Light from the sun, moon, and other heavenly bodies must pass through the earth’s atmosphere before it illuminates the surface of the earth. As it passes through the atmosphere, light interact with matter in the air which absorbs and scatters a fraction of the light, reducing the overall flux received surface. The longer the path through the atmosphere light must take before reaching the surface, the greater the likelihood that more of it will be scattered or absorbed.
The minimum path length through the atmosphere is that for light coming from directly overhead, such as from the sun at noon near summer solstice. Light coming in tangential to the surface, such as at sunset, must pass through many times as much air, which is why one can often view sunsets with the naked eye, whereas directly focusing on the sun at noon can cause retinal damage. As the sun or moon approaches the horizon, the atmosphere transmits progressively less light. Astronomers call this effect “atmospheric attenuation” or “atmospheric extinction”, and say that the degree depends both on the path length through the atmosphere as well as the optical density of the air itself. Air containing relatively greater concentrations of water vapor absorb more light than dry air, and dust and haze-causing aerosols (smog) absorb even more.
When using light from the sun as a source for photography, the decrease in light intensity away from noon can easily be observed with a light meter. If you use an automatic camera with a built-in light meter, you will note that the lens aperture selected by the camera increases (moves toward smaller f-numbers) as the sun falls away from noon toward the horizon. With an entirely manual camera, such as a view camera, use of a hand-held light meter will show the light fall-off even more directly as the day progresses. If you rely upon the Sunny f/16 Rule, you will find that an adjustment must be applied in order achieve optimum exposure. This is also true when doing photography by moonlight, where overall light levels are too low for most photographic light meters to function.
I prefer to make moonlight photos when the moon is far from directly overhead, in order to providing “modeling” and depth to the landscape. Thus I have the need to apply such a correction. Early attempts to use low-angle lighting from the moon usually came out severely underexposed when the indicated exposure assumed normal moonlight illumination, meaning that provided by the moon when well up in the sky. After giving the problem a little thought, I decided to measure the falloff in incident light indirectly by measuring the brightness of the moon itself as it travels its path across the sky. For this test, I used a Pentax one-degree spot meter. The fact that the moon subtends an angle less than the measurement spot of the spot meter means that placement of the moon in the spot is critical to obtaining a correct result. By experimenting, I found that the meter had a “sweet spot” at the lower right corner of the measurement circle; placement of the moon in the “sweet spot” gave a maximum reading, and, repeated readings gave repeatable results.
Having the measurement method in hand, I set out to measure the moon brightness over a period of time. I tried to take measurements as close to moon rise as possible, with further measurements taken at twenty to thirty minute intervals throughout the evening. The data obtained by this method over many evenings had to be normalized by taking into account the brightness of the moon at the zenith each night. This was complicated by the fact that, at my location, the moon only gets close to the actual zenith in mid-winter, and never quite reaches it. However, the measured brightness tended to stabilize whenever the moon reached elevations exceeding 50 degrees above the horizon, which led me to believe that the potential error was small if I took that into account. In addition, predictions from my NightLandscape 4 program gave the lunar “noon” brightness with sufficient accuracy that I could rely on it as a basis for comparison.
The normalized data are presented in the graph below as reduction of moon brightness relative to a zenith moon, as a function of moon altitude angle above the horizon measured in degrees of arc.
Atmospheric Attenuation Correction
There are several things that can be observed in the data. The first is that, when the air is very clear, the attenuation was very repeatable from measurement to measurement. I was able to obtain measurements of the moon very close to the horizon on days just after the air had been cleaned of haze by a storm; under these conditions, the moon is six stops dimmer at the horizon than at the zenith. The second thing to note is that the presence of haze has a significant effect on lunar brightness, and that this effect is rather unpredictable without having some independent indication of the optical density of the air when haze is present. Thus the result could only be used as a guide. However, since most of the time I like to work in the desert under conditions of calm winds and clear weather, the likelihood of having to deal with heavy haze and dust is low, so the results can still be used, though with care.
Further research into the haze problem lead me to several scientific papers that provide mathematical atmospheric extinction models. The best one is also described on a web site, Correcting for Atmospheric Extinction. This model is based on the relation
I = I* x 10^(-0.4 k Xm )
where I* is the illumination at the outer edge of the atmosphere, I is the illumination at the earth surface, k is the “extinction coefficient” in units of magnitudes per air mass, and Xm is the air mass transited by the light path. One air mass is defined as the amount of air in the light path for an object in the sky directly overhead. The value of Xm can be calculated from the Zenith Distance, or angle in degrees from the object to a point directly overhead, using the Rosenberg Equation:
X=1/(cos(Z)+0.025e^(-11cos(Z)))
The value of the extinction coefficient, k, depends on three primary absorption and scattering modes: molecular absorption, Rayleigh (molecular) scattering, and scattering by aerosols (particles larger than molecules, such as water droplets). Typical values of k range from 0.20 to 0.27, with values for extremely clear conditions high on a mountain being as low as 0.11, and values for extreme haze being as large as 0.7 or more. Please refer to the site at the link above for further details regarding calculating values of the extinction coefficient.
Using this model, I have added four curves to the plot of my test data. These curves represent the following situations: 1) extreme clarity of the atmosphere; 2) very clear air with visibility of over a hundred miles; 3) “average” conditions giving twenty mile visibility; and 4) very hazy air, giving two mile visibility. (The visibility distances are from my subjective, non-scientific judgment).
As you would expect, the correction for “hazy sun” fits the model pretty well, calling for a one-stop correction that corresponds to the difference between “clear” and “hazy” conditions from the model.
This atmospheric attenuation model is being incorporated into NightLandscape 5, so as to improve the accuracy of prediction. Experience with its application so far indicates it works very well. I highly recommend this model to anyone in similar circumstances.
Correlating to the Sunny f/16 Rule
As part of this exercise, I spent a little time trying to account for why the Sunny f/16 Rule works. This exercise starts with the brightness of the sun, and accounts for all factors that reduce the amount of light that finally reaches the film in your camera. The two major factors are atmospheric attenuation, and lens efficiency. The first factor has been covered briefly above.
Lens efficiency is a measure of the quantity of light that a lens focuses into a sharp image, relative to the quantity of light entering the lens. There are numerous effects that can cause a lens to have poor efficiency. If light reflects off of one of the lens surfaces instead of passing through it, the lens efficiency is reduced. If the lens shape is not perfect, it will produce a soft image that distributes the light over the plane of focus instead of providing sharp focus. Thus all the various focusing aberrations decrease lens efficiency. In the end, not only does an efficient lens allow a smaller aperture for a given image brightness, enhancing depth of field, it also minimizes flare and provides a sharper image overall.
What surprised me was the low lens efficiency values quoted for some early lenses, or even for some more recent lenses from the mid-Twentieth Century. A soft, uncoated lens can have an efficiency as low as 40 percent, and some cameras from fifty years ago had lens efficiencies around 70 percent. The best lenses today, consisting of multi-coated apochromatic optics, can have efficiencies as high as 97 percent. But what does all this mean if we are trying to use the Sunny f/16 Rule?
I haven’t yet been able to place the origin of the Sunny f/16 Rule in time, however it seems to me that it’s origin corresponds to a time when most lenses had efficiency in the 70 percent range. Thus, trying to use it with a highly efficient modern lens should result in an overexposure of a half-stop or so. This goes a long way toward explaining why I tend to prefer the results from closing down a lens by a half-stop or so relative to the aperture indicated when applying the Sunny f/16 rule. Of course, all of this is moot if you are using a camera with a built-in light meter. But it is something to be aware of if you are using a hand-held meter, or are in a situation where light levels are too low for a meter to read.
This is default description text on Padangan Themes, of course you can change this text via you profile administration.