Real-world depth-of-field demonstration

Conveniently, it's become fashionable for manufacturers to produce 85mm equivalent, F1.2 lenses, which makes it relatively easy to demonstrate the ways in which they are, and aren't equivalent.

Format Focal length F-number Crop factor Equivalent Focal length Equivalent aperture
Full Frame 85mm f/1.2 1 85mm f/1.2
APS-C 56mm f/1.2 1.5 84mm f/1.8
Four Thirds 42.5mm f/1.2 2 85mm f/2.4
1"-type 32mm f/1.2 2.7 86.4mm f/3.2

Here we've used the ratio of the sensor diagonals (more commonly referred to as the crop factor), to work out the equivalent aperture. If it helps you relate this back to the difference in sensor area, which is ultimately what equivalence is about, you can use the square root of the ratio of sensor areas (it's essentially the same number).

Depth-of-field equivalence

Here we have a set of portraits all shot at F1.2. As you can see, the amount of depth-of-field varies with sensor size (and the consequent change in aperture diameter of the associated F1.2 lens).

Technically, what you're observing is background blur, which depends on lens design as well as depth-of-field. Optical design can dictate how concentrated or diffuse each blur circle appears - something worth remembering when you read press releases suggesting that it's just about the number of aperture blades.

Full Frame
Four Thirds
1" Type

You'll not be surprised to find that the cameras (and their lenses) end up blurring the background based on their sensor size. The question is, do they do so in proportion to the sensor-size difference?

Equivalent Apertures

Below we've shot the same portrait, but this time at 'equivalent' apertures.

As the Nikon 1 has the smallest maximum equivalent aperture, we'll stop the other lenses down to match it. The fourth column in the table below shows the F-number required on each lens to offer an F3.2 equivalent amount of depth-of-field, while the fifth column shows the closest available F-number to that target. The final column expresses the difference, in EV.

Format Lens Max equivalent aperture Common equivalent apertures F-numbers equivalent to F3.2 Closest available F-number Difference from ideal
Full Frame 85mm F1.2 f/1.2 f/3.2 f/3.3 f/3.2 +0.1 EV
APS-C 56mm F1.2 f/1.8 f/3.2 f/2.1 f/2.0 +0.2 EV
Four Thirds 42.5mm F1.2 f/2.4 f/3.2 f/1.6 f/1.6 +0.1 EV*1
1"-type 32mm F1.2 f/3.2 f/3.2 f/1.2 f/1.2 0 EV
Full Frame
Four Thirds
1" Type

As you can see, the real-world examples bear-out the expectations to a pretty good degree - when set to 'equivalent' apertures, the background blur is very similar. It also helps illustrate the distinction between background blur and depth-of-field - the background dots have all been spread to a similar degree, suggesting the same depth-of-field, but the appearance of them varies, depending on lens design.

In this instance, the lens on the 1"-type sensor is producing more concentrated blur circles - making them appear darker. This suggests the lens exhibits lower levels of longitudinal chromatic aberration than the others, such that different colors are being focused at the same depth. This would explain why the blur circles are less spread out and why they appear black, rather than the more diffuse, green-tinged rendering the other three lenses are offering.

Key points:

• Depth-of-field and background blur are not the same thing

• Equivalent aperture will accurately predict depth-of-field (except at very close focus distances)

• There's more to bokeh (the quality of out-of-focus rendering) than the number or shape of aperture blades

*1 The calculated optimal aperture for Four Thirds is f/1.64, whereas, mathematically, the lens setting marked f/1.6 should be f/1.59.