sun and you get this marvelous starburst effect where the light scatters in a pattern unrelated to the actual path of the sun's rays. The burst bends, as it were, off the clouds in front of it, I guess, 30 to 40 degrees away from the original path of the rays.

In any case, the rule can get mighty complicated, I guess, depending on the influence of our watery planet.

artistguy said...

The falloff from the sun is different than the falloff from a light source that is close to a subject. For example a room light, or camera flash or, window light. They are all within a relatively short distance to the subject. You can actually place objects far enough away from each other to see the effects of light falloff in those cases. Like a lamp sitting 3 feet from a subjects face and 6 feet from another subjects face will make a big difference. Now the sun on the other hand is 93 million miles from earth. In order to put subjects far enough away from each other to show light falloff you'd have to have the subjects on different planets. Totally possible in sci/fi art! But there is no noticeable light fall off from the sun here on earth no matter how far away the subjects are from each other. But atmosphere can cause light dispersion and also absorb some of the light, but that's technically a different ball of wax.

Michael said...

artistguy I don't think you have explained the difference except to mention distance. The sun is the source behind window light. The difference between the sun and all other light sources encountered on this planet has to do with the intensity of the light source. A laser beam is going to have different falloff than a halogen bulb in a reading lamp at the same distances from an object. Anything interfering with a light's intensity makes a difference i.e. water and dust particles, glass, leaves, etc.

Les said...

, Google translated as, "The article does not seek fame, whims and is really....."

James Gurney said...

Les, I think Artistguy has it right: the sun is so far from the earth that the fall off between objects on the earth would not be appreciable.

On a further planet in the solar system, however, the power of the sun would be diminished by something close to the inverse square law (assuming the sun were a point source).

You're right in saying that the sun's power is noticeably diminished by the distance it travels through atmosphere. The sun, traveling nearly tangent to the earth's surface at sunset, is passing through so much atmosphere, and losing so much light through scattering, that we can often safely look directly at the disk of the sun just as it goes behind the horizon.

The apparent effect of the angular spreading of beams of light from the sun is simply the effect of perspective. Like railroad tracks going back to a vanishing point, they're effectively parallel but only appear to spread apart.

Don Cox said...

A laser beam is not a point source, as it does not radiate equally in all directions.

Direct sunlight coming through a window is a case of light from a distant point source, but the diffuse sky light coming through a window is not a point source.

In artificial light, a single candle flame in a large room approximates to a point source. So does a bare bulb hanging from the ceiling, especially if it has a compact filament as in quartz halogen lamps. Frosted lamps, lamps in shades, or fluorescent tubes are not really points and the inverse square law applies only very roughly. The light from a large lamp does obviously fall off with distance, but not exactly in inverse proportion to the distance.

James Gurney said...

Well said, Don. True point sources are relatively unusual, ideal types.

These principles are especially important to lighting designers in film who are illuminating actors who approach the camera (and often the light) during a scene. The light has to be gradually diminished in proportion to proximity to keep the apparent exposures constant.

cheesecake-weasel said...

hi there, i do 3d modelling and often use these referencse from a help file, don't know if it will be of use to anyone: http://cheesecake-weasel.blogspot.com/2010/06/lighting.html

James Gurney said...

Thanks, CW--those are fascinating image comparisons. You can really see how the bounced light changes each scene.

andeeroo said...

light falloff alone does not affect brightness and dimness. In the codex urbinas, Leonardo Da Vinci said light rays falling upon an object at more or less equal angles will be brighter (especially those bounced straight back). In a square room with a ceiling light fixture directly center, remove the fixture leaving only the bulb. The tops of the walls will be brighter than the fringe of the ceiling even though they are further away. This is because the light hitting the fringe of the ceiling is deflected more readily like a ball thrown against a wall at a shallow angle.

Can anybody help me with the relationship between falloff and what Da Vinci noticed? are there other anomalies?

James Gurney said...

Andreeroo, you're right in theory, but I'm only looking at one variable at a time to explain what's going on. That's why in the diagram, the planes are held parallel. In the interesting example you cite, the light changes not only with distance, but also with changing angles of incidence.

The behavior of light from a single source as it strikes walls at various angles would fall under the category of the form principle, where the brightness is proportional to the angle of incidence. The reflectivity of the paint becomes another variable.

In an actual case of a bulb in a room, you'd also have to factor in perceptual effects, since the fringe of light around the bulb may not look as bright as the top of the wall because of the comparison of what's around it. You'd need to test it with a light meter to see what's really brighter.

andeeroo said...

Apologies if my question feels redundant. I know it's hard to answer because of the shear number of variables, but what variables do you think are the most important to make a convincing representation of light? I mean, if you had to choose say, a maximum of 3 or 4? The reason I ask is because I'm going for a cartoony style nowhere close to photographic realism but still conveys a sense of light and depth.

Cheers

Anonymous said...

Can this approach be measured in terms of Munsell value steps? If so, how?

James Gurney said...

Anonymous, that's a good question, but I don't know the answer. It makes sense that as the surface recedes from the light source that it should darken by some formula, but I'm not sure what that formula would be.