Night Photography: A Tip to Photograph Stars (and Other Point Light Sources)

Mastering night photography is not that difficult, nonetheless it has its own peculiarities you should be aware of. In this blog post we will see how one of the basic rules we learn about exposure is no longer valid when shooting stars.

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When shooting stars, or more generally point light sources, however, the model changes and this result is no longer valid.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.

Hyperfocal Distance: Advanced Depth of Field and Focusing Tips

The Basics: Depth of Field

Focusing is invariably one of the tasks you perform while taking a shot. You also know that focusing isn't only about having your subject in focus: you can use depth of field as a composition technique to give your photo a particular mood.

Depth of field is the distance between the farthest and the nearest object that will appear in focus in your photo (we will later clarify what does in focus mean). You may use a shallow depth of field when you want to isolate your subject from the surrounding objects, as you can see in the following image:

Shallow Depth of Field

The yellow flower is in focus, while the background is blurred. The characteristics of the blurred part of the image is called bokeh, and mainly depends on the chosen aperture and on the physical characteristics of the lens you're using.

On the other hand, other times you may want every part of your image to be in focus, such as in a typical landscape shot.

Being able to understand how you can control the depth of field is fundamental if you want to use it proficiently and get the shots you want.

Depth of field is mainly affected by these parameters:

• The focal length of your lens: the greater the focal length, the smaller the depth of field.
• The aperture you're using: the smaller the aperture, the greater the depth of field.
• The distance to the subject: the shorter the distance to the subject, the smaller the depth of field.

As we'll see later, and as you've probably experienced yourself, it's much more difficult to get a shallow depth of field than a deeper one. How many times were you striving to get a portrait with a good bokeh without success? You tried raising your aperture (reducing the f-number) but nothing, the background wasn't sufficiently blurred. Why?

We will soon discover it. These rules are fairly basic and are pretty well known to the average amateur photographer. However, these are only approximations of a more complicated formula and sometimes you may strive without success to get the results you want even if you're following all of the above mentioned advices.

Understanding the Nature of Depth of Field

Depth of field behind and in front of the object that is on focus isn't symmetric: on most conditions, depth of field will be deeper behind the subject and shallower in front of it. We won't explore the details of the depth of field equations, but it's important that you realize the following:

• The ratio between the focus zone behind a subject and the focus zone in front of it tends to 1 when the distance between the camera and the subject gets shorter and is about the same order of magnitude of the lens focal length. Unless you're shooting with a macro lens, this won't be the case.
• The depth of focus zone behind the subject increases as the distance from the subject increases and will reach the positive infinity at a finite distance, usually called hyperfocal distance.

What does this mean? Well, amongst other things it means that:

• It's way more difficult to blur the foreground rather than the background.
• If the distance from the subject is greater than the hyperfocal distance you aren't going to get that beautiful bokeh you're looking for, no matter how much you strive for it.
• On the other hand, if you're looking for a picture with a really deep depth of field, just be sure your subject is farther than the hyperfocal distance.

Hyperfocal Distance

We now understand that the hyperfocal distance is responsible for at least some problems we had while getting the focus condition we looked for our shot. The hyperfocal distance H can be expressed as:

H = (f²) / (N c)

where f is the focal length, N the aperture and c the diameter of the circle of confusion. The circle of confusion, as suggested at the beginning of this post, is the criterion used to establish when a region of a photo can be considered in focus: it's the minimum diameter of the circle generated by a cone of light rays coming from a lens when a point is not in focus. Being the diameter of a physical light spot on your sensor (or on your film), this value depends on the size of the sensor: the biggest the sensor, the biggest can be c to get comparable sharpness. You can use 0.03 mm as a typical value for c.

Some properties of the hyperfocal distance are:

• The biggest the focal length, the biggest H is. Please note that the relationship is quadratic: a lens with a double focal length will give an hyperfocal distance four times as big, keeping the other parameters fixed.
• The biggest the aperture, the smallest the hyperfocal distance.
• When focusing on an object at the distance H, the depth of field will be extend from H/2 to infinity.
• When focusing on an object at a distance H or greater, the ratio between the focus zone behind the subject and the focus zone in front of the subject is infinite.

But how big is H? Here are some values for H(f, N) some common focal lengths and apertures (assuming c = 0.03 mm):

• H(18mm, f/4) = 2.7 m
• H(18mm, f/16) = 0.67 m
• H(55mm, f/4) = 25.21 m
• H(55mm, f/16) = 6.30 m
• H(100mm, f/4) = 83.33 m
• H(100mm, f/16) = 20.83 m
• H(200mm, f/4) = 333.33 m
• H(200mm, f/16) = 83.33 m

It's now apparent why focal length is often really important if you need a good bokeh. If you're shooting with a 18mm-f/4 lens, if your subject is more than 2.7 meters away there's no way to get a decent bokeh. And even if it got closer, the boken wouldn't be that good either. On the other hand, this is the reason why wide lenses are really good to get a really wide landscape in reasonable focus. Even if you were shooting with a 55mm lens at f/4, any object farther than 12.6 m (25.21 m / 2) would be in focus.

We've understood why, if you want to shoot at a subject at a given distance and you want to get a good bokeh, you must take the hyperfocal distance into account:

• If your subject is nearer than the hyperfocal distance, you can shoot and tweak your depth of fields using the other parameters.
• If your subject is farther than the maximum hyperfocal distance you can get with your lens, your only option is changing it.
• If your subject is very close to the hyperfocal distance of the lens configuration you're using, you should consider changing the lens anyway to get a good bokeh (the reason will be explained in the next section).

Evaluating the Depth of Field

Learning your lens parameters is important and knowing the approximate hyperfocal distance of your lenses (at least for some apertures) is important if you need to quickly evaluate if the conditions in which you're going to take a shot are correct.

There's another advantage of knowing the hyperfocal distance: using a curious mathematical property of H, you can quickly evaluate the characteristics of the depth of fields at distances smaller than H without learning the complex, and not-as-easy-to-evaluate, depth of field equations. Here's how.

The nearest end and the farthest end equations of the depth of field can be expressed in terms of H and s (the distance from the subject), when s is much larger than the focal length (which is always true unless you're doing macro photography, which is not the case):

D_N = H s / (H + s)
D_F = H s / (H - s)

This equations are pretty simple, but not enough for a photographer to quickly use them when shooting without the help of a calculator! If we now consider distances s = H / n (where n is a natural integer), then these formulas simplify ever further:

D_N = H / (n + 1)
D_F = H / (n - 1)

• The depth of field at a distance H/n (where n is an integer number) is the range [H/(n+1), H/(n-1)].

Much easier to calculate by mind! Also, it's apparent that for relatively small H or relatively big n you're going to have a shallow depth of field. You often won't even need to calculate the result, just remember the principle.

Using this trick, you can evaluate approximately the depth of field. For example: if you're shooting with a 200mm lens at f/4, you know that H is approximately 333 m. What's the depth of field if we're making a portrait to a subject at 10 m? 10 meters is approximately 333/30 so that, from the above formula, the depth of field will be the range [333/31, 333/29] = [10.74, 11.48]. Pretty shallow, indeed.

From this formula it's also clear why the ratio between the focus zone behind the subject and in front of it goes down from infinity to 1 when the distance from the subject goes down from H.

Conclusion

In this blog post we've introduced the concept of hyperfocal distance and explained why it is so important to understand the basic characteristics of the depth of field. Depth of field is an important tool for you as a photographer and it's omnipresent in every photography course. However, very often a photographer isn't able to evaluate the depth of fields he's going to obtain from a specific camera configuration and he's left with trial and error, without even being able to assess if the shot he's looking for is even possible to achieve.

The hyperfocal distance equation is very simple and is much simpler of many depth of fields models you can find. If you don't need to calculate it exactly, known H is sufficient in most everyday situations.

Have fun.