The rear part of the car was approximately 6 m away from the camera. Let merklinher explain the classical theory of sharpness, analyzing the degree of fuzziness. The basic assumptions on which the theory is based are simply not appropriate for some photographic applications. It must be admitted that the larger the distance from the camera, the more details are captured by a circle of confusion of a constant diameter. The parameter c can be interpreted as the diameter of the imaginary round photobrush, with which the image on film is created. According to the traditional approach, only in this case the size of the DOF area does not depend on the focal length provided the image magnification is maintained constant.
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Merklinger Harold Merklingeris a well regarded expert in the field of optics and author of several books on the topic. Boke or Bokeh if you prefer , is the Japanese-originated concept of the difference between out of focus areas of an image due to lens design.
This article will be heavy going for some, but should be of interest to anyone desiring a technical understanding of this complex and controversial topic. Michael Exploring the Out-Of-Focus Photographers know that one of the characteristics that separates photographic imaging from drawing or painting is the matter of focus.
When we humans look at the world about us, our autofocus eyes tend to see everything in-focus. While the main subject might be emphasized with brighter colors and greater detail, the less prominent objects were usually still rendered sharply. Observant photographers have noticed that not all lenses are created equal: large aperture lenses show strong out-of-focus effects while small-aperture lenses lead simply to a softening of the image.
And even among lenses of equal focal length and aperture, there are differences. The Japanese apparently refer to the quality of the out-of-focus image as "boke". What is boke, and why are lenses different from one another? Figure 1 A triangular stop behind the lens results in a triangular cross-section beam of light focused on the plane of sharp focus.
If the film were placed in front of the focus, an upwards pointing triangular image is produced while behind the focus, the image of the lens opening is upside down. Remember, the photographic image itself will be upside down. Lenses, whatever their quality, obey the physical laws of optics and thus, I reasoned, boke should be explainable in straight-forward technical terms. In the explanation that follows it seems fitting to begin with a painting analogy.
The concept ofconvolutionessentially means replacing every basic element of one image with a second image, but constraining the overall brightness of each replica of the second image to be equal to that of the image element it replaces. Then we add up the overall result point by point over the whole scene. We start with a mental picture of every tiny detail in the scene to be painted. Our tools are round brushes varying from very fine to very coarse, and paints. To begin we choose a point on the most distant object in the scene.
We position the brush over the canvas, centering the brush precisely over the point where that distant detail should appear in the image. We dab the brush to the canvas, transferring a faint quarter-inch diameter smudge to the canvas.
Then we repeat the process over and over, detail by detail. We work with distant details first, then move to progressively nearer details, using smaller and smaller brushes as we go. When we get to the person we have chosen to focus upon, we use just a single bristle to apply that same 0. Then as we work to objects yet nearer, we use progressively larger brushes again. Throughout our painting we work detail by detail; only the size of the brush and the color of the paint change.
If we had used the single bristle brush throughout, we would paint a perfectly sharp and detailed picture. The camera functions very much like a painter having access to set of round brushes of all sizes. The camera chooses the size of brush based upon pure geometry: the effective brush size depends only upon where the object is, where the camera is focused, and upon the aperture of the lens. The camera then paints a fully detailed picture, using an amount of light corresponding to that for each detail, spread over a disk the size of the circle of confusion appropriate for each detail in turn.
Boke, the quality of the out-of-focus image, is determined by the set of brushes: the circles of confusion characteristic of the lens, its aperture and how far out-of-focus it is. Figure 2 The effect of a triangular stop can be seen clearly in this photograph. Note the downwards pointing triangles on the figure in the foreground and the upward pointing triangles on the figure in the background. The example suggests we should avoid triangular lens stops. To understand boke, then, we need simply look critically at the circle of confusion.
Ideally, a lens produces a circle of confusion that is simply a uniformly illuminated shape corresponding to that of the lens aperture. The size diameter of the circle of confusion depends simply upon how far the film is from where that particular detail of the image is focused. Figure 1 illustrates the principle, but for a triangular aperture. For a triangular aperture we no longer see a circle of confusion, but rather a triangle of confusion. Figure 2 illustrates an image taken with a triangular stop aperture placed in the lens.
Notice especially how the out-of-focus highlights appear as triangles. In this case, the highlights nearer to the camera than the plane of sharp focus have the triangles pointing downwards, while highlights beyond the plane of sharp focus show as upwards-pointing triangles. The triangular opening in the lens pointed upwards for this example. So, boke depends to a large degree upon the shape of the diaphragm opening. We probably should avoid triangles! Figure 3 Figure 4 The simple white-on-black test pattern used to determine some of the effects of aperture shape on the out-of-focus images.
I tried photographing a test pattern Figure 3 using openings of various shapes, and varying degrees of focus error. Figure 4 illustrates one of the results for the triangular aperture. Note especially the images of the out-of-focus triangles at the upper right of the figure. The triangle oriented the other way around is more interesting. Here we see a six-sided figure with three bright lines through it. Now the really interesting part of this is that the three bright lines do not exist!
They are a visual illusion! What this illusion tells us is that the details of boke depend upon physiological effects as well as physical optics effects.
The lower six-sided figure looks as though there are three white lines running through it. A fourth line has been intentionally drawn across near the bottom of the figure to show where a scan of image brightness was made.
There are no peaks corresponding to the positions of the white lines. The three white lines are a visual illusion.
Another principle illustrated by Figure 4 is that any object having edges that line up with the edges of the lens aperture will tend to be resolved to some degree. In Figure 4 we see, for example, that in the fan of lines at the bottom of the figure, horizontal lines and lines at approximately 30 degrees to the vertical are resolved, while lines at other angles are not.
So what is the ideal shape for the lens opening? It depends upon the subject! A perfect circle is probably about as neutral as we can get: it shows some degree of spurious resolution for lines at all angles! The circle plays few favorites. But photographers also know that particular lens designs have individual boke character, even when diaphragm shapes are similar. What makes the difference?
The circle of confusion as seen on a plain ground glass screen by looking at the out of focus image of a pin hole illuminated from behind was simply a uniformly illuminated shape, perhaps with just a touch of a thin bright outline around the perimeter.
And the circle of confusion was much the same whether it was on the lens side of the plane of sharp focus or on the far side. The thin bright outline, I reasoned, is most probably a physiological illusion.
Although a bright outline could be produced by Fresnel diffraction, we should see color fringing if that were the case. The outlines I saw appeared to be mostly white. Figure 6 Here is a sequence of images of a pin hole illustrating the circle of confusion at four distances behind the Rodenstock Imagon. From left to right, the images were obtained 4 cm in front of the plane of best focus, 2 cm in front, at the plane of best focus and 2 cm behind it.
Below the images is a graph showing the brightness of the image along a straight line through the centers of the circles. Figure 9 Here is a sequence of images of a pin hole illustrating the circle of confusion at seven distances behind the Nikkor-W.
The rounded corners can be expected to result in smooth, soft out-of-focus images. The most unusual lens I examined was a mm Rodenstock Imagon. Figure 6 shows a sequence of images of its circles of confusion at various distances behind the lens. On the lens side of the plane of sharp focus, we see a bright ring surrounding the circle of confusion.
The circle of confusion is also smaller than it is supposed to be, although this fact only becomes obvious with careful measurement. Behind the plane of sharp focus, we see the reverse effect.
The circle of confusion has a central bright core, and the overall diameter of the illuminated circle is larger than it should be.
These effects are the consequences of intentional spherical aberration. Light from the outer periphery of the lens aperture is focused closer to the lens than the nominal focal length of the lens would suggest it should. Figure 7 shows the result. On the left we see the distinctive sink-strainer pattern. At the next image, however, note that the two rows of holes have now converged to a single row. Fig 8 shows an enlarged view of these two patterns. The image at the far right of Fig 7 shows how the spots produced by the sink-strainer holes have become radial streaks.
I interpret this as a sign of over-corrected spherical aberration. The striations seen in these images are probably the result of a very slight smeared finger print later discovered on the back surface of the lens. Figure 10, by Kevin Hawk, shows a background out-of-focus spire as a very distinct double image. I suggest the bright core circle of confusion leads to pleasant out-of-focus images, provided the core is not too strongly concentrated.
Out-of-focus objects closer to the camera will be imaged more harshly. The Summicron gains its reputation by showing smooth out-of-focus images on both sides of the main subject.
It will in general also change with the actual aperture used. And it can depend upon how the lens is corrected off-axis. To close this discussion, I offer two last photographs.
Technical Books on Photography by Harold M. Merklinger
The papers on Resolution were added on 30 July The Photography Links page was revised - removing many non-functional links - on 15 December It now includes a version of VuCamText. An Essay entitled " Photography Today and Tomorrow " about the future of photography was added on 5 November It now contains a comparison with a dye sublimation print.
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JoJoll Moreover, it is easy to notice that an increase in focal length results in better resolution of details. The largest depth of field can be obtained if we focus the lens at the hyperfocal distance. Now let us see at the foreground Fig. This is an interesting concept that I know I have often used with analyzing it when I was worried the hyperfocal method would not render sufficient distance detail, often as a secondary safety shot.
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Tak Of course, the two theories describe different things, i. Then, one simple focusing motion of the camera back puts the image in proper focus. A Merklingeg VII 35 mm camera. Measuring unsharpness Traditional approach Unfortunately photographers often do not know how to interpret the results of the classical theory.
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