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| Plein-air study painted on the north rim of the Grand Canyon, looking west. |
Blog reader Rockhopper asked about how tones get lighter in the distance as a result of atmospheric perspective:
"How do you define value as the image recedes? I know it gets lighter and I know it goes bluer. Is there a rule in place to define distance with the value? So for example a mountain is 10 miles away, is the mountain at 20 miles way half the value of the 10 mile mountain?"
Here’s a preliminary answer. As you can see, I'm still trying to figure this one out:
I've always assumed it's a linear progression. In other words, if a dark tree near you is a #8 value (with white=0), and the farthest hill twelve miles away is a #2, then dark objects will shift one step lighter in value for every two miles of distance. But the more I think about it, I have a hunch that this assumption may be wrong. I have a feeling there's more to it.
Let’s begin by supposing that the air is evenly distributed with dust and moisture and that the volume of air is equally illuminated throughout.
Would it be reasonable to suppose that looking through atmosphere is like looking through an evenly spaced series of wedding veils? Each parcel of air introduces a fixed amount of additional scattered light.
By this way of thinking, the tonal shift relative to distance would be geometric rather than linear. In other words, let's suppose you suspend wedding veils 20 feet apart from each other in an infinite progression away from the observer. To test the lightening effect, you can have a person with a black velvet coat stand behind the first veil, then run back a little farther and stand behind next, thereby being obscured by two veils. The process continues as the subject goes back in space. Now let's suppose each layer of wedding veil makes the black 50% lighter. The resulting value progression would be #10 @ 20 feet, #5 @ 40 feet, #2.5 @ 60 feet, #1.25 # 80 feet, etc, continuing toward pure white.
I have a hunch, too, that our perception of steps in value is influenced by features in our visual system just as much as it is by external reality, and that the whole problem is beyond any easy math.
I remember reading that the perceptually based value scale that we know from art school is not as simple as it seems. The change in the actual amount of light coming to the eye at each step in the value series is not a linear progression of constant units, like the markings on a water beaker. Instead, it's a non-linear relationship, with each step representing a much greater volume of light than the last. As David Briggs puts it in his excellent website HueValueChroma, "value has a nonlinear relationship to luminance - a surface that looks visually halfway between black and white reflects only about 18% of the light energy reflected by a white surface."
Perhaps there’s a photographer, meteorologist, mathematician or a vision scientist who can help cut through the confusion here.
19 comments:
I would have thought that the inverse square law would come into play, making the regression exponential?!?
Oh, and I assume that exponential loss of intensity would apply even before we take atmosphere into account. So, even in space, you can presumably stare at distant stars without burning your eyes out.
What I've found useful is using saturation as the "visual code" to explain depth in the backgrounds I do for work. Depending on light source and atmosphere (since is not always a blue sky exterior), the foreground planes are more saturated, and I desaturate as I move to Background. This is specially useful when you need to make a dark object all the way to the back, and you already have some dark elements in the foreground. In theory, you could have dark-but-saturated elements in the foreground, and dark-but-desaturated elements in the background. Is not Value what makes them different, is saturation.
Of course, what I do for work is cartoony and graphical, so it becomes acceptable to use any "code" to visually explain depth. I should do more plain air painting and find out if the saturation trick stands in different situations.
Thank you for your awesome blog!
Not that the existence of a rule isn't interesting to ponder, but I wonder how useful such a rule would be to the artist anyway, since the effect on color and value isn't (I assume)only a matter of distance, but also of humidity and air quality. In terms of painting, I'd think that the advice to "paint what you see, not what you think you see" is more applicable than a rule in this case.
Brilliant post, heres hoping a scientist can figure it out, I too thought about the inverse square law, but that would be fade to black. Really difficult to answer, also thank you for taking the time to work it out and looking into it. Sometimes gut feeling helps, but with my eyes they struggle with aerial perspective.
Cracking post and great write up.
Rich
The thing that trips me up in your line of thinking James, is the "evenly lit" part. I think that in order to do any serious math, or even estimation, the position and strength of the light has to be a consideration, and with that, the inverse square law.
With regards to sunlight, the question is where in the vault of the sky is the sun? There may be some conditions that will diffuse the sunlight enough to give the appearance of even lighting, such as an overcast sky, but then you also introduce the effect of water vapor in the clouds, and how equally distributed that is, into the equation.
So with regards to evaluating a landscape: Is the sun high overhead? Behind you? Beyond the subject? I think each of these would affect the relative values perceived between two objects of an identical local color. There's not only the amount of diffusion between your eye and the subject, but also between the light source and the subject to consider. Long light, for example has such amazing color effects due to the fact that it is traveling further through more particulate matter.
I agree however that our relative perception may not be easily quantifiable. I think for more insight, I would recommend everyone look up your posts on James Perry Wilson and his notes on the subject. I can think of few artists who wrote so articulately about their observations on exactly this issue.
Thanks, everybody.
Tom, you're right: understanding this rule isn't necessary for plein-air painters who have the luxury of measuring against what they actually see. But suppose you were a lighting director on a video game with a fly-through shot past city buildings on a hazy day. It might help to know how nature works so that you can set your rendering programs accordingly.
Regarding the inverse square law, that's usually invoked to describe the fall-off of light intensity from a point-source light.
Abraham, the fall-off of saturation with distance is a good rule of thumb in general, but remember that some light-emitting objects get more saturated with distance—the setting sun is often the most highly saturated object in the sky. Likewise, white clouds get slightly more saturated with orange color in the distance until they fade into the gray light of the far sky.
Dear Mr. Gurney.
I recently posted an art and science related quote by Isaac Asimov on my Facebook page (http://www.facebook.com/ClassicalAtelierAtHome/posts/498824730198327). He wrote hundreds of books in his lifetime on many different topics - such as science fiction, all fields of science, the Bible, Limerics (nine out of ten major categories of the Dewey Decimal Classification) - but he never wrote a book about art.
I think that you fill this gap perfectly. You're the Isaac Asimov of art. You're not only as prolific as he but you also combine science and technology with fantastic stories and you explain it in a clear language.
Thank you for this blog and your books!
great subject and good comments. i enjoy dealing with atmospheric theories (and other theories) in painting, yet am always amazed and impressed how artists like Aldro Hibbard, William Wendt, and Edgar Payne were able to bring so much color into the distant sections of their paintings, and still have them read with good depth. They were more colorists , or however we may refer to them; but this is the challenge i often have, i.e. the tradeoff between realistic distance and atmosphere versus color (attractiveness).
Thank you, Björn, that's a very generous compliment. I have the greatest respect for Mr. Asimov's writing and thinking.
John, you raise an important point. The painters you mentioned were masters at using chroma and hue to add to the effect of distance. We're lucky that as artists (unlike photographers) we can completely control all of our variables, and as photographers say, we get it all "for free."
I like to read about "rules" because it makes you think about the principles of art, but painting is not a finite expression. The infinite variables that come into play in any given painting must take precedent over "rules. Observation must trump rules,. And certainly, since the artifact becomes the reality to the viewer, the painter must make adjustments to what he observes in order to more clearly express whatever it is that is being painted. If not, then why not use a camera. Oh, I forgot, cameras have limitations too. Anotherwhy I prefer to paint.
OMG, why? As someone who doesn't possess an ounce of analytical brain cells you just made my head hurt. I'm with Tom .
The attenuation of the light is exponential; this is from the Beer-Lambert law.
However, the "wedding veil" model doesn't quite work because light scattering in the atmosphere is different from a macro-scale object.
It's a good model if the particles in the atmosphere are large compared to the wavelength of light, such as in smog or cloud. This type of scattering is known as Mie scattering. If the particles are small compared to the wavelength of light, then it behaves quite differently, in a process known as Rayleigh scattering.
If the sky is relatively clear, Rayleigh scattering is what dominates. Rayleigh scattering is strongly wavelength-dependent, which is why the sky usually has a definite colour. The effect is that the objects take on the colour of the atmosphere. When the sky is blue, blue gets mixed in.
Of course, the sky isn't always blue. At sunrise and sunset, it can be other colours (all explained by Rayleigh scattering). At those times, objects take on whatever colour the sky is in that direction.
If the particles are large, then Mie scattering dominates. Mie scattering is not strongly wavelength-dependent, which is why clouds and fog tend not to contribute colour of their own.
Interesting discussion.
Pseudonym makes sense in the scattering, particles, wavelengths physics way of thinking. I believe the word math has an element of confusion attached to it even for those who aren't.
Very nice post, man! Wanna bet the exponential rate is the golden ratio? haha
I think a concept I refer to as "apparent value" comes into play. Color perception over distance is relative to which colors we are looking at. Colors have different wave lengths. Some drop out of the spectrum faster. It matters in a value discussion because bright warm colors often appear lighter than they really are. Seen at a distance the "apparent values" change at different rates.
The best advice is not to attempt copying what you see tone for tone but paint the relationships in such a way as they make a good painting.
Not everything needs to be measured. Just eyeball it and if it looks right it is right. Or basically; "What Simone said".
Maybe the "apparent value" could actually be linearly changing with distance. from my now dated studies in computer vision i remember there's a law called Weber's Law which states that our senses (all of them, not only the sight) have a logarithmic response to stimuli. in the seventies another Stevens' law, claims to generalize even more and in the wikipedia page are reported some exponents for the law.
I don't know how atmosphere particles affect the color of an object, but in the void reflected light by lambertian surfaces reduces its intensity with the square of the distance. It could be possible that atmosphere affects color of an object in a even stronger way.
If Weber's Law is correct, it could be possible to test the linearity of value change with CMOS cameras, which have a logarithmic response to intensity.
Your "wedding veil" model seems right to me, though I'd think of the veils as light grey or blue-grey rather than pure white, to allow for objects such as a sunlit cloud or white house that can be lighter than the sky. (These bright objects as you know get darker as they approach the sky colour). Each parcel of air introduces a fixed amount of additional scattered light, and also scatters a fixed proportion of the light coming from the distant scene to your eye. So with one "veil" of atmosphere, what I expect we'd see is not the sum but a weighted average of the unveiled scene light and the veil light. With two "veils" we'd get a weighted average of this veiled scene and the second veil of sky colour, and so on, so I'd expect that objects would approach the colour of the sky at a declining rate, as you describe. I simulated this model in Photoshop using a series of low-opacity atmosphere-coloured normal-mode layers in the figure on this page:
http://www.huevaluechroma.com/108.php
That example, which looks plausible to me, would have been calculated by Photoshop using nonlinear RGB units, but I agree with your suspicion that really the averages should be calculated in linear units.
The inverse square law mentioned in the comments doesn't really come into play here because the fall-off in light energy is exactly balanced by the reduction in apparent size of the object. (An object twice as far sends only a quarter of the light energy to the eye, but also only occupies a quarter of the visual area, so the light energy per area of the visual field is the same).
Thanks very much for linking to my site once again! I'm about halfway through a long-intended upgrade of the section on "Hue", so please take a look if you haven't recently:
http://www.huevaluechroma.com/071.php
http://www.huevaluechroma.com/072.php
http://www.huevaluechroma.com/073.php
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