One of the first things you certainly learnt when you started learning photography was how exposure is determined by three parameters: aperture, shutter speed and ISO sensitivity. Each one has multiple effects on the final result (most notably depth of field, motion blur and noise), but each one can be used to determine how much light enters your camera and reaches the sensor. Aperture, though, has a peculiarity: it's not an absolute measure, but a relative one. In fact, the f-number is not a measure strictly speaking: it's a pure number. The f-number N is the ratio between the focal length f of the lens and the diameter r of the entrance pupil:
Basically, the luminance (the "brightness" of the resulting image) depends only on the relative aperture and not on the absolute value of either lens parameters alone. In fact, when evaluating exposure, you just use the f-number: no matter the focal length or, more generally, no matter which lens you're using, if the f-number is the same, exposure is going to be the same. If you stop your aperture up or down, exposure will stop up or down accordingly.
This is true most of the time and is a consequence of the physical model of an optical system such as a single aperture camera (or the human eye). We've seen many time the equation
which summarizes this basic rule: luminance (in f-stops, hence the logarithm) is proportional to the square of the aperture N and inversely proportional to time t the shutter remains open.
What Happens When Shooting Point Light Sources?
When shooting stars, or more generally point light sources, however, the model changes and this result is no longer valid. A point light source, in this context, will be defined as a source of light whose size in the resulting image will smaller or equal to one pixel. Perfectly in focus, and depending on your sensor's resolution, some stars and planets may in fact appear bigger than one pixel, but not that much. Hence, this approximation can be considered good enough.The reason why this happens is not complicated but requires some knowledge of Mathematics and Physics but since a photographer is usually only concerned with results and the rules to apply, I'll try to provide just a very summarized and intuitive explanation.
Let's start with a couple of analogies, although pretty "rough". It's absolutely intuitive that, the farther from a sound source, the fainter the sound you perceive. It's also intuitive that when shooting with a flash, the farther from the subject, the fainter the light that reaches it and, hence, the fainter the light reflected to your camera sensor. Now: why doesn't a similar effect exists when shooting any subject? A picture is produced by the light reflected on the subject: why isn't exposure affected by the distance from it?
It turns out it's a consequence of two competing phenomenons which, under certain circumstances, "balance" themselves and cancel out the contribution of the distance. It also turns out that the result is the general well known law we were talking about at the beginning of this article, hence the importance of the relative aperture, the f-number, in the field of photography.
On the other hand, when shooting point light sources (as the majority of stars in the night sky can be considered) the two competing phenomena don't balance themselves any more. In fact, one of the two practically disappears and the focal length f of the lens doesn't affect exposure any more. In this case, the result is similar to what we described in the analogies we above: luminance is inversely proportional to the distance from the subject but, much more importantly, it is proportional to the diameter of the entrance pupil. Having disappeared f from the equation, the result depends solely on r2 (a quantity proportional to the area of the entrance pupil) and not on the relative aperture. This fact is somewhat intuitive, if you think about it: the larger the area of the entrance pupil, the more light it can gather. Seen from this point of view, in fact, the usual rule is probably less intuitive: lenses configuration with the same aperture N may have entrance pupils of different sizes. Why, then, they give the same effect? That's because of the two components we were talking about, but we won't enter into mathematical details.
Since
it turns out that focal length does affect the final exposure, given N.
How? This model predicts that an increase in the focal length of the lens keeping the aperture N fixed increases exposure, since it increases the area of the entrance pupil. Although you won't be usually shooting skies with long lenses, you could take advantage of this fact to reduce shutter speeds, especially taking into account that detected luminance varies with r2 and, hence, with f2, the square of the focal length.
Some estimations are quickly done: if you increase the focal length from, let's say, 18 to 35 (using the same aperture), you'll increase the quantity of light reaching the sensor of a factor
that is, 2 stops.
It's important to realize that this effect applies only to point light sources, that is, small stars whose size in the picture is comparable to, or smaller than, the size of a pixel. It doesn't apply to the moon, to bigger stars and planets and not even to the sky itself. Nevertheless, it's a good trick to know if you want to maximize the number of visible stars in your picture.
Sometimes you may be tempted to stop down the aperture to have a better focus at infinity, especially when the lens you're using hasn't got a hard stop at infinity (many cheaper lenses, such as most Nikkor DX lenses, have not). In this case, instead of indiscriminately or heuristically stopping down the aperture, use the hyperfocal distance instead (which we talked about in a previous post) to get a good focus lock at infinity and determine exactly the depth of field you need. If you can, open your lens as much as you can.
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