Focusing the View Camera: A Scientific Way to Focus the View Camera and Estimate Depth of Field. by Harold M. Merklinger. Merklinger’s method is less widely used, but is much easier to apply in the field. . Harold Merklinger describes his method for optimizing depth of field here. Harold Merklinger on Depth of Field. If you arrived at this page by a direct link, it will be helpful for background information if you read my article, More on Depth.
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Main page List of articles. Understanding physical meaning of sharpness Is Harold Merklinger’s theory correct? In my previous articles [ 12 ] I have already explained the basic ideas of depth of field and described all the necessary formulas to calculate it. But according to my bitter experience, people do not like to analyze boring mathematical expressions. They prefer to implement simple recommendations instead. However, as a Russian saying goes, simplicity can be worse than nerklinger.
Excessive simplifications often lead to false understanding. This article was written to deflate two mistakes that are quite common nowadays: If we change the focal distance of our lens while maintaining the same image magnification and keep the lens set to the same f-number, the merklinver of acceptable sharpness does not change.
If we merilinger our lens at infinity instead of focusing it at the hyperfocal distance, objects at infinity will be shown considerably sharper in our picture. I accept that this book contains a lot of correct and interesting ideas. But, ironically, the book also gave rise to a number of misleading recommendations. This article compares Merklinger’s approach with the traditional theory and puts his ideas to the test.
All the explanations here put an emphasis on graphs and real photographs instead of mathematical formulas. As a result, I hope, this physical text is easier to understand. And finally, I would like to remind you that the traditional theory is not exact either. Merklingger is based on a number of reasonable assumptions, however it still works perfectly most of the time. Any special cases, like micro-photography, for example, are not analyzed yarold.
Measuring unsharpness Traditional approach. Unfortunately photographers often do not know how to haeold the results of the classical theory. They believe the formulas give them the exact description of the zone of acceptable sharpness. But they often do not understand that in some cases objects became fuzzy very quickly beyond the area of sharpness, while in other cases objects out of focus look only slightly diffused. Let us explain the hagold theory of sharpness, analyzing the degree of fuzziness.
In article [ 2 ] I showed how to derive the formula that describes fuzziness behind the focusing point. Applying that approach to the general situation, we can obtain the universal mathematical expression: I put this tiny formula here just for your reference. You will not find any other pieces of math in this text.
The parameter c can be interpreted as the diameter of the imaginary round photobrush, with which the image on merklihger is created. The smaller this value, the sharper the image. Now let us analyze the graph that haorld to this simple formula see Fig. Strictly speaking, c is not actually equal to zero at this point due to diffraction. But this effect can be considered negligibly small for the purposes of this article.
Moreover, the differences between the classical theory and Merklinger’s approach lie ouside this small area. Beyond the distance of exact focus fuzziness grows. However, this growth is limited by the value of c’. In front of the focusing point, the degree of fuzziness grows sharper. If the camera-to-object distance is four times shorter than dthe objects are three times unsharper than at infinity. The graph in Fig. Because of this, it is not easy to derive simple practical formulas from it.
However within a limited vicinity of the focusing point it is not that difficult to develop a good approximation.
Merklinger’s Photo Books
Now let us look at the same graph calculated exactly in accordance with our formula Fig. One merklingeer easily notice that within the green oval i. Let us call this area the green zone. All approximate theories work perfectly within the boundaries of this area.
However, we have to use the initial non-linear model, when our parameters do not comply with the green zone requirement. Harold Merklinger offered another approach to linearization.
BAC Event Photos
His object space, where fuzziness varies linearly, can be obtained from the traditional film plane model with the help of a non-linear transformation. But let us be patient. Merklinger’s theory wil be discussed a little bit later. How to calculate depth of field graphically. The procedure is very simple. First we have to draw a horizontal line that determines the acceptable circle of confusion c 0i. T wo intersections of such a horizontal line with the fuzziness curve will show us the limits of depth of field DOF.
The exact formulas to calculate DOF can be found in [ 1 ]. Now let us consider most important cases. In the table below, the green horizontal line shows the acceptable level of fuzziness c 0while the dash blue line corresponds to the fuzziness of an infinitely distant point c’. The relatively thick green band under each graph shows the DOF area.
The graphs in the table serve exlusively to demonstrate the general arrangement of curves and lines. All the distances are meaured in units of dwhile fuzziness is measured in units of c’. Thus, the equal distance between the focusing point and the origin of coordinates in cases A to D does not mean the distance between the camera and the object is the same in all those cases.
The focus is set at infinity.
The closer the object, the fuzzier it gets. The front limit of the DOF area equals the hyperfocal distance.
Again, I have to remind you that all of the above is the classical theory. The description of its results is not traditional, but the results themselves are well-known. Now let us analyze Merklinger’s approach. In his opinion, it is better to describe DOF in terms of the resolution in the object field rather than concentrating on the characteristics of the final image. The idea looks vague, doesn’t it?
The general idea of Merklinger’s approach is quite simple. The sketch in Fig. The lens is focused at the hsrold djust where the object is located. The DOF area is determined by the acceptable divergence two green arrows of the blue dash lines that represent a cone in the object field. According to Merklinger, the bigger the diameter of harrold cone at a certain distance, the fewer emrklinger can be resolved.
And poor resolution means poor sharpness. In a sense, Merklinger’s theory is a linear approximation of the traditional theory. With the help of a non-linear transformation, the merkinger field, where fuzziness varies linearly, can be recalculated into the image field model, where fuzziness is described by non-linear functions.
Technical Books on Photography by Harold M. Merklinger
In this article I can give only a brief explanation of Harold Merklinger’s approach. If you want to learn more details, please read the original book. It is fair to say that some of Merklinger’s conclusions are quite reasonable. But at the same time, it is important to remember that there are many differences between his rules and traditional recommendations.
Of course, Merklinger’s approach is basically correct. However, the problem is that his theory perfectly works when the resolution is discussed, but it is not suitable for the purposes of sharpness.
One may also ask a natural question: Is it possible to compare two so diferent approaches? Of course, the two theories describe different things, i. But at the same time they both deal with sharpness. When I compare them, I try to find out which theory better matches the intuitively obvious concept of sharpness.
Thus, a person, who is far from physics and math, typically faces the following contradictions: According to the traditional theory, the degree of fuzziness grows quite sharply merllinger front of the focusing point. Moreover, this growth is non-linear. Merklinger claims the disk-of-confusion in the object space grows linearly.
Merklinger’s disk-of-confusion in the object field can be infinitely large. In the object field, the zone of acceptable resolution is absolutely symmetrical. The traditional zone of sharpness DOF can be asymmetrical under certain circumstances. If focusing can be described by Fig. The harod condition means that we must increase or decrease d and f simultaneously.
According to the traditional approach, beyond the limits of the green zone see Fig. Merklinger wrote that in spite of many differences, both methods can be used in practice.
This sounds quite strange, because the recommendations of the two theories critically diverge.