Wednesday, December 14, 2011

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):

DN = H s / (H + s)
DF = 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:

DN = H / (n + 1)
DF = 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.

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