We calculate the depth of field. Part 2

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What is depth of field or depth of field. Part 1

From the previous article, you already know what depth of field is and what parameters it depends on. Today we will get acquainted with this concept in more detail. How to accurately calculate the depth of field? How to achieve maximum depth of field, and why are depth of field calculator programs often mistaken in their calculations? Read about it later.

NIKON D600 Installations: ISO 125, F4, 1/80 s, 200.0 mm equiv.

When to worry about accurate depth of field calculations?

Very often, the photographer is required to take sharpness of certain objects, it is required to achieve a certain depth of field. Therefore, he needs to calculate it accurately. Experience is experience, but not always it works one hundred percent. Accurate calculation is necessary in landscape, subject, macro photography, if you print photos in large formats and their sharpness is crucial. But if you shoot purely amateurish, not at all worried about the quality of the photos, and print the pictures in small formats such as 10x15 cm, or do art photography under the motto “who said that the pictures should be sharp ?!”, then all this is for you not that important. An accurate calculation of the depth of field helped me get the most out of my camera: after all, I didn’t buy an expensive multi-megapixel camera in order to use its capabilities to the end.

IPIG formula

Once upon a time, a formula was developed for calculating the depth of field. In the last lesson, we already talked about the main criteria that affect the depth of field - it's focal length, focusing distance, aperture. All of them are presented in the formula.

R1 - the front line of the depth of field;
R2 - the rear boundary of the depth of field;
R is the focusing distance;
ƒ is the absolute focal length of the lens;
K is the denominator of the current relative aperture (aperture value);
z is the diameter of the scattering circle. A very interesting parameter that fundamentally affects the calculation of the depth of field. We will return to it more than once in this article.

Accordingly, the depth of field P will be calculated by the formula: P = R1 - R2 Do not forget that the focusing distance, as well as the closest one from the far edge of the depth of field, is measured not from the front lens of the lens, but from the place where the device’s matrix is located - from the focal plane.

This icon on the camera indicates the focal plane in which the matrix of the camera is located. It is from this place that the focus distance is measured.

Of course, in practice no one uses this formula today, but it is useful to know about its existence. It is on the basis of this formula that numerous IPIG calculator programs work in which you can simply enter the shooting parameters and find out the depth of field without any mathematical exercises. We will talk about these programs below.

What is sharp in the photo? Scatter circle

We already know that a clear border between sharp and unsharp areas of the frame does not exist. This knowledge will help us understand how the depth of field of the depicted space is generally formed. For simplicity, we agree that we will photograph points of a negligible diameter laid out in a row on an ideally sharp lens. Then the sharpness in the frame is distributed as follows: Only that point that appears exactly at the focusing distance of the lens will be ideally sharp. Points in front of or behind the focus distance will be blurry. In the resulting photograph, until a certain point, this blur will not be noticeable to the eye of the observer. However, then the points will begin to smoothly turn into small circles, and the observer will begin to notice a blur in the frame. The minimum diameter of such an unsharp circle, visible to the eye, was called the "circle of scattering" (in English - circle of confusion or abbreviated COC). All points with a diameter smaller than the scattering circle are considered sharp in the photograph. All points with a large diameter are considered unsharp. At what point does the blur become visible to the eye? It all depends on the observer. Therefore, the depth of field is a subjective value. A keener and more meticulous observer will make higher demands on the sharpness of a picture than a less sophisticated one. But it is not only an observer. Much will depend on the resolution of the matrix (or film). As long as the scattering circle is smaller than the pixel size on the camera’s matrix, all the points in the photo will be equally sharp. And of course, a lot depends on the observation conditions. If we consider a small photo, we will see fewer details on it than on a large one. Based on all these assumptions, since the time of the film, the diameter of the circle of confusion is 30 microns or 0.03 mm. Based on this value, manufacturers on some lenses make a depth of field scale like this:

Simple scale of depth of field on the Nikon 50mm f / 1.4D AF Nikkor lens. How to use it? The scale shows the aperture values F11 and F16 with risks (highlighted in yellow), above them - the focus distance scale (highlighted in blue). When focusing on a certain distance, we will see what, the distances will be between the risks of the depth of field scale. They will say to what extent the depth of field will spread. It is worth mentioning that on modern lenses they are increasingly less likely to make such a scale, since it is possible to estimate the depth of field by it only very roughly.

Depth of field calculator

Depth of field calculator (or DOF calculator in English) is a program that allows you to accurately calculate the depth of field without using complex formulas. Today on the Internet there are several publicly available depth of field calculators. They are easy to find using the Internet search. However, calculators designed for smartphones have far greater practical benefits. After all, they can be used right at the time of shooting, wherever it takes place. In the AppStore (for Apple iOS), Google Play (for Android OS) and WindowsPhone application stores , when searching for “DOF Calculator” or “DoF Calculator”, many applications are issued. Most of them are fully functional: they all work according to the same formula described above. I’d like to highlight a little more than three free applications developed for different operating systems among the general mass. In my subjective sense, they are most convenient to use.

HyperFocal Pro

F-stop calculator

DoF calculation for WindowsPhone

We use the DOF rationally

When calculating the depth of field and using this data when shooting, it is important to consider that it extends to both sides of the focus point. Often photographers forget about this, believing that the depth of field extends only beyond the focus point. With this approach, the depth of field will be calculated incorrectly and the sharpness at the rear of the plot will be lost. In addition, in practice, you will encounter the fact that the front and rear boundaries of the depth of field are located at different distances from the focus point.

An example of a depth of field distribution.

For example, when shooting a landscape and focusing in the foreground, you will definitely notice that basically the depth of field extends beyond the focus point, and just a little in front of it. But the general pattern is this: the farther the focus distance, the sharper the depth of field goes beyond the focus point and less significantly spreads in front of it. In each case, the distribution parameters of the depth of field will be slightly different. So here you can give only one practical recommendation: every time you need to strictly calculate the depth of field, it is worth considering that the front and rear boundaries of the depth of field are at different distances from the focus plane.

We will observe how the depth of field is distributed when focusing on the bumper of the car: most of it went back, the smaller part went forward.

NIKON D810 / 70.0-200.0 mm f / 4.0 Installations: ISO 200, F4, 1/400 s, 100.0 mm equiv.

Why do depth of field calculators sometimes lie? Circle of scattering and modern realities

Often from users of the above programs you hear that the program displays data that does not correspond to reality. In the photo, the depth of field is less than what the program showed. The whole problem is that the depth of field calculators usually use the 0.03 mm scatter circle parameter for calculations. At the time of film photography, a value of 0.03 mm was quite enough: the film did not have as much detail (resolution) as the matrices of modern cameras. The diameter of 0.03 mm is too large for modern devices. A circle with such a diameter will include quite a few pixels of the image obtained from a modern matrix, and therefore, such a circle will be clearly visible in the photo.

A scattering circle with a diameter of 0.03 mm in comparison with image pixels with a resolution of 6000x4000 points (24mp) obtained from an APS-C format matrix.

As you can see, quite a few pixels of the image entered the circle of confusion with a diameter of 0.03 mm. This means that in the photo such a circle will no longer look like a point, but rather a circle. And at the boundaries of the depth of field, the image will be noticeably less sharp. We obtained the area of one pixel by simply dividing the area of the matrix by the resolution of the images it provides. Of course, this is only a rough estimate: one pixel on the matrix does not give one point on the image: one pixel on the photo is obtained by analyzing data from several pixels on the matrix at once. By the way, that is why pixel-by-pixel image refinement is not possible on modern matrices - there are too complicated relationships between a point in the image and physical pixels on the matrix. However, even such a rough assessment helps to understand the essence of the problem: film standards of sharpness are outdated today and require adjustments. Especially if you use high-quality modern optics that provide high image detail. Especially if you shoot on cameras with APS-C matrices or more compact: the smaller the matrix, the smaller the size of one pixel (to fit all of them in a given area), therefore even a small scattering circle will be noticeable. The same applies to multi-megapixel full-frame devices like the Nikon D810, Nikon D800 and Nikon D800E with 36 megapixels on board. Today, for effective calculation of the depth of field, a revision of the diameter of the circle of confusion is required to reduce it. What does it look like in practice? When shooting this still life, I paid special attention to calculating the depth of field. So that the whole composition “from and to” gets into it. To calculate the depth of field, I used the diameter of the scattering circle of 0.03 mm. In theory, everything that went into the depth of field zone should be equally sharp. But what picture will we observe in reality?

The focus area is highlighted in yellow, and the area located on the border of the calculated depth of field pipeline is highlighted in green.

NIKON D810 Installations: ISO 100, F11, 100 s, 85.0 mm equiv.

The sharpness in the focus area is great! Thanks to the bunch of Nikon D810 + Nikon 85mm f / 1.4D AF Nikkor

What is at the borders of depth of field can no longer be called clear. It can be seen that both the tray and the far part of the bouquet are very blurry.

How to be? How to calculate depth of field without errors? For this, in the calculations of the depth of field, I recommend using a smaller diameter circle of confusion. Based on my subjective experience, I chose a diameter of 0.015 mm. To use a circle of a smaller diameter is not very rational: it is unlikely that you will encounter such sharp optics that will shoot with such high detail. Of course, the smaller the diameter of the scattering circle we use in the calculations, the smaller the depth of field we get. However, such a calculation will be more correct. In the parameters of most IPIG calculators, the diameter of the scattering circle can be set manually. Take this opportunity! Note that if you use not too sharp optics, for example, a lens-hypersum, then you can safely use a scattering circle of 0.03 mm in the calculations, since the lens will not allow to achieve greater sharpness. It is also worth noting that, according to the above data, it may seem that in such a case, compact cameras should be able to blur the background better and stronger ( and the blurred background is a consequence of the small depth of field ): because they have very small matrices and they will have a large scattering circle noticeable even more. We disagree: compacts use too short-focus optics, so the depth of field will still remain very significant, no matter what scattering circle we use in the depth of field calculations.

We make everything sharp to infinity. Hyperfocal distance

Often it is necessary to make the whole frame, from the beginning to the end, be sharp. This is especially necessary in landscape, architectural, interior photography. Focusing on infinity will not help: in doing so, we will lose focus in the foreground. But often you want to sharply show both the foreground and the very distant background. To achieve maximum depth of field, starting as close to us as possible and encompassing infinitely distant objects, photographers use hyperfocal focusing . Hyperfocal distance is a distance when focused on which everything from ½ of this distance to infinity will fall into the depth of field. The most difficult thing in hyperfocal distance is its calculation. But once you have calculated the hyperfocal, you can easily and quickly shoot any landscape without first focusing and calculating the depth of field, just by focusing the lens on the hyperfocal distance you already know. Like depth of field, the hyperfocal distance will depend on the focal length of the lens and the aperture value. The shorter the focal length and the stronger the aperture is closed - the closer the hyperfocal will be to us.

Focusing on hyperfocal distance allowed me to sharpen both the stone in the foreground and the distant mountains.

NIKON D810 / 18.0-35.0 mm f / 3.5-4.5 Settings: ISO 100, F14, 1/60 s

All the depth of field calculators described above can also calculate hyperfocal distance. Using them is easy and convenient. In calculating the hyperfocal distance, all the same remarks regarding the diameter of the scattering circle will be valid. It is especially convenient to aim at hyperfocal distance when the lens is equipped with a scale of focusing distances. Then you can simply manually visit the desired distance on the scale, as I always do.

Nikon 12-24mm f / 4G ED-IF AF-S DX Zoom-Nikkor

Nikon AF-S 16-35mm f / 4G ED VR Nikkor

Nikon AF-S DX Nikkor 16–85 mm f / 3.5–5.6G ED VR

A wide-angle lens with a focus distance scale is a great choice for landscape photography. Practical difficulties in working with hyperfocal distance are that the scale of focusing distances, even on top-end modern lenses, is greatly reduced: it is small and only approximate estimates of the focusing distance can be made from it. Whereas for absolutely accurate aiming at a hyperfocal distance, sometimes it is necessary to calculate the distance not only in meters, which allows the scale to be made, but also in centimeters.

Typical wide-angle focusing distance scale. A wide-angle lens is perhaps the main tool of a landscape photographer. And it is precisely when using a wide-angle that basically it makes sense to use hyperfocal distance. However, you can see that on this scale between “infinity” (and “infinity” can start from tens of meters!) And focusing on 1 meter, there are no notations. When focusing on the hyperfocal, you usually have to point the lens at 1.5-2 meters. It is very difficult to accurately do this using this scale.

Personally, I came up with a solution to this problem. The same solution will help to direct a lens at hyperfocal distance that does not have any focusing scale at all (for example, a whale scale). For shooting, I take with me the usual building tape measure. And when I need to visit strictly at a certain distance, I lean it against the mark of the focal plane on the camera and pull the tape measure into the distance of the hyperfocal distance calculated before. After that, you can aim at the tip of the roulette wheel - it will be at the required distance. Of course, this method is very extravagant and I use it only in very difficult situations, when the depth of field needs to be used really as accurately as possible. There is a simpler way: knowing the hyperfocal distance, you can find an object located at that distance in the frame and focus on it.

So to summarize

To accurately calculate the depth of field, it is convenient to use the depth of field calculators. The calculator program can be installed on your smartphone and use it directly on the set. Enter in the program various parameters of the shooting distance, focal length of the lens, aperture: see how the depth of field will change from this.
To achieve perfect sharpness, when calculating the depth of field, you should use a scattering circle with a diameter not of 0.03 mm, but smaller. It all depends on your requirements for sharpness in the photo and the equipment used. When using insufficiently sharp optics, a decrease in the scattering circle in the calculations will not give any improvements. I use in calculations the diameter of the scattering circle is 0.015mm.
To distribute the depth of field as accurately as possible, remember that it does not spread uniformly from the focus point: some of it goes forward from this point, and some (usually much larger) goes back.
To achieve sharpness when shooting a landscape from objects closest to us to infinity, it is worth using focus on the hyperfocal distance. The same depth of field calculator programs can calculate the exact distance you need to travel to get sharpness from ½ of this distance to infinity.
Remember that the sharpness and technical quality of a photo is often not as important as its artistic component. Create, experiment, look for interesting subjects, work on composition and lighting: this is what will make your photos interesting first of all. A precise calculation of the depth of field will only help to create a photograph at the proper technical level.