How
do out-of-focus areas look like? Theory
of bokeh, ni-sen and other weird phenomena ________________________________________________________
Sometimes
blurry twigs become double in photographs, making the entire picture
quite unpleasant. Sometimes twigs are represented by tubules. In
such cases, photographers often say that the lens displays very
poor bokeh. This Japanese term serves to describe how out-of-focus
areas are rendered in a picture. Bokeh is responsible for not only
double images, but other interesting phenomena as well. Double-line
twigs are just an example of bad bokeh. Sometimes this special case
is also called ni-sen, which is another Japanese word commonly used
in the theory of photography.
Some
examples of poor bokeh can be found even in photographs by famous
authors (see ).
This
article attempts at giving rather simple explanations to such kind
of effects. The readers can not only learn the theory but also carry
out simple experiments with the help of any suitable image processor,
such as Adobe Photoshop or Paint Shop Pro.
The crucial role of the lens
Bokeh
depends on many various factors. However lenses are major contributors
to it.
If
we take a picture of a small bright point located within the out-of-focus
area, we will see that it will turn into rather a large disc that is called
the circle of confusion. According to the theory, the appearance of that
disc determines how out-of-focus objects are rendered in a picture. Figure
1 demonstrates the main types of such discs on the assumption that the
lens aperture is perfectly round. Under each image, there is a curve that
shows how brightness changes along the diameter of the spot. Such a curve
is called "a point spread function" or PSF, but we are not going
to use this term in this article in order to keep things simple.
Figure 1
1.
Type A. An evenly illuminated disc. This case relates to
almost perfect lenses without any signs of spherical aberration. Such
lenses are sharp and artistic at the same time. Nevertheless they still
can produce unpleasant backgrounds. We will discuss the related details
a little bit later.
2.
Type B. Discs with well-defined edges and spots in the center.
Spherical aberration was not successfully corrected in such lenses.
They can be pretty sharp; however their sharpness sometimes looks unnatural,
because image points are rendered as doughnuts. The uneven structure
of the Type B discs often causes bad-looking bokeh, including double-line
streaks. By the way, the Unsharp Mask filter, which can be found in
almost any image-processing software, also uses masks that are somewhat
similar to the discs of Type B.
3.
Type C. Discs with fuzzy edges. Brightness changes gradually
along the disc. Such kind of unsharp circles are produced by soft lenses.
However their softness is compensated by very pleasant bokeh. They never
render double lines in the pictures.
It
is very important to understand that there is always a trade-off between
sharpness and good bokeh. On the one hand, sharp images consist of elementary
points that look like tiny sharp peaks. On the other hand, those elementary
points should be smooth and dome-shaped to produce good bokeh. Only soft
lenses cannot split twigs in the background reliably. Thus, designers
have to reach a successful compromise to produce a perfect lens. That
is where professional skills become art.
Lenses
may have different circles of confusion at different f-stops. Moreover,
the type of the blurry disc may be different in the foreground and in
the background. As an example, Harold Merklinger describes Rodenstock
Imagon in his famous article [2]. This lens renders Type B circles in
the foreground and Type C circles in background. Unsharp discs can also
be different in different parts of the image. If a photographer wants
to have pleasant-looking out-of-focus areas in his pictures, he has to
learn all such details about his optical equipment.
Bokeh
and visual illusions
Surprisingly,
in some cases double-line streaks can be attributed to visual illusions.
It is a fact that abrupt changes in brightness patterns can produce illusory
curves in a picture.
Two
examples of this phenomenon are shown in Figure 2. The graphs under the
gradient rectangles show how brightness changes along the images.
Figure
2
The
eye perceives two dark vertical lines in the first image and two light
vertical lines in the second. They are located at the points marked
by the arrows. Those are the points where brightness abruptly starts
or ceases to be constant. The perceived brightness is shown by the
blue and yellow dashed curves correspondingly. However the actual
curves are absolutely flat.
Generally
speaking, unsharpness often produces gradients. In their turn, gradients
often can be blamed for illusory effects. Figure 3 is an obvious illustration
to this.
Figure
3
The
square is filled with regular gradients from the center to the sides.
The most surprising fact is that bright diagonals do not exist! If
we measure illumination along the A-A line, we will fail to detect
any bright spots at the intersection points.
This
phenomenon is also described by Harold Merklinger (see Figure 5 in [2]).
Please
keep in mind the described illusion while reading the rest of the text.
Studying
ni-sen with the help of image processing software
Some
rigorous scientific approaches to bokeh and ni-sen will be described in
the next section. Here we will discuss a couple of approximate but obvious
methods. I hope that even those of you who hate math and physics will
be able to catch on to the basic ideas.
Our
main instrument will be the blur filters that can be found in many image
processing programs, such as Photoshop, Paint Shop Pro, and many others.
Personally I used Photoshop 6.0 for this article.
Experiment
#1
In
our experiments we are going to use three objects (see Figure 4):
-
rather a long vertical rectangle to represent a twig (in the center);
- a triangle to represent a twig of variable width (on the right);
- a curved figure to make our demonstration more obvious (on the left).
Figure
4
To simulate blurring with an evenly illuminated circle of confusion
(Type A), Motion Blur filter was selected. Since it works only in
one direction, Angle should be set to zero. The Distance parameter
corresponds to the diameter of the circle of confusion.
Now
let us apply this filter to our images. If Distance is not zero,
the upper part of the side images doubles. When Distance is big
enough (e.g. D = 17, see Figure 4), two distinct streaks within
the central rectangle become visible.
Feel
free to copy the picture to your image processing program and carry
out your own experiments.
Please
pay attention to the fact that if we measure brightness along the
A-A' line with the Eyedropper tool, we will not be able to detect
any trace of splitting. Thus, we can say that we deal with visual
illusions in this case.
Conclusion
#1: Even Type A circles of confusion can result in visual splitting
of lines in a picture. The thinner the line, the smaller the circle is
required to produce double streaks. This effect can be mainly attributed
to illusions related to peculiarities of visual perception.
Experiment #2
Figure
5
Now
let us modify our initial test images. The shapes will remain unchanged.
All we are going to do is to add white edges to them (see Figure
5).
Apply
the Motion Blur filter to our new test images. The comparison of
Figure 5 to Figure 4 shows that splitting became more distinct.
It is little wonder, because double streaks can be technically detected
now (see the brightness curve at the bottom of Figure 5).
The
conclusion #2 is quite simple: some objects are more susceptible
to splitting than the others. According to our terminology, objects
can also be of Type A, Type B or Type C. Objects with highlighted
edges or aureoles are more likely to be split in the out-of-focus
area. Such Type B objects can be poorly rendered even by high quality
lenses with circles of confusion of Type A.
Conclusion
#3: Any additional accessories
that are attached to the lens can produce halo effects, so they can spoil
bokeh. Photographers should avoid using cheap accessories of low quality.
Experiment
# 3
Let
us apply the Gaussian Blur filter to our test objects (Figures 4 and 5).
As you can find out during your experiments, double streaks do not appear
in this case. This is a natural result, because the Gaussian curve is
quite smooth. It is similar to circles of confusion of Type C.
Conclusion
#4: This experiment proves that lenses with the circles of confusion
of Type C are very unlikely to cause splitting if twigs in a picture.
Additional
Experiment #4
We
saw that blurring may produce additional lines in a picture. Strangely
enough, sometimes blurring can also decrease the number of lines in an
image. Our next experiment will demonstrate this effect.
Figure
6
Let
us apply the Motion Blur filter to the target shown at the top of
Figure 6 (Angle = 0).
When
Distance = 23, strange changes happen to our image. Now
we can see only four dark strips instead of five. One strip has
disappeared!
Moreover,
the black and white strips have switched places. Now the four dark
strips are located where we could see white gaps in the initial
picture.
If we increase Distance again (i.e. make the image more blurry),
we will see that the number of strips continues decreasing. When
Distance = 39, only three dark strips are left (see Figure 6).
This
phenomenon can be obtained in actual photography as well. Please read
Chapter 6 in [3] to learn the details.
Mathematical
models of bokeh
(brief notes for those who likes physics and mathematics)
This
section deals with some general ideas related to the strict mathematical
description of bokeh. If you consider math to be boring, simply skip this
part of the article or read it selectively.
If
we want to see how a blurry image looks like at a certain distance from
the focusing point, we have to substitute its elementary points with their
respective circles of confusion. In mathematics this operation is known
as convolution:
In
this formula g(x,y) stands for the object, h(x,y) is a function that
describes how brightness changes within the circle of confusion, f(x,y) is
the resulting image.
It
may be quite difficult to make exact calculations based on this formula.
In many cases computer simulations give quicker and more convincing results.
The simplest approach is to use the Customs Filter from Photoshop (Filter
-> Other -> Custom). It provides the 5 x 5 matrix to describe circles
of confusion. A slightly bigger matrix (7 x 7) can be found in the . The
results of computer simulations carried out with the help of this filter
are shown in Figure 7.
Figure 7
The
initial target (the leftmost frame) consisted of two wedges, one of which
is surrounded by the white contour. On the black strip you can see various
types of the circles of confusion used during experiments. If you want
to see the details please download the picture to your favorite image
processing program and analyze it at a convenient magnification.
Here
again we see that the A(4) shape, which is very close to the circle, is
the best performer among peers of the A group. It produces the minimal
splitting of the thin lines. The B shape gives the worst picture with
distinct double-line streaks. The C disc is the absolute winner, since
it blurs the lines smoothly without any trace of doubling.
The
wedge with the white contour tends to split to a greater extent, other
things being equal. This result is easy to predict, if we recall that
convolution is a commutative operation.
g *
h = h * g.
Conclusions
1.
The appearance of blurred images in the out-of-focus area depends on
many factors, the most important of which are:
—
properties of the lens,
— properties of the object,
— qualities of additional optical accessories,
— peculiarities of human visual perception.
As
appears form the above, even a very expensive high-quality lens may
produce a bad-looking images in the out-of-focus area.
2.
To be sharp and to produce a good-looking bokeh, lenses should render
bright points as evenly painted circles. If blurry points are shown
as doughnuts or any other shapes with distinct contours, bokeh is very
unlikely to be pleasant.
3.
If a lens renders bright points as shapes within which brightness changes
very smoothly, such a lens will also produce a good bokeh. However,
such lenses tend to be quite soft. Special soft lenses practically never
produce double-line streaks in pictures.
Recommendations
1.
Learn the properties of the lenses you use! It is very useful to know
how your lenses show blurry bright points in a picture.
2.
The shape of the lens opening should be as close to the circle as possible.
3.
Never use cheap filters and other optical accessories of low quality.
Various defects in manufacturing may give rise to additional spots of
light and bright contours that surround objects in your pictures. As
a result bokeh may be spoiled.
4.
Sometimes unpleasant bokeh can also be attributed to misalignment of
optical elements in a budget lens. Although this important phenomenon
was not described in this article, you should be aware of it. If a lens
is stopped down, the harmful effects of misalignment diminish.
5.
If double-line streaks are predictable and unavoidable, only one thing
can be done. You should change the f-stop. In other words, you should
try to make split twigs either sharp or completely unsharp.
Links
1.
I. Yefremov. Blurring the background. A scientific
approach. (Yet another my article on this web site)
2. H. Merklinger. A Technical View of Bokeh. Published
in Photo Techniques Magazine, May/June 1997. (This article
can be found at or downloaded as a pdf-file from )
3. H. Merklinger. The INs and OUTs of Focus. Chapter 6. (The
book can be dowloaded from )
4.
5.
6.
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