Axiconlens

In this image of a downtown San Francisco street, the four story buildings to the left and the right look larger than the 48 story Transamerica Pyramid (the long building in the distance), when in fact they are much smaller if you were to put them side by side. Because I used a wide angle lens, I was able to show the front buildings much bigger than they really are.

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However, this is a perfectly natural perspective with no distortion, because your eyes would see this exactly the same way. Lens manufacturers offer “perspective control” or “tilt-shift” lenses to deal with this particular situation, but the result actually turns out unnatural, since that’s not how it looks in real life when we look up. Take a look at the below examples of before (left) and after (right) perspective control change:

It is important to note that most zoom lenses that go from wide angle to standard or telephoto focal lengths typically suffer from barrel distortion at the shortest focal lengths, which gradually transitions to pincushion distortion towards the longest end. A good example of such behavior is the Nikon 18-300mm VR, which starts out with strong barrel distortion at 18mm, then quickly switches to pincushion distortion at 28mm and stays that way till 300mm.

I have a 70 yr. old family photo with 7 subjects. The parents are in the back of basically two rows on the right and left. It appears that the photographer was slightly to the right of the center of the group. The male parent on the right side appears to be much taller than the female parent on the left, which was not the case in real life! It also looks as if those on the right side of the photo appear taller than they really were in comparison to the rest of the subjects. Is this some sort of camera or perspective distortion? Or just uneven ground.? It is an outdoor photo.

The car looks completely distorted, because I stood very close to it and photographed it with a wide-angle lens (Nikon 14-24mm). Note that the left part of the car looks disproportionately big – even the left light looks about 50% bigger than the one on the right, although you know that they are both the same in size. The car is occupying the majority of the frame and everything in the background looks relatively small. If I used a normal lens and stood in the same spot, I would have ended up with only a part of the car filling the whole frame. Yet, if I were to crop both images for the same field of view by heavily cropping the wide angle shot, the perspective distortion effect would be the same on both.

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Take the last image (of two men blowing up balloons) as an example. If you enlarge that image sufficiently to enable you to view it from close enough, then you will see it with no distortion at all. It will look perfectly normal. It should be viewed from the “centre of perspective” or “centre of projection” to see it without any distortion. If you view it from further away, then the image shows wide-angle distortion (because the viewer’s angle of view is less than the camera’s angle of view). If you view it from closer than the centre of perspective, then the image shows perspective compression (because the viewer’s angle of view is greater than the camera’s angle of view).

thank you for organizing concepts nicely in this article. it was very helpful. ironically, it also enabled me to articulate my disagreement in an intelligible way. I think perspective distortion is not always same for every lens or circumstances. the difference is very visible when you use expensive camera system like leica, naked eye, or a cheap small phone camera lens. Can you make a follow up article about how perspectice distortion can be different depending on certain circumstances?

Such “perfect” lenses are very rare, since most lenses suffer from at least one kind of distortion defined below. Very good lenses have lens elements that significantly reduce distortion, where it is not noticeable to our eyes. Many zoom lenses, especially superzooms like Nikon 18-200mm VR suffer from multiple types of distortion such as barrel and pincushion at different focal lengths.

Another application is the generation of Bessel beams, which length and width can be influenced by the input beam diameter (Fig. 6). To adjust the length and width of the Bessel beam different Beam Expanders can be combined with the axicon.

This is the reason why mustache distortion is often referred to as “complex” distortion, because its characteristics are indeed complex and can be quite painful to deal with. While this type of distortion can be potentially fixed, it often requires specialized software. You cannot just use the built-in tools in Lightroom and Photoshop, unless a specific lens profile is already built to combat such distortion. If you attempt to deal with such distortion as barrel-type, you will end up curving the extreme corners a lot more. And if you attempt to compensate for pincushion distortion, you will end up curving it for even stronger barrel distortion towards the center.

An optical design with a combination of two axicons a perfect collimated ring-shaped beam can be generated. In practical use it is quite challenging to build this constellation. First of all, both axicons need to have a maximum axicon angle deviation within 0.05°. Another point is the alignment of both lenses with a minimum tilt and decentration of both elements. Even small a tilt deviation (> 1 “) will lead to significant distortion of the ring shape.

„Beam shaping concepts with aspheric surfaces“ von U. Fuchs, D. Braun und S. Wickenhagen. Erschienen in Proc. SPIE 9581, Laser Beam Shaping XVI, doi:10.1117/12.2186524, September 2015

A detailed description of the functionality and the specifics of axicons can be found in our whitepaper, which is available for download here.

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Axicons are conical lenses which create a ring-shaped beam used in research or rather different laser applications. They can be either convex or concave and made from almost any optical material. By combining two or more axicons and lenses multiple intensity profiles can be created.

In photography, distortion is generally referred to an optical aberration that deforms and bends physically straight lines and makes them appear curvy in images, which is why such distortion is also commonly referred to as “curvilinear” (more on this below). Optical distortion occurs as a result of optical design, when special lens elements are used to reduce spherical and other aberrations. In short, optical distortion is a lens error.

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This is the part that seems to confuse a lot of photographers – the relationship (or lack thereof) of focal length to perspective distortion. You might hear some photographers say that one should use longer focal lengths to photograph people, or they will get distorted due to the lens’ short focal length. This is a mostly false statement, because lenses have no perspective. Other than fisheye lenses, all lenses have the same perspective – it is the camera to subject distance that determines perspective, not the focal length. There is an illusion of different perspective of lenses, because with long focal lengths you have to stand further away from the subject to frame them the same way. If you were to stand at the same distance, the subject would appear exactly the same! So if you take a 50mm lens and an 85mm lens, there is no difference in perspective between the two, as long as you stand in the same spot and keep the subject to camera distance the same. Yes, the subject would certainly appear smaller with the 50mm lens due to shorter focal length / wider field of view, but the perspective and proportions would be the same on both. So the point of longer focal length lenses in such cases, is the possibility to enlarge the subject in the frame, while keeping normal perspective. Telephoto lenses do not magically fix perspective distortion – they force you to move back from the subject, which is what changes the perspective.

Barrel distortion is typically present on most wide angle prime lenses and many zoom lenses with relatively short focal lengths. The amount of distortion can vary, depending on camera to subject distance. Even standard 50mm prime lenses can potentially yield barrel distortion at close distances. Barrel distortion can be decreased significantly by using compensating optical elements, but completely eliminating such distortion is nearly impossible. Some lenses like Nikon 14-24mm f/2.8G have a number of such distortion compensating elements, which heavily increase both the weight and the size of the lens. This is why wide-angle lenses are typically bigger and heavier than standard / normal lenses.

Pincushion distortion is the exact opposite of barrel distortion – straight lines are curved outwards from the center. This type of distortion is commonly seen on telephoto lenses, and it occurs due to image magnification increasing towards the edges of the frame from the optical axis. This time, the field of view is smaller than the size of the image sensor and it thus needs to be “stretched” to fit. As a result, straight lines appear to be pulled upwards in the corners, as seen below:

Note how the balloons in the center of the frame appear natural, while the heads of the groom and the best man look egg-shaped. This is a direct result of using an ultra-wide angle lens at a very close distance and badly placing the subjects. If both sat back to back and inflated balloons in the opposite directions, their heads would have looked pretty normal being in the center, while the balloons would have been egg-shaped.

Here are a couple of more examples of converging lines, where one part of the image appears much larger than the other simply because it is closer:

To generate a collimated ring-shaped beam, to axicons are combined. By varying the distance between both, the ring diameter can be adjusted (Fig. 3). Axicons can also be used in laser eye surgery. Their ability to focus a laser beam into a ring (Fig. 4) is useful in surgery for smoothing and ablating corneal tissue.

The Manual of Photography by Jacobson et al. explains this in Chapter 4 on the geometry of image formation. The last section of that chapter is on perspective.

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If you are interested in reading more, below is the list of articles on other types of aberrations and issues that we have previously published on Photography Life:

Furthermore, axicons are also used in optical trapping. The ring of light (Fig. 5) creates attractive and repulsive forces, which can trap and hold micro particles and cells in the center of the ring.

For example, if you photograph a person with an ultra wide angle lens up close, their nose, eyes and lips can appear unrealistically large, while their ears can look extremely small or even completely disappear from the image. Take a look at the following photos of a subject captured with a wide-angle lens at very close distances:

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Some lenses are optically designed to be “rectilinear” (like the Nikon 14mm f/2.8D and the Canon EF 14mm f/2.8L II USM), where they yield straight lines without bending them (resembling human vision), while other lenses like “fisheye” lenses are designed to be “curvilinear”. Rectilinear lenses generally stretch objects to make them appear straight, especially towards the edges of the frame. Curvilinear lenses, on the other hand, do not stretch anything, but they heavily distort images by curving straight lines (like in door peepholes). Take a look at the following image samples that show both rectilinear and curvilinear lens effects:

Perspective distortion occurs when the photograph is viewed with an angle of view that differs from the angle of view captured by the camera.

Pincushion distortion is also a very common aberration, especially on zoom lenses. Expensive super telephoto prime lenses have compensating elements that can significantly reduce pincushion distortion to negligible levels, but most consumer and even pro-level zoom lenses like Nikon 80-400mm VR suffer from pincushion distortion. In fact, pincushion distortion can be very heavy on consumer-grade lenses, something that you will quickly notice in images.

Fixing barrel distortion is usually a pretty straightforward process. Post-processing software such as Lightroom and Photoshop, as well as many other third party tools, can easily fix barrel distortion issues, as long as the lens has a supporting profile in the database. Since every lens is different, such lens profile data must be carefully tested in a lab environment and created. I wrote a detailed article that outlines this process in my Lightroom Lens Corrections article.

A number of older lenses, as well as some modern lenses have mustache distortion. A good example of this is the Nikon 18-35mm f/3.5-4.5D lens, which shows a rather nasty case of a mustache distortion.

A special application is the generation of (non-diffractive) Bessel beams, which are mainly defined by the cone angle (α) of the axicon. Accordingly, for a lot of applications there are two regions of interest:

Spherical aberration is one of the basic imperfections of a spherical lens. It means, that parallel rays of the incoming beam do not find the same focal point after passing a spherical lens. The use of axicons also provide relief here. By modifying the incoming beam to a ring (Fig. 7) the focus of a spherical lens can be improved. This phenomenon can be explained by zonal decomposition of the spherical surface. Illuminating just one ring-shaped zone, the effect of spherical aberration can be avoided. Changing the distance between the axicons, it is possible, to vary the ring-shaped zones and subsequently, to shift the generated spot along the optical axis. Using the same setup to illuminate an aspheric lens will allow focussing below the diffraction limit (Fig. 8).

Look at the size of his head on the left photograph – it appears disproportionately large relative to his body. His eyes, nose and lips are very much enlarged, while his ears are dwarfed.

The image on the left is how you would see it with your eyes if you stood there, while the image on the right is what a perspective control / tilt-shift lens would do to the image, after it is aligned to the building.

Thank you for the article. It was very interesting. I read an article about front mobile phone cameras that they can distort faces up to 30% and the reason was perspective distortion. They suggested to used longer focal length would correct this and gives a realistic shot. Front camera’s have focal length of around 25mm. Human eyes have a focal length of 17mm. If their argument is true, they mean that human eye doesn’t see objects as they are? Or in other words, if you want to take a picture of an object from 30cm, and you want it to appear as human eye can see it, you can to take a picture of the item with focal length of 17mm, standing 30mm from the object?

Just like barrel distortion, pincushion distortion can also be easily fixed in post-processing software like Lightroom and Photoshop. Lens profiles built into Lightroom and Camera RAW have the capability to completely eliminate it with a single click.

As you can see, the fence on the curvilinear lens sample appears unnaturally curved – that’s because I photographed it using a fisheye (curvilinear) lens. The image on the right is what you would see from a rectilinear lens – the fence looks straight and natural, just like you would see it with your eyes. The size of the fence appearing large in the front of the frame and getting smaller at longer distances is perspective distortion (see below), which has nothing to do with optical distortion.

The nastiest of the radial distortion types is mustache distortion, which I sometimes call “wavy” distortion. It is basically a combination of the barrel distortion and pincushion distortion. Straight lines appear curved inwards towards the center of the frame, then curve outwards at the extreme corners, as shown below:

So far we have been only talking about optical distortions. Another distortion type that is often seen in images is perspective distortion. Unlike optical distortion, it has nothing to do with lens optics and thus, it is not a lens error. When projecting three dimensional space into a two dimensional image, if the subject is too close to the camera, it can appear disproportionately large or distorted when compared to the objects in the background. This is a very normal occurrence and something you can easily see with your own eyes. If you take a smaller object like your mobile phone, then bring it very close to your eyes, it will appear large relative to say your big screen TV in the background (and the farther your phone is from your TV, the smaller the TV will appear relative to your phone). The same thing can happen when photographing any subject, including people.

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That was really educational. I knew something wrong was happening when objects were too close to the lens. Specially in selfies. But thought it a problem with lenses. Now I know how to explain this phenomena.

Lastly, there is also the case of converging lines. When the camera sensor is not perfectly parallel to the photographed object such as a building, it produces an image that at first might seem unnatural, due to its “leaning” effect, as shown below:

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There are three known types of optical distortion – barrel, pincushion and mustache / moustache (also known as wavy and complex). Let’s examine each in more detail, but before we do that, let’s take a look at a lens with zero distortion:

The length (a) depends on the axicon angle (α) and the diameter (ØEP)of the incoming beam, whereas the width of the Bessel beam is regulated by the angle only (Fig. 2). Fig. 1 shows the diameter of the ring-shaped light distribution (d) which depends on the distance (l) and increases with growing distances (l). Thus, the ring width is about half the diameter of the incoming beam

When straight lines are curved inwards in a shape of a barrel, this type of aberration is called “barrel distortion”. Commonly seen on wide angle lenses, barrel distortion happens because the field of view of the lens is much wider than the size of the image sensor and hence it needs to be “squeezed” to fit. As a result, straight lines are visibly curved inwards, especially towards the extreme edges of the frame. Here is an example of strong barrel distortion:

I hope this article clarifies differences between the different types of distortions. If you have any questions or comments, please let me know in the comments section below!

Hello, Thanks very much for this information. I found your article about lens distortion really useful, in particular your article about Lightroom lens correction. I have used Lightroom for some years, but had not discovered the lens correction feature. I feel like I have just found gold!! Thank you. All the best, Ojārs

I know this an old post and you probably have moved on. But I was browsing looking for a way to explain what I call closeup distortion when I came across this article. The author in my opinion does a great job explaining the effects and differences in perspective and distortion. I wish the author offered ways to prevent perspective distortion especially for closeup images which occurs more often these days because of cell phone photography. That said, maybe proportional distortion would be to your liking?

How do I correct for perspective distortion in real time and after the fact using software such as Lightroom or Photoshop?

We will cover three different types of optical distortion, then discuss rectilinear vs curvilinear nature of wide-angle lenses. We will wrap it up by showing what perspective distortion does to images, as shown in the table of contents below.

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I don’t know why you would call perspective a distortion and I don’t know how you say the car looks distorted. It look like a close perspective, which it is. Of course we lose the depth of focus and parallax that go with this effect in the real world and help cue our brains in to what’s going on, but the proportions are real, not distorted.

Using mounted axicons is one possibility to avoid this effect. asphericon developed special mountings with an outer diameter of 30 mm, which can easily be integrated into existing optical systems via adapters. The axicons are perfectly aligned to the optical and mechanical axis and provide comfortable solutions for laser applications. Find out more about mounted optics and adapters in our webshop.

Note that the lines appear straight at the very center of the frame and only start bending away from the center. That’s because the image is the same in the optical axis (i.e. the center of the lens), but its magnification decreases towards the corners.

The above examples of perspective distortion are known as “wide-angle”, or “extension” distortion. There is another kind of perspective distortion, which is the opposite of wide-angle distortion – it is called “telephoto” or “compression” distortion. Compression distortion is only possible with telephoto lenses, because it requires the photographer to stay at a long distance relative to the subject, which essentially makes very distant objects appear larger than they are when compared to “normal” perspective.

In photography, there are two types of distortions: optical and perspective. Both result in some kind of deformation of images – some lightly and others very noticeably. While optical distortion is caused by the optical design of lenses (and is therefore often called “lens distortion”), perspective distortion is caused by the position of the camera relative to the subject or by the position of the subject within the image frame. And it is certainly important to distinguish between these types of distortions and identify them, since you will see them all quite a bit in photography. The goal of this article is to explain each distortion type in detail, with illustrations and image samples.

Axicons are used in research and multiple laser applications which need a ring-shaped intensity profile. They are mainly used in the following areas:

Nasim Mansurov is the author and founder of Photography Life, based out of Denver, Colorado. He is recognized as one of the leading educators in the photography industry, conducting workshops, producing educational videos and frequently writing content for Photography Life. You can follow him on Instagram and Facebook. Read more about Nasim here.