Depth of field

Image with little depth of field.

Image with moderate field depth.

By depth of field or PDC is traditionally understood in optics, and in photography in particular, the area that includes from the closest point and the furthest point of our field that is acceptable in terms of sharpness, once its image is formed in the same plane of focus. A closed aperture increases this depth, while long focal lengths (especially telephoto lenses) decrease it.

It depends on four factors:

• The size of the maximum confusion circle or CCM (and therefore the format and size of the printing, in addition to the observation distance and the resolutive capacity of each observer).
• The focal distance.
• The opening of the diaphragm, or number f.
• The distance of focus.

Depth of field limitations can sometimes be overcome with various techniques and equipment. The approximate depth of field can be given by:

DOF≈ ≈ 2u2Ncf2{displaystyle {text{DOF}}{approx {frac {2u^{2}Nc}{f^{2}}{2}}}}}}{f^{2}}}}}}}}}}}

for a given circle of confusion (c), focal length (f), f-number (N), and distance to subject (u).

It's important not to confuse depth of field with depth of focus, which is the range by which the film or sensor can be placed behind the lens in such a way that blur is not noticeable.

CCM Maximum Circle of Confusion

Confusion circle: only the central line appears focused, the rest instead does not; although a resolution of 250 pixels wide appear to be focused on the 3 central lines.

In its original resolution of 997 pixels wide the circle of confusion does not hide the blur.

The circles of confusion are the small circles of light that form each point of an image that is not in focus. If a point of a subject is in the focused plane, it produces (or should produce) a point in the plane of the sensor or film. What we usually say is that a subject point produces an image point. But if we place an object in front or behind that focused plane, instead of an image point, a more or less large disk of light will be formed depending on what is more or less close to the focused plane.

The maximum circle of confusion is the size that a circle of confusion must have on the film or sensor so that when we enlarge it and see the copy under certain conditions it is indistinguishable from a lower point in size, so that from that point size to larger we begin to perceive things as blurry. Internationally it has been established that a dot of 0.25 mm on a 20x25 print seen at about 635 mm (25") is considered the maximum dot size from which the images would appear to us lacking in sharpness. This value has been established with data from direct observation of a large number of individuals and an average value has been established, since it is evident that for people with visual acuity above normal the size of that circle must be less than the normal values. 0.25 mm and in people with less visual acuity it will be the other way around and visual acuity does not depend on the correction that is needed through glasses (this correction is taken for granted), but on the density of receptor cells in the retina. To finally calculate the value of the maximum circle of confusion, we must divide that value of 0.25 mm by the magnification factor that results from going from a certain format to the 20 x 25 copy size established as canon. Thus, in 24 x 36 format considering the values with respect to the shortest side 24 mm (the longest side is variable depending on the proportion of the sides, 2/3 or 4/3, etc.) to go on to measure 200 mm (the copy) 200/24 (from the sensor)= 8.33 and it will give us that 0.25/8.33=0.03 mm as the size of the CCM for this 24 x format 36. The table shows the values for different formats.

Focal length

The effect of focal length on depth of field is inversely proportional and the shorter the focal length, the greater the depth of field "PDC" if we keep the rest of the parameters constant.

What happens is that the proportion is not linear and we go from having a PDC from very close to infinity at wide angles, to drastically reducing as we increase the focal length. For each case there is a focal distance from which the PDC distances go from being infinite to being finite. A 37.5mm focal length lens in 24 x 36 format at f16 focusing at 3m has a PDC from 1.49mm to ∞ and a 38mm goes from 1.51m to 195m and from there the decline, a 50mm under the same conditions has a PDC from almost 2m to almost 7m, total 5m and a 100mm would have a PDC from 2.63m to 3.49m, total 0.86m. As you can see the reduction of the PDC is important when the focal length is proportionally increased.

F-number

The effect of f-stop value on depth of field "PDC" it is also easy to study. A more closed diaphragm, higher PDC or what is the same the higher nºf more PDC. The physical reason is because when the diaphragm is closed, the light cone that it forms with the point of the object is reduced in angle, so the maximum circles of confusion would be located further from the focused plane than if the angle is more open. In the drawing you can better understand this.

Effect of the diaphragm on the depth of the field. The points in the focused plane (2), project points in the picture plane, but those that are out of the focus plane (1 and 3) cause a circle of confusion, projecting a blurred image. When using a diaphragm, the actual area of the lens (4) is reduced, reducing in turn the size of the circles of confusion (since the angle between the maximum angular separation beams from the same point is reduced that angular separation by the diaphragm), so objects away from the focus plane are more sharp, which increases the depth of the field (the distance around the plane focused on which the objects are seen with a certain sharpness).

Speaking of the eye and its diaphragm system such as the iris, it explains the fact that a very open diaphragm reduces the depth of field, thus, at night we see worse definition not only due to the reduction in light intensity but also due to the lower general PDC as our eye has an open pupil and it costs us more to focus on the different planes. If we have a vision defect, the problem worsens, for example, a person who finds it difficult to focus closely under normal conditions indoors to read a text in low light (the eye iris opens), if he goes outside in the sun It is possible that if the problem is not very acute, it is possible to be able to read it by the simple fact of drastically closing the iris when receiving so much light.

Focus distance

The closer the object to be photographed is located, the shallower the depth of field will be and if we focus further away the depth of field increases up to the limit of the hyperfocal distance, which is the focus point where we have the maximum depth of field. If we focus further than this distance, we will again lose depth of field, although not as much as if we got closer.

There is a widespread fallacy that there is twice as much PDC behind the focused point as there is in front of it and this is true only for an exact combination of #f focal length and focus distance. For example, if I focus at 2 m with a 50 mm at f16 the fallacy is approximately fulfilled, but if I focus closer the PDC gradually becomes equal to the point that when we move at distances typical of macro photography the PDC is the same ahead than behind and if we focus further than 2 m the PDC behind increases many times more than in front to the point of focusing at the hyperfocal distance in which the PDC behind shoots up to ∞.

Other factors to consider

Combined effect of focal length and focus distance in close-up photography

As long as we are in focus ranges less than 1/4 of the hyperfocal distance, the depth of field as long as we maintain a certain magnification will not vary regardless of the focal length we are at. This is perfectly true in macro photography since we are below these focus distance values less than 1/4 of the hyperfocal distance, but in distant photography above these values it is not true. In these cases within the mentioned ranges, with a telephoto we have less depth of field than with a normal or wide-angle lens and that is true as long as the other parameters remain constant, but if we maintain the same magnification even if we change the focal length, proportionally changing the focus distance to frame the same thing, the depth of field will not vary, the PDC that I lose if I increase the focal length was gained by putting myself further away. What happens is that with telephoto lenses the blurred background looks larger than with a wide angle, so it seems to us more blur, but if we look closely we will see that both the background of the photo taken with the wide angle and the background of the one made with the tele has the same lack of sharpness if the subject is framed at the same magnification and we work with the same format and diaphragm and in fact in the subject that we are photographing, we will see that there is the same PDC if we focus on the same plane with an angle that with a telly

Influence of the change of format in the PDC

Another issue that comes up is whether the PDC increases or decreases with one format or another. Let's see, if I look for the same angulation in the registration of an image, if you used a small format I will have more PDC than with a larger format because for the same angulation with a larger format you also have to increase the focal length and as We saw when analyzing this factor it turns out that the PDC is reduced more quickly in long focal lengths than in short ones. But in this equation we have not considered the factor of the size of the maximum circle of confusion, and it turns out that sticking to this, the small format will lose PDC by the simple fact of having to expand more to get the same large copy, what happens is that the focal length factor is more important than that of the maximum circle of confusion, which is why the smaller format continues to win in PDC, but it does not win as much as it seemed at first, since it is partially compensated with the CCM.

Now, if we intend to make a copy of the same size with two different formats with the same optics, f.º and focus distance (obviously each photo will have different framing) it turns out that the photo with the smaller format will have less PDC than that of the larger format since the only factor that we are changing is that of the CCM. But in this same case, if instead of making a copy of the same size, we make a copy proportional to each format and we observe it at the same distance, then the PDC will be the same with both formats.

Considering the observation distance

We've assumed from everything we've seen before that the look distance was constant in all our tests for a fixed copy size, but if we alter this parameter three things can happen:

1. If we keep the size of the copy while away, the PDC will increase.
2. If we move away or approach proportionally change the size of the copy the PDC will be the same
3. If we increase the size of the copy but we observe it at the same distance will decrease PDC. This is realized at the moment we want to make a picture of a general view of a city for example with its buildings. If we want to play with some element that is closer than the ∞ in which are the buildings of the city, we can make use of the hyperfocal distance to get sharpness with a lot of depth, then we will focus a closer point than ∞ and we will get to see well the entire picture while we see it at the right distance with the standard copy size, but if we do a mural with that photo and we still want to see it closely