Apertia · Library
What does the infinite-background blur limit tell you?
Calculate the infinite-background blur limit f² ÷ (N × (u − f)) for an 85 mm f/1.8 portrait at 2 m, and compare it with backgrounds at 4 m and 6 m.
How the limit is computed
Apertia's background-blur figure is the diameter of the blur circle on the sensor for a point behind the focused subject. For a background at distance x from the lens it equals f² ÷ (N × (u − f)) × |x − u| ÷ x, where u is the lens-side subject distance. As x grows without bound the last factor approaches one, leaving f² ÷ (N × (u − f)) — the largest blur any background can reach for that focus setting.
Apertia's bokeh preview divides a blur diameter by the sensor's short side, because its preview frame is a vertical 3:4 portrait whose width corresponds to the sensor height. The resulting percentage appears beside the background blur disc while you drag the background up to 200 times the subject distance; the infinite case is the ceiling that drag approaches but never reaches.
Worked example
For this 85 mm, f/1.8 setup focused at 2000 mm, the background limit is about 2.198 mm. The null distance input here explicitly represents infinity, not a missing measurement.
- Infinite-background geometric limit (mm)
- 2.198134
Read the limit for a portrait setup
- Note the focal length, aperture and focus distance measured from the sensor plane.
- Convert the focus distance into u; for 85 mm at 2000 mm this is about 1911.043 mm.
- Compute the ceiling f² ÷ (N × (u − f)) and keep it labelled as the infinite-background limit.
- Then evaluate the real background at its own measured distance with the same focus setting, in the bokeh preview or the library's background-blur calculator, and compare the two.
Worked example: how far is far enough?
With 85 mm at f/1.8 focused at 2000 mm, the limit is 7225 ÷ (1.8 × 1826.043) = 2.198 mm, or 9.16 percent of the 24 mm frame width. A background 6000 mm from the sensor gives 1.488 mm (6.2 percent), and one at 4000 mm gives 1.124 mm (4.68 percent). Even a background three times the subject distance reaches only about two thirds of the limit.
For comparison, a 50 mm lens at the same aperture and focus distance has an infinite-background limit of 0.732 mm, 3.05 percent of the frame width.
- Background at infinity
- 2.198 mm · 9.16%
- Background at 6000 mm
- 1.488 mm · 6.2%
- Background at 4000 mm
- 1.124 mm · 4.68%
Common mistakes
- Quoting the infinity value for a wall a few metres behind the subject.
- Typing a large finite number such as 999999 mm instead of choosing infinity, which hides the fact that the result is a limit.
- Comparing limits from two different focus distances as if only the lens had changed.
- Treating a bigger disc as better-looking bokeh; the model says nothing about highlight shape or smoothness.
What the limit does not describe
The infinite-background value is a geometric bound for the stated focus distance and aperture, not a measurement of any actual background. It does not predict cat's-eye highlights, onion rings or how pleasing the rendering looks. The DOFMaster equations linked below give the same blur-disc relation.