On the depth of field, of course, known to all who came to hold the camera or camera. The corresponding formulas for the calculation can be easily found in various references and articles. So why do I need to write another text on this subject?
Frankly, I had two objectives:
* Collect all the useful formulas within the same article;
* To draw the reader’s attention is not quite obvious conclusions arising from these formulas.
Of course, many people long involved in photography, can easily assess the depth of field on the basis of their experience. Others prefer to limit viewing the filmed story through the lens SLR camera. It is unlikely that this article will tell photographers such as something new. Indeed, intuition and experience are at times when taking a much more important. Those, who have long experience is not so great, but intuition is not so developed, can be useful to have set out below.
The article consists of two parts. The first shows the formula. In the second – a discussion of these formulas. If one type of mathematical expressions you feel uneasy, go directly to reading the second part.
Before you go directly to the point, I note that all of the following approximate formula, ie, is based on several assumptions. For example, they do not take into account the difference in the size of the entrance and exit pupil lenses. They also suggest a shot, when focusing distance substantially greater than the focal length of the lens. But in most cases, these formulas can be used in practice. Consideration of the finer details is beyond the scope of this article (macro, use of special optics, etc.).
The diameter of the permissible range of blur shows a spot diameter of a permissible blur the point on the negative, to the human eye, it was still “point”. In a typical narrow screen pictures with the frame 24h36 mm is often assumed c = 0.03 mm (about 1 / 1500 of the diagonal frame). Such a blur circle diameter, you can view a picture 13 x 18 cm at a distance of about 25 – 30 cm In any case, the objective scale of depth of field (DOF), most manufacturers are based precisely on this figure. In digital photography for the calculations must take the value, usually less (often an order of magnitude). The exact value depends on the size and structure of the matrix of photosensitive cells. Restrict the exemplary and very rough estimates. Suppose, for example, the matrix of the digital device has a diagonal half inch, ie 12,7 mm. Let this matrix consists of 2 million pixels. With these data we can estimate the linear size of one pixel at a level of about 0,006 mm. In this case, c = 0,003 mm means that the permissible blur circle diameter is polpikselya.
As can be seen, when d = h Lza value becomes equal to infinity. Negative values Lza should also be considered as an infinite length of the field sharpness of the object.
The third group of formulas is convenient to use when it comes to filming in the same scale. For example, the photographer decided to shoot half-length portrait. Thus, it is determined on the scale location. As the depth of field will depend on the lens focal length in this case? Here to answer such questions, and a third group of suitable formulas.
Supervisory reader can easily notice that these formulas were obtained from the first group with the help of simple transformations. Applying a similar transformation to the second group can be obtained and the fourth group of formulas. But in any case the main thing – to stop. The formulas of the third group are convenient for analysis, while the formula of the first and second groups are more suitable for practical calculations. For the purposes of this article, no need for other additional formulas do not.
Let us now discuss useful conclusions that follow from the above formulas.
1. First of all, it is important to understand that there is no clear boundary between sharp and blurred in the picture. All that is before the point of focus, and for her, in more or less fuzzy. When people talk about the depth of field, the mean size of the region in which the blur does not exceed the specified value.
2. Depth of field depends, in general, the scale of the location of M, N and aperture value on the ratio d / h (ie the ratio of the distance of the focus lens to the hyperfocal distance).
3. If the hyperfocal distance is small (ie almost equal to the minimum focusing distance), then we are dealing with a large depth of field. Strictly speaking (scientifically) can not be said that the region of 1 m to infinity more area of 2 m to infinity. Therefore, I will explain what I mean. Suppose, for example, h = 1 m and a minimum focusing distance of the lens is equal to 1 m, then, obviously, for whatever we are focused, everything will turn sharp. Cheap camera with fixed focus just fitted with lenses that are focused on the hyperfocal distance.
4. If the lens bring to infinity, the near-border area of field will be equal to the hyperfocal distance: d1 = h.
5. If the subject is at a distance much less than the hyperfocal (d <<h, or that the same thing, c N <<f M), then in this case (and only if) the depth of field does not depend on the focal length of the lens with constancy of M and N. What does that mean a lot less? Well, let’s say, 10 times or more. Elucidate this by examples.
Suppose we want to remove the object on the scale of M = 0.1, ie the object 24h36 cm in full frame. Suppose we have chosen the aperture N = 8. Then we may be surprised, we find that the depth of field lens f = 200 mm will be almost exactly the same as for the lens f = 50 mm, namely, where a 2.5 cm before and 2.5 cm for object. (Of course, we approached the object during the transition to a short-optics to maintain the scale).
Another example: when N = 8 shoot a portrait of the scale M = 0,05. In the first case we use a lens with f = 50 mm depth of field and get +11 / -9 see the second case we use the lens 135 mm. In this case the calculation gives the depth of field +10 / -9 cm, which is almost the same as in the first case.
The effect of the independence of the depth of field of the focal length is expressed more strongly, the greater the scale of M and smaller aperture value N. So, if we decided to rent a scale M = 0,02 for N = 16, it would immediately notice the dependence of depth of field on the focal length.
7. As the distance to the object front area of field becomes smaller than the rear. When d is equal to one third of hyperfocal distance, the rear depth of field is twice the hall.
8. As mentioned above, when d = h rear boundary of the depth of field is extended to infinity. It is also useful to know that in this case Lpered = d1 = h / 2, that is closest boundary of the field is equal to half of hyperfocal distance.
9. If you shoot a subject with two lenses in one scale, at distances comparable to the hyperfocal (ie, the condition of Section 5 is not satisfied), then a short-lens would be consistent with a large rear and smaller front area of focus.
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Of course, of great importance not only dramatically depicted the elements of the photograph, but also a region with blurred image. It is important not only to the extent and nature of the blur. Picture blur depends on many design parameters of the lens and can not be a simple mathematical analysis. The degree of background blur when shooting deserves a separate article and is not considered here. (See my text entitled “blurs the background scientifically.)
It is clear that neither the beginning nor the professional photographers are not always inclined to engage in calculations. The very last time I remembered these formulas, when he moved to capture so-called “zumami”, which, of course, was not familiar to me scale GRIP. Then, for each “zoom” I have prepared the appropriate plates, laminated them and began to wear in his coffer. As the available reference material they seemed to me quite comfortable.
As an example, such plates lens 28-70/4 (see Appendix). If necessary, everyone can own a similar plate, focusing on their own needs. Thus, we can make these plates for the other values of the permissible range of blur, for example, equal to 0.02 mm. It may make sense, if you want to print photos with greater magnification.
I note also that, in my view, such a table is not so easy to get specific numbers, how to quickly obtain overall estimates. How to increase the depth of field at tightening the diaphragm? What happens during the transition to smaller focal lengths? Quickly find answers to such questions just described me and help boards.