Depth of field is one of the most significant artistic techniques in photography – in portrait photography, with the help of a small depth of field (depth of field), the photographer blurs the background and focuses on the model, and when shooting from a large one, he conveys on a flat photograph the entire depth of space in the landscape.

Parameters affecting the depth of field when shooting

Focal length of the lens – the smaller the focal length, the greater the depth of field and vice versa

Aperture – the wider it is open (the smaller the f-number), the less the depth of field and vice versa

Focusing distance – the greater the distance to the subject, the greater the depth of field

In the instructions for modern cameras, depth of field is given no more than a couple of lines and, as a rule, it all comes down to aperture alone. The approach is simplified and effective, but if you are asking questions like:

“How far should the lens be focused so that everything looks sharp in a landscape photo from the nearest bush to the horizon?”

“Why did the model, sitting in half a turn, suddenly turn out only one eye and how to avoid this in the future?”

Then this article is for you.

DOF calculation formula, hyperfocal distance and a bit of history

In the formula for calculating the depth of field, in addition to obvious and understandable parameters, such as focusing distance, lens focal length and aperture, there is one more parameter – the diameter of the circle of confusion or the permissible circle of dispersion. For full-frame cameras (negative or sensor size 24×36 mm), it is taken equal to 0.03–0.05 mm (the value in meters is substituted into the formula).

Sometimes, in calculating the diameter of the circle of confusion, it is calculated as 1/1500 of the frame diagonal, which gives the same 0.03 mm for a full-frame camera and simplifies calculations for cameras with a sensor of a different size (you can also substitute z/crop in the formulas above).

Hyperfocal Distance (H) – Focusing the lens at this distance provides maximum depth of field (H/2 to ∞). It is calculated by the formula H=f2/(Kz).

An example of calculating hyperfocal distance: if you focus a 50mm lens mounted on a full frame camera at a distance of 6.2m, set the aperture to 8 and take a picture, then everything from 3.1m to ∞ will be sharp, however this is true for a circle of confusion equal to 0, 05 mm, and for a value of 0.03 mm, you will have to focus on 10.5 m and everything will be sharp starting from 5.25 m.

And some practical examples:

Minolta MC Rokkor-PF 58 mm f/ 1.4 lens, specimen from the 70s of the last century – the depth of field scale is calculated for a circle of confusion of 1/1500 of the frame diagonal, next to Helios-44 from the 90s and the depth of field scale is calculated for another 1/1000 diagonals.

The depth of field scale of the most massive amateur camera “Smena 8M” is designed for a circle of confusion of 1/850 diagonal (0.05 mm) and occupies almost the entire circumference of the lens.

Modern, autofocus lenses, as a rule, lack depth of field and distance scales, and the aperture control is carried out on most of them from the camera.

And since the circle of confusion is not a constant, it’s time to see what this concept means.

Circle of Confusion or Permissible Circle of Scattering

The figure above shows the passage of light through the lens, in both cases the lens is focused on a point (2) – and its projection on the matrix (5) looks like a point.

For points (1) and (3) that are out of focus, the projection on the camera’s matrix looks like a circle – the rays converge either to the matrix or behind it. In the case of a closed aperture (4) in the lower figure, the beams converge at a sharper angle, leaving circles of a noticeably smaller diameter on the matrix than with a fully open aperture.

So, the acceptable circle of scattering should show to what extent a fuzzy-focused spot will look like a point for the viewer, but not on a matrix or negative, but on the final image – not necessarily on paper, it can be a computer screen or an image on a cinema screen.

And since we are talking about the viewer, we will have to remember the resolution of the human eye, the angular resolution of which is about 0.02°–0.03°. It is precisely because of this feature of human vision that it is possible, by only slightly increasing the distance to the monitor or TV screen, to stop distinguishing between individual pixels. And, moving back a little more, stop distinguishing a Full HD picture from 4K on screens of the same size. The poster on the facade of a neighboring house looks quite attractive from a distance and is not impressive when viewed up close.

The further you move away from the monitor, the less blurry and more hard-edged circles you will see.

DOF is in the eye of the beholder

An angular resolution of 0.02°–0.03° is not the most obvious value, but if you translate it into print size and viewing distance, then the whole depth of field formula will become clearer.

It is precisely because of the angular resolution of the human eye that the value of 0.03–0.05 mm for the diameter of the circle of confusion got into the depth of field formula – on prints of 10×15 cm (the most widespread format of that time), a speck of 0.03 mm on the negative will increase to 0.125 mm, but from a viewing distance of 25 cm will still be indistinguishable to the naked eye.

Obviously, with a larger print size and a small viewing distance, when calculating the depth of field, it is necessary to use the value of the circle of confusion less than 0.03 mm.

For example, focus on the size of one photosensitive element on the matrix of your camera (how much they are smaller than the traditional 1/1500 can be seen in the picture above).

This approach allows you to get predictable results when printing at very large formats or viewing on a large screen.

In Fujifilm cameras, the depth of field preview can be shown both for a circle of confusion of 1/1500 diagonal, and for a circle commensurate with the size of one photosensitive element on the matrix. The first option is recommended if the image is printed in a small format, and the second option when viewing the image on a large monitor or large format printing.

Practical part

The inquisitive can recommend an online depth of field calculator that takes into account all of the above parameters, takes into account the effect of diffraction, and even visualizes the picture. Of course, it’s better not to drag a calculator to the shooting, but to get your bearings in advance (if you lack experience, this can significantly reduce technical defects).

However, this formula can be used without calculators and complex calculations – just remember a couple of numbers.

Shooting a classic landscape is not complete without calculating the hyperfocal distance – by focusing the lens at this distance, you can get a picture where objects located at different distances (from half hyperfocal to ∞) will be shown with almost the same sharpness.

The shaded area around the model shows the depth of field.

Having once calculated and remembered that for a lens with a focal length of 23 mm with an aperture of 5.6, the hyperfocal distance will be 4 m (calculation for a 10×15 cm print viewed from a distance of 25 cm), you can easily determine the parameters for other print sizes, distances view and determine hyperfocal for a different aperture value.

So, for a twice as large print of 20×30 cm, you will have to close the aperture by two steps (up to 11), for an even larger size of 40×60 cm (twice as much), you will again have to close the aperture by another two steps (up to 22). In all these cases, the hyperfocal remains the same and is equal to 4 m. A 40×60 print is no longer looked at from 25 cm and you can safely double the viewing distance, up to 50 cm, and here again you will have to change the aperture by two steps, but by opening it wider (up to 11 ).

Those. to double the original print, you need to close the aperture by two stops, and to double the viewing distance, open the aperture by two stops. Moreover, if you decide that 4m hyperfocal is too much and the foreground in your landscape is not sharp enough, just stop down two stops and the hyperfocal distance will be halved (the opposite is also true).

This magic of the two will collapse if you take a multiple of the focal length, but exactly twice – so, for a lens with half the focal length for a hyperfocal distance of 4 m, the aperture will have to be opened by four steps (up to 1.4) and closed by four (up to 22) if The new focal length is twice the original one.

In some cases, to create a depth of field on the final image that cannot be obtained in one frame, focus stacking is used – an image is collected from several frames, in each of which the focus was at a different distance, but this is a completely different story.