DOF and Bokeh - Explained

 

F=6.3, L=145mm, D=1m

DOF stands for "depth of field". It is the maximum minus the minimum distance where an image is acceptably sharp.

Bokeh refers to the smoothness and blurriness of the background. We also include other details in the concept of pleasing Bokeh, such as roundness and smooth light falloff in light specks. A creamy background is desired to make the subject stand out. 

The picture above demonstrates both concepts. The DOF is large enough to cover much of the rose. But on both the front and the back of the flower, blurriness is clearly visible. I estimate the DOF to be about 2cm. The background is creamy and blurry. You can see individual spotlights on the top. Such pointy, well-defined points of light become circles. In fact, each point in the background becomes a circle of diffusion. The white points at the top of the image just make these circles more visible.

We need a bit of math to understand the effects of DOF and Bokeh. A point in infinity sends light into the lens, which is not focused on the sensor plane but spreads out into a circle. The formula for the diameter of this circle of diffusion of a point at infinity is simply

r = L² / (D-L)F

Here, L is the focal length, D is the focused distance, and F is the F-stop of the aperture. While the formula is the same for all sensors, its effects differ depending on sensor size. For other sensors, we can use the "full frame equivalent" focal length and F-stop. Just multiply your focal length and F-stop by the crop factor to compare a camera with a "crop factor" to a "full frame" camera. The images on this page were taken with the Nikon Z5, which uses a 36x24mm sensor.

You can derive an approximation for the size of the Bokeh balls at infinity as a percentage of the sensor diagonal.

Bokeh = L² / (200 FD)

Here, L is in millimeters. It has to be entered as a full-frame equivalent, along with the F-stop. The distance D is in meters.

You can find a DOF calculator on Photopills. For the math, see my EMT notebook. It also includes a DOF calculator that shows the hyperfocal distance and the size of the Bokeh balls.

A quick computation for the image above shows that the circles of diffusion are about 1/6 the sensor diameter. This agrees with the optical impression of the background in the image.

The following formula for the DOF in front of the focused subject is only an approximation, valid for small DOF and large distances.

DOF  ~= a FD² / L²

The factor "a" depends on your individual tolerance for blurriness.

Actually, we prefer not to use the formulas or actual computations. We use them to see what happens when we change one factor relative to another. This is best illustrated by examples.

Portraits

F=6.3, L=130mm, D=2m

As a guideline, here are the values for a portrait of the upper body.

• L=100mm, F=4.0, D=2m.
• The Bokeh will be about 6% of the image. That is creamy.
• The DOF will be around 10cm, 5cm before and 5cm behind the subject.

Now, let us change some parameters to see how the formula can be used.

• We could use a 50mm instead (2x shorter). For the same image, we need to get closer and set D=1m (2x closer). This means that L/D is constant if we want the same angle of view. We get approximately the same DOF. The person will be a bit more distorted, but the image will show the same body length. We will see twice as much of the background, making it even more distracting. Moreover, the Bokeh will be half as good because the remaining factor, L/F, is half as large (remember that L/D is constant). To get the same Bokeh (but with more background), you need F=2.0, which loses DOF. Consequently, long lenses are preferred for portraits.
• We could use a 35mm lens (3x shorter), stay at 2m, get a whole person shot, and use F=8.0 (2x closer aperture). The DOF will increase considerably, bringing the person and their surroundings into focus. The circles of diffusion in the Bokeh will be 18 times smaller, and the subject and background will be easily recognizable. Use this if you want to show more.
• We could use a 200mm lens and get a headshot instead, keeping D=2m. This will reduce the DOF to only 2cm. You can counter by setting F=16.0, which restores the DOF to its original value. The Bokeh will be the same again. The longer the lens and the closer you get, the less DOF and the more Bokeh you get because you cannot increase the F-stop beyond F16. The extreme is a macro shot.
• We could use another camera, let's say an MFT (micro four-thirds) camera with a "crop factor" of 2. To get the same image as above, you simply take a 50mm lens at F2.0. As long as you can compensate with wider apertures, you can get precisely the same result as on a full-frame camera. The faster lens also helps counteract the higher noise on MFT cameras, since you can use lower ISO and often even a longer shutter speed due to better image stabilization. 
• To compensate a 85mm lens at F2.0 on a full frame camera using MFT, you can take a longer lens, like a 85mm on MFT (170mm equivalent) at F4, to get the same Bokeh and double DOF. You will have to back off from the subject, of course.

Landscapes

F=11.0, L=28mm, D=20m

This is the opposite of portraits. We usually want everything acceptably sharp. The term to know is "hyperfocal distance". This is the closest distance D we can focus on and still get DOF to infinity. Here is a guideline that I use and remember.

• L=50mm, F=8.0, D=10m.
• Everything will be reasonably sharp from 5m (half of D) to infinity.
• In its recommendations, Nikon uses this relaxed hyperfocal distance of D=10m. But I find this not sharp enough for modern sensors, and prefer to compute with D=20m.

A good approximation for the hyperfocal distance is

D=L² / (30F)

Here, L is the full frame equivalent focal length in millimeters, and F is the full frame equivalent F-stop.

You can use the formula for the circle of diffusion above to transfer this to other situations.

• Using a 35mm lens, L² is half as big. So, you can focus on half the distance, i.e., to D=5m, getting everything sharp from 2.5m to infinity. 
• Obviously, F=16.0 is another option. Your lens will start to get less sharp due to diffraction. Combining with 35mm, you get about D=5m, and everything is sharp from about 2.50m to infinity.

There is old advice to focus on 1/3 of the scene. I never quite understood what this meant. Instead, you should focus to twice the distance where you want the reasonable sharpness to start, if you need sharpness up to infinity.

Street and People

F=4.0, L=50mm, D=15m

This genre is between landscape and portrait and requires the most care. The lenses range between 35mm and 70mm, with 50mm being the most common. Since the situation is constantly changing, you will have to make compromises if you want a quick setup. I use two different user modes that can be easily switched on the Z5.

User mode 1:

• Set this user mode to F8.0, assuming a 50mm lens. This is for images where you want a lot of DOF.
• The lens will be reasonably sharp, and usually, you get enough DOF. In the case of a 35mm, you can switch to F4.0 to get the same effects. But I use my 50mm for streets most of the time.
• For a small group of people, focused to 5m, you get around 4m to 9m in reasonable focus. Focus on the second row. You will not get very blurry backgrounds this way. Step back for larger groups with the 50mm lens. You get an even blurrier background. So make sure that it is not distracting.
• For a street scene, focus on something at around 10m. You get reasonable sharpness across the scene.
• For a single person at a close distance, like 1,50m, you get quite a good background, which will still be very recognizable.

User mode 2:

• Set this user mode to F4.0 or wider. This is for images where you want your subject to stand out from the background.
• You need to focus closer than 5m for the background blur to work.
• Above 10m, the blur will be much less visible, like in the image above.

In low light, you will use a much wider aperture, such as F2.8 or wider. You should plan for images with little DOF and much Bokeh. Alternatively, place the subject parallel to the sensor, or farther away, to get much sharper images. Also, be aware that your lens is sharpest in the center. You can crop the photo later to get your subject off-center.

So much for now, it is difficult, and I keep fighting all the time, sometimes with disappointing results. But I am always grateful for all the opportunities modern technology offers me. You cannot be thankful and frustrated at the same time. In the past, it was just "F8 and hope" most of the time.