Physics · optics

Depth of Field

How much is sharp, where the hyperfocal sits, and the aperture past which stopping down makes things worse.
H = f²/(Nc) + f

Format

Lens and subject

What is sharp

total depth of field

Stopping down, and the point of no return

The same picture on another format

same framing, same depth of field
Same subject size in the frame and the same depth of field needs the same physical aperture diameter — so the f-number scales with the crop factor, and the focal length scales with it too.
The surprising one

At the same framing, the lens barely matters

Everyone knows a long lens gives shallow depth of field. It is not quite true, and the way it is untrue is worth knowing. Depth of field falls off hard with focal length at a fixed distance — but if you change lenses and then walk until the subject is the same size in the frame, almost all of that difference vanishes.

A head-and-shoulders shot at f/2.8, full frame

At 24 mm you stand a metre away and get 293 mm of depth of field. At 200 mm you stand eight and a half metres away and get 287 mm. An eight-fold change of focal length moves the depth of field by two per cent.

What actually changes is the background: the long lens magnifies it enormously, so the out-of-focus area is far more blurred even though the in-focus slab is the same thickness. That is what people are seeing when they say a long lens has less depth of field — and that is the part the aperture diameter governs, because a 200 mm at f/2.8 is a 71 mm hole against a 24 mm lens's 8.6 mm.

The sharp slab itself is a different quantity. At constant framing it is set by the f-number and the format, and the focal length cancels out of the arithmetic almost exactly. Put a 200 mm at f/11.2 next to a 50 mm at f/2.8 — identical 17.9 mm holes — and the long lens has four times the depth of field. Same hole, four times the depth: it was never the hole.

The ceiling

Why stopping down stops working

Depth of field grows as you stop down, without limit. Sharpness does not. Light passing a small aperture spreads, and the blur it makes — the Airy disc — grows in direct proportion to the f-number: 2.44 × wavelength × N. Somewhere the diffraction blur gets bigger than the circle of confusion you were willing to accept, and from there on every stop buys depth of field by spending resolution you cannot get back.

Where the crossover sits

On the standard print criterion, diffraction reaches the circle of confusion at about f/21 on full frame, f/14 on APS-C, f/11 on Micro Four Thirds and f/8 on a one-inch sensor. Smaller sensors hit the wall sooner, for exactly the same reason they have more depth of field in the first place: everything is scaled down except the wavelength of light.

What is the circle of confusion, really?

A decision, not a measurement. It is the largest blur circle you are prepared to call a point, and the traditional figure is the sensor diagonal divided by 1500 — which works out as roughly what an unaided eye resolves on a 10×8 print at arm's length. Every depth of field number anywhere depends on it, which is why two calculators can disagree and both be right. Switch the standard here to see how much it moves.

Is hyperfocal focusing a good idea?

It maximises the range that is acceptably sharp, from half the hyperfocal distance to infinity — but it puts infinity right at the edge of acceptable, which means distant mountains are exactly as soft as you said you would tolerate and no sharper. If the far detail is the subject, focus on it instead and accept a nearer near limit. Landscape photographers who focus a third of the way in are using a rougher version of the same idea.

Why does the far limit go to infinity so suddenly?

Because it genuinely does. The far limit is u(H−f)/(H−u), and as the subject distance u climbs towards the hyperfocal distance H the denominator goes to zero. One small step closer to H and the far limit leaps from a few tens of metres to unbounded. It is a real feature of the geometry, not a rounding artefact — and it is why hyperfocal focusing feels like a trick.

What this page assumes

A thin lens in air, focused by moving the whole lens, with the subject distance measured to the lens rather than the sensor plane. Real lenses are thick, many focus internally, and their focal length changes as they focus — focus breathing — so close-up numbers drift from reality first.

That the only blurs are defocus and diffraction. Lens aberrations, which improve as you stop down, are not modelled, so the true optimum aperture on a real lens is usually a stop or so tighter than the pure diffraction crossover suggests. Sensor resolution and the anti-aliasing filter are absent too.

A wavelength of 550 nm for the Airy disc, green light at the eye's peak sensitivity. Red diffracts more and blue less, so a real image goes soft in the red channel first.

The depth-of-field limits are the classic thin-lens ones and are exact within that model — no small-angle shortcuts. Verified in dof_model.py.

Field notes

Things that follow from the geometry

Version history · unchanged

No change to this page at all since the earliest archived release (v5.66). The full history for the site is in the changelog.

Exact thin-lens geometry on a criterion you chose. Every depth of field figure rests on a circle of confusion, which is a judgement about acceptable blur rather than a physical constant — change it and every number here changes with it. Real lenses add aberrations and focus breathing that this model does not have. See Sources.