Distortion : A Guide for Photographers


This is a series of articles that conceptually explain aberration, which is an index of lens performance.

Of all the aberrations, this section introduces "distortion aberration" in a simple and easy-to-understand manner using figures and simulations.

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Introduction to Lens Design

Aberrations and Distortions

First, aberration is an index that shows the deviation from the ideal imaging relationship.

The camera lens is designed to focus the light emitted from the "subject" precisely on the imaging surface (film or CMOS).

However, it is difficult to focus light accurately, and the small amount of deviation is called "aberration".

These aberrations are classified and named according to their characteristics.

This article explains "distortion aberration."

The spherical aberration and axial chromatic aberration explained in the past are the aberrations that show the performance of the center of the photo, but the distortion is the aberration of the peripheral part of the photo.

By the way, isn't distortion the only aberration whose image can be understood from its name?

In this section, I would like to explain perspective, which is easily confused with distortion, so that we can understand it as a simple concept as possible.

Let's imagine

When you visit a famous castle, there is an extremely beautiful stone wall and you try to photograph it.

For example, this is a stone wall.

Stones cut out at right angles are lined up without a break.

If there was such a beautiful stone wall, I would shoot it.

But when I looked at the picture, it looked like this with some lenses.

It is photographed as if the peripheral part is shrunk.

Also, other lenses show different images.

This time, the peripheral part appears to be stretched.

Such distortion is called "distortion aberration".

barrel shaped or spool shaped

The two forms of distortion that I mentioned earlier are named.

The shape in which the periphery shrinks relative to the center is called barrel shaped.

On the other hand

The shape of the extended perimeter is called spool shaped.

barrel shape is an aberration often seen in wide-angle lenses, and spool shaped is likely to occur in telephoto lenses, but barrel shape is often seen.

Start with one lens

I will explain how the distortion looks in the optical path diagram that appears in the lens analysis article of this blog using a simulation.

The above example of "copying a stone wall" is shown as an optical path diagram below.

This time, we have prepared a wide-angle lens with a focal length of 28 mm Fno2.8 that consists of only one lens.

Since there is only one sheet, the aberration is large and the optical path is difficult to understand. Therefore, rays passing through the aperture center in each ray bundle are drawn.

It became clear and easy to see.

The distortion has already occurred in this state, and we can see the effect.

If you look closely at the optical path diagram, the light does not hit the high position of the image pickup device (the position corresponding to the corner of the screen).

This indicates that the light rays are shrinking toward the center of the screen due to distortion.

Then, let's display "ray path without distortion" and "with distortion" again.

The gray line is the ray path without aberration, and the red line is the ray path with aberration taken into account.

You can see that the red rays are all centered on the screen.

Conceptual diagram of Distortion Aberration

The diagram below illustrates the concept of an aberration diagram by adding auxiliary lines.

In this case, the true path (red line), which accounts for aberrations, is closer to the center of the screen than the gray line, which ignores aberrations.

When this is expressed as an aberration diagram, it becomes a shape that falls to the minus side, which suggests that it appears as a "barrel shape shape".

Conversely, if the graph falls to the positive side, this indicates a "spool shaped".

Represented by an Aberration Diagram

Now, let's try to express it with the aberration diagram introduced in the usual analysis article.

In the usual lens analysis article, "spherical aberration", "field curvature", and "distortion" are listed in order from the left.

In addition, the horizontal axis scale of the spherical aberrations and field curvature in the longitudinal aberration diagram in the usual lens analysis article is ± 0.5 mm, but the aberration amount of this single lens is too large, so the horizontal axis scale is ± 10 mm. Please note that it is 20 times the normal value.

The distortion scale is ± 5%, the same as in the usual analysis article.

So I'm going to talk about this. If you look at the distortion diagram, it's over 5% at the top of the graph, and it appears to be about 8%.

Generally, a cheap zoom lens has distortion of about 5% at the wide-angle end, but the value of 8% is so large that we hardly see it.

Single-Focus lenses, even those that are reasonably priced, are typically as low as 3%.

Do you understand that the distortion is large with only one lens?


Perspective is often confused with distortion.

For example, you may have heard the expression, "A wide-angle lens is hard to parse".

In short, perspective is the phenomenon of "distant objects looking small."

Many people misunderstand this as distortion caused by the lens.

Let's take a quick look at the perspective.

Imagine taking a picture as if you were looking up at the base of a building.

(This is our dream building, isn't it?)

The actual picture will look like this.

If you take a picture from the base, the top side of the building looks like it has shrunk.

This is due to the "distant objects look smaller" perspective and has nothing to do with lens aberrations.

The wider the lens, the stronger the effect.

At this time, correction of distortion aberration is more difficult with wide-angle lenses, so distortion aberration and perspective are often confused.

A typical example of frequent confusion is when shooting a person with a wide-angle lens, strange feelings such as "arms and legs are stretched" or "the face is shot small" often appear, and this is sometimes mistaken for distortion.

It depends partly on the shooting conditions, so it's not possible to separate completely, but most of the time I feel strange due to perspective.

Because a wide-angle lens shows a range far beyond the human eye, the perspective is more exaggerated.

For this reason, objects that are farther away than the sense of the human eye appear much smaller, which causes discomfort such as "hands and feet are too long."

However, it's also one of the ways to enjoy wide-angle lenses, so there's no need to explain how to use them.

Digital distortion correction

Since distortion can be viewed as a geometric phenomenon on a two dimensional plane, it is easy to correct it digitally.

If digital processing is expressed as an image, for example, if there is an aberration of barrel shape, it can be restored by processing to stretch the peripheral part.

Among recent interchangeable lenses, there are more and more lenses which are based on distortion correction by digital processing.

Correct for the Distortion Aberration

Up until a while ago, I explained with one lens, but in reality, if it is such a wide angle and Fno bright lens, it consists of many lenses.

Let's look at the characteristics of the lens corrected for distortion.

Earlier, I introduced the aberration of 28 mm F2.8 lens composed of only one lens.

The graph below shows the distortion of a standard retro-type 6-piece wide-angle lens on the graph scale of distortion.

Optical Path Diagram

This optical path diagram shows the NIKON NIKKOR 28 mm F2.8D, which we have analyzed in the past. This retro-type wide-angle lens has a nostalgic look.

Aspherical lenses that are effective in correcting distortion are not used.

Longitudinal Aberration

Graphs of spherical aberration, field curvature, and distortion

According to the horizontal axis scale of the first single-component lens, the graphs of spherical aberrations and field curvature are made at 20 times the normal size.

The distortion scale is ± 5%, the same as normal.

The number of lens components is small, and the lens composition is very modest and neat, but the distortion is corrected to about 3% at the maximum.

In the film age when there was no digital processing, it was common for a wide-angle lens to have such a small amount of distortion remaining in the barrel shape. Therefore, I think that a wide-angle lens with such a small amount of distortion remaining would be preferable because it would look like a wide-angle lens and it would be tasteful.

The recent high picture quality using digital processing is impressive at first, but you will get tired of it soon.

Now, if you want to see it at its usual graph scale, check out the original article.

Nikon NIKKOR 28 mm F2.8D


In a few words, "distortion" refers to the distortion of the peripheral part of the screen as if it were expanded or contracted.

I am sure that you can enjoy our blog 20 times by understanding the distortion aberration.

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Modern Optical Engineering: The Design of Optical Systems