In two previous articles devoted to the depth of field [1, 2], I reminded readers of the main provisions of the classical theory. However, as shown by my sad experience, people do not tend to comprehend the physical meaning implied in the tedious mathematical expressions. Much more they like guided simplified clear recommendations. But, alas, the simplicity can still be worse than stealing. The desire for simplification often leads to a completely wrong understanding of the facts.
By writing this article has prompted me to want to dispel two common misconceptions:
1. When shooting ravnomasshtabnoy DOF does not depend on lens focal length. The scale and the diaphragm completely determine the depth of field.
2. Focusing at infinity gives a substantial gain in sharpness and detailing plans for remote as compared with focusing on the hyperfocal distance.
Both these ideas are largely based on the theory of Harold Merklingera, which he outlined in his book «The INs and OUTs of focus» [3]. Admittedly, in his book there are many sensible and useful ideas. But, ironically, some of the ideas Merklingera served as the basis for a number of unfortunate errors.
This article attempts to frame the issue and clarify the scope of applicability of different approaches to the assessment of depth of field. In this important role in the presentation will play no formula, which if necessary can be found in two of my first articles, and graphics and real photography. I think this approach is less tedious and more compelling for the reader, far from physics and mathematics.
In conclusion, this small entry is also appropriate to remind dear readers, that the classical theory of aberration-free, which will be discussed in this article, too, is not absolutely accurate. It is based on a number of simplifying assumptions. However, in most cases the classical approach gives good agreement with the practice of the result. Consideration of the finer details is beyond the scope of this article (corrected for aberrations, the use of special optics, etc.).
The degree of blur
Incorrect interpretation of the classical theory, occurs frequently. In my opinion, this incorrectness primarily related to lack of understanding of the degree of accuracy, which provides the traditional approach to determining the boundaries of field. Indeed, one thing – when outside the settlement zone of sharpness at once greatly reduced, and quite another thing – when outside the image field is only slightly more blurred.
Let’s try to explain the key points of the classical theory, analyzing the degree of blur for objects distant from the camera at different distances. In other words, try to explain the sharpness through its opposite, that is, the degree of fuzziness. In [2] has already been described, as you can get a formula to describe the degree of blurring of the focus point. It is similarly possible to obtain a mathematical expression for the magnitude of blur in the area between the camera and the object in focus. Universal formula to describe the blur is as follows:
Strictly speaking, due to diffraction effects, the degree of fuzziness point of focus will still be nonzero. That is, in practice, a sharp “beak” at d0 = d always be smoothed (see red dotted line in Fig. 1). The size of the diffraction spots (ie the size of the minimum achievable points on the film) is directly proportional to the aperture value N. Its value can be estimated from the approximate formula N/1600 [mm]. Henceforth the diffraction limit will not be taken into account, as in most practical cases, the sample size of the circle blur (0,03 mm) larger than the size of the diffraction spots. Also, discussed here a contradiction between the approach of Harold Merklingera and classical theory are related to a rather extended regions of field, rather than to a small neighborhood near the point of precise focus.
During the focus point increases the degree of fuzziness. The greater the distance from the camera to the remote point, the higher the degree of fuzziness. However, this does not mean that infinity is infinitely blurred. The degree of fuzziness at infinity does not exceed the value c ‘.
Prior to the focus point as it approaches the object to the camera its degree of fuzziness on the film increases much more sharply. At the point, which is located exactly halfway between the camera and the object on which it focuses (d0 = d / 2), the degree of fuzziness is the same as at infinity.
Outside the Green Zone, “almost all the approximate methods give unsatisfactory result, since we are considering our curve can not generally be replaced by two straight lines with sufficient accuracy.
Achieve linearization model can be another way. For example, you can use a nonlinear transformation to transform the plane of the film into some new space. That’s what Harold Merklinger. But let’s not get ahead. On the approach G. Merklingera will be discussed below.
Calculation of depth of field
How can using our schedule, calculate the depth of field? Nothing is easier! To do this, hold it straight horizontal line, which corresponds to the range acceptable to us blur. The intersection of this line with our curve, and give us the classical computational point of depth of field.
Classic formulas, which are usually used in practice, can be found in [1].
Consider and comment on the most common options. The plots, which are placed in the table below, the blue dotted line shows the level of c ‘. The solid horizontal green line corresponds to the range acceptable to us blur c0. Typical (but certainly not the only possible) the value of c0 in the narrow screen images as well 0,03 mm. The green bar below the graph represents the area of field, which makes use of the classical theory.
! NOTE: Charts in the first column of the table demonstrates the very different relative positions of the lines that affect the area of field. The fact that the graphs A – D point of focus is on one and the same distance from the origin, does not mean that in all these cases, the distance between the camera and the object of the same. In all graphs the horizontal axis represents the distance in units of d, while the vertical axis – the degree of blur in units of c ‘.
This assessment (9,5 – 11 megapixels) is very common, but erroneous. However, give the reader to decide who is right. Do not multiply entities beyond necessity. To answer the question about the number of pixels in a film frame is not needed nor Nyquist theorem, no discussion about scanning. I think Sergei embarrassed the first version of my reasoning, I offer for absolute amateurs. But for people at least a little prepared, I brought in his article approach № 2. I propose once again to trace the course of my thoughts:
