# Lens 101: Focus and depth of field

The focal point is the point at which parallel light rays from an infinitely distant object converge after passing through the lens. The plane perpendicular to the optical axis on which this point is located is called the focal plane. On this plane, where the film is in the camera, the object is seen sharply and is said to be “in focus”. With conventional multi-lens photographic lenses, focus can be adjusted so that light rays from an object closer than “infinity” converge at some point on the focal plane.

## Circle of confusion

Since all lenses have certain aberrations and astigmatism, they cannot perfectly converge the rays from the object point so that they form a true image point (i.e., an infinitesimal point with zero area). In other words, images are formed from a complex of dots that have a certain area or size. Because the image becomes less sharp as these dots get larger, these dots are referred to as “circles of confusion”. Thus, one of the factors that determine the quality of a lens is the smallest dot it can produce, or its “minimum circle of confusion”. The maximum allowable dot size in an image is called the “allowable circle of confusion”.

## Permissible circle of confusion

The largest circle of confusion that still appears as a “dot” in the image. The sharpness of the image, as it is perceived by the human eye, is closely related to the sharpness of the actual image and the “resolution” of human vision. In photography, the sharpness of an image also depends on the degree of magnification of the image, or the projection distance and the distance from which the object is seen. In other words, in practical work it is possible to determine some “tolerances” for the reproduction of images, which, although they are blurred to a certain extent, still appear sharp to the observer. For a 35mm SLR, the acceptable circle of confusion is about 1/1000 – 1/1500 of the length of the film diagonal, assuming the image is enlarged to a 5′ x 7” photograph.

Electronic focus lenses are designed to give a minimum circle of confusion of 0.035mm. It is from this value that the calculations of such parameters as the depth of field are based.

## Depth of field

The area in front of and behind the in-focus subject in which the image is seen sharply. In other words, it is the depth of field in front of and behind the subject, where the film plane blur is within the acceptable circle of confusion. The depth of field varies depending on the focal length of the lens, the aperture value, and the shooting distance. Therefore, if these parameters are known, the depth of field can be roughly estimated using the following formulas:

front DOF = dx F xa 2 / (f 2 + dx F xa)

rear DOF = dx F xa 2 / (f 2 -dx F xa),

where f is the focal length, F- the number F , d – the minimum diameter of the circle of confusion, and – the distance to the object (the distance from the first main point to the object).

If the hyperfocal distance is known, the following formulas can also be used:

* near distance limit point =

hyperfocal distance x shooting distance/hyperfocal distance + shooting distance

* far distance limit point =
hyperfocal distance x shooting distance/hyperfocal distance – shooting distance
(shooting distance is distance from the film plane to the object).

In most situations, the “depth of field” parameter has the following features:

• 1. Depth of field is large at small focal lengths, small at large focal lengths
• 2. Depth of field is large when the aperture is closed (for large numerical values), small when the aperture is open.
• 3. Depth of field is greater when shooting distant objects than when shooting close objects. (takes on dangerous values ​​in macro photography)
• 4. Forward depth of field (relatively sharp gap in front of in-focus subject) less than rear depth of field (behind subject)

Accordingly, the following follows from these rules:

If you want to achieve maximum depth of field, use small focal lengths (35 or 50mm for example), cover the aperture to reasonable limits, shoot from a relatively large distance. (for example 5 or 10 meters)

If you want to achieve a shallow depth of field – use telephoto optics, open the aperture as much as possible, shoot from a short distance. (for example 1-1.5 meters

## Depth of focus

The area in front of and behind the focal plane in which the image can be photographed as a sharp image. The depth of focus is the same on both sides of the focal plane (film plane) and can be determined by multiplying the minimum circle of confusion by an F number, regardless of the focal length of the lens. In modern autofocus single-lens reflex cameras, the focusing process is accomplished by detecting the position of focus on the image plane (film plane) using a sensor that is both optically equivalent (1:1 magnification) and located off the film plane, and automatically controls the lens so that enter the image of the object into the area of ​​depth of focus.Check for more info on dzofilm.com.

## Hyperfocal distance

If the principle of depth of field is applied, with the lens gradually focusing at the farthest distance to the subject, then eventually a point will be reached where the farthest limit of the back depth of field becomes equal to “infinity”. Shooting distance at this point, i.e. the shortest distance at which “infinity” falls within the depth of field region is called the hyperfocal distance. Hyperfocal distance can be defined as follows:

Hyperfocal distance = f 2 /dx F where f is the focal length, F is the F number, and d is the minimum diameter of the circle of confusion.

Thus, if you pre-set the lens to the hyperfocal distance, then the depth of field will increase from a distance equal to half the hyperfocal distance to infinity. This method is useful for presetting a large depth of field and snapshots without having to worry about adjusting the lens focus, especially when using a wide-angle lens. (For example, if a 24mm lens is set to f/11 and the shooting distance is set to a hyperfocal distance of approximately m/4.9 ft., then all objects within approximately 70 cm/2.3 ft. of the camera to infinity will be in focus.)