NIKKOR - The Thousand and One Nights No.53

The Profound World of the Fisheye Lens

Ai AF Fisheye-Nikkor 16mm f/2.8D

Tale 53 is about a fisheye lens. Just what sort of lens is a full-frame fisheye lens? What was the world's first fisheye lens to incorporate a close-range correction mechanism? How did the lens perform?

Tale 53 brings to light the secrets of the Ai AF Fisheye-Nikkor 16mm f/2.8D.

by Haruo Sato

I. Who came up with the name, "fisheye lens"?

As the history of fisheye lens development by Nippon Kogaku K. K. (now Nikon) is detailed in Tale 6, I will not cover it here. Rather, with tonight's tale, I would like to consider the person responsible for the naming of "fisheye lenses".

In his paper, "Fish-eye views, and vision under water" (Phil. Mag. S. 6, vol. 12, no. 68, pp. 159-162, 1906), R.W. Wood reported that he took a whole-sky photo with a 180° angle of view using a camera with which the space between the pinhole and the dry plate had been filled with water. The paper described the effect achieved as the way a fish would see the external world from the water. This was the first appearance of the word "fish-eye". Therefore, it can be said that this is also the origin of the name, "fisheye lens". Since then, optical manufacturers have pursued the scientific meaning and technical possibilities of fisheye lenses. The pioneer in the field was Robin Hill, working at the R & J Beck company of London.

Hill called this type of lens a whole-sky lens, and is known as the father of whole-sky cameras. However, the name is mysterious. Why was "fish-eye" not used? For a time, "whole-sky camera" and "whole-sky lens" were the names commonly used in the industry. So what was the first lens to be named a "fisheye lens"? After looking into the matter fully, it seems likely that the name originated with Nikkor lenses manufactured by Nippon Kogaku K. K. (now Nikon). It seems that the term "fisheye lens" has been used by Nippon Kogaku K. K. (now Nikon) since before WWII. "Fisheye lens" is noted on design blueprints produced in 1938. In addition, "FISH-EYE NIKKOR" is stamped on a whole-sky camera lens released in 1958. Based on these records, it seems highly likely that the name "fisheye lens", which is now recognized around the world, originated in Japan.

II. Circular fisheye and full-frame fisheye

Fisheye lenses are generally divided into two types: circular fisheye and full-frame fisheye. Originally created for scientific purposes, fisheye lenses only later became used in the field of artistic photography. Circular fisheye lenses project a circular image of a 180° (or greater) angle of view on the imaging surface. They were primarily used for scientific applications such as meteorological observation, and recording of stars and aurora. They were also used to check the field of view from the driver's seat of automobiles, and played a role in the development of side mirrors that compensate for, or eliminate, the vehicle's blind spot. Photographers gradually began using fisheye lenses because the distortion produced by them is unique.

However, as the images produced were always round, handling them was difficult.

This resulted in the full-frame fisheye lens, which was developed with less emphasis on scientific applications and more on photographic applications. The Fish-eye-Takumar 18mm f/11, released by Asahi Optical Co., Ltd. in 1963, was the first full-frame fisheye lens. The release of this lens led other manufacturers to also develop and release full-frame fisheye lenses. Fully prepared, Nikon, which came to offer the most fisheye lenses, finally released the full-frame fisheye Fisheye-Nikkor 16mm f/3.5. Nikon's history with full-frame fisheye lenses then continues to the AF Fisheye-Nikkor 16mm f/2.8D.

III. Development history and the designer

Now let's track the history of development.

Not to brag, but I designed the Ai AF Fisheye-Nikkor 16mm f/2.8D when I was just 28 years old. At that time, I became interested in the depth of fisheye lenses, and was put in charge of development of the lens with the switch to AF.

Design and development began 23 years ago, and the design was completed in the early summer of 1991. Trial production began in 1992, and mass production began in the summer of 1993 after successful mass production trials. The lens was finally released in November of the same year. As of 2014, this lens has continuously sold well for 21 years.

IV. Rendering performance and lens performance

Lens cross-section

First, let's take a look at a cross-section of the lens. Just as with other fisheye lenses, this lens has a typical retrofocus structure. It differs from common wide- and ultra wide-angle lenses in that it is structured not to suppress generation of negative distortion, but rather to generate excessive distortion. Ensuring good compensation for distortion is always a burden when designing wide-angle lenses.

In the age of rangefinder cameras, the refractive power arrangement of lenses utilized a "symmetrical lens" structure that was nearly symmetrical. This symmetrical lens structure provides better compensation for distortion and curvature of field than does the retrofocus structure. However, if we consider the common projection formula (y=f·tan θ) with fisheye lenses, excessive negative distortion is generated. Therefore, it can be said that the retrofocus structure is the optimal structure for fisheye lenses.

Now let's look at the unique characteristics of this lens in terms of design. First, I think you'll notice that the structure of the entire optical system is incredibly simple. The first and second lens elements are concave to generate excessive negative distortion. This structure offers strong negative refractive power, while the use of only concave lens elements and adoption of the optimal meniscus shape ensures the proper passage of light through the lens and suppresses aberration generation. The doublet behind these provides compensation for spherical aberration, coma, and chromatic aberration. The aperture is inserted, and the structure of the rear group is also simple. With two sets of doublets, aberrations generated both on- and off-axis are suppressed for consistent rendering performance to the edges of the frame.

It should be noted that this was the world's first fisheye lens for which the close-range correction system ("floating element" design) was adopted. We'll go into the reasons the close-range correction system had not been considered with previous fisheye lenses later. The result, however, was a consistently high level of sharpness in images captured at shooting distances of infinity to extremely close up.

So, how does the AF Fisheye-Nikkor 16mm f/2.8D perform? Let's look at the lens's aberration characteristics, MTF curve, and spot diagrams.

The aberration characteristics of this lens are unique. There is very little spherical aberration, and curvature of field is exceptionally flat.

In addition, MTF evaluation shows that the lens reproduces excellent contrast all the way to the edges of the frame at both 10 and 30 lines/mm. Further, adoption of the close-range correction mechanism ("floating element" design) also preserved excellent performance in terms of image quality with shooting at distances from infinity to extremely close up.

Next, let's look at point image formation with spot diagrams.

Point image formation is good at the center of the frame and little flare is visible. However, points closer to frame peripheries tend to exhibit slight flare in the sagittal direction. Though the amount of flare is low for a fisheye lens, I think that better results would be achieved with astrophotography by stopping down the aperture one or two stops.

V. Considering the relationship between the object plane and the image plane

What is the best way to consider a fisheye lens's object plane? At 28 years old, this was a huge question for me. This fundamental theme was a vital to achieving superior image quality. With a fisheye lens, it is good to consider the object plane as a sphere with a dome-like surface with which a photographic subject at infinity spreads over the sky. However, as the entire frame is in focus at infinity, it is okay to consider that light pours through the lens from the flat photographic subject at infinity. When the subject is at infinity, there is little need to concern yourself with the shape of the object plane. What happens, though, when the shooting distance decreases from infinity to a finite distance? What happens at close distances?

Considering this, as well as the way in which the relationship between the object and image planes is defined, is extremely important. This is because image quality varies depending upon the way in which the relationship between the object plane and the image plane is defined. With common narrow angle lenses, the relationship between the object plane and the image plane is considered as a flat plane to a flat plane. However, with fisheye lenses that have an angle of view of 180° or more, considering the object plane as a flat plane theoretically leads to problems. For example, when a subject is three meters away, the distance to that subject is three meters when it is positioned at the center of the frame. But where is the subject for light from the 180° angle of view? The answer is infinity.

This makes it impossible to consider this the object plane. Further, the issue becomes even more complicated when the angle of view exceeds 180°. At that time, we considered this from a number of viewpoints. After analyzing the issue, we reached two hypotheses. The first was the view that photographic subjects at close distances have the same dome-shaped spherical plane as those at infinity. Imagine a large dome gradually coming closer. Considered in this way, the solution is simple with peripheral light formed at the same distance as that at the center of the frame. The second hypothesis also defined the relationship between object images as a flat plane to a flat plane with portions exceeding the 180° angle of view as a singular point.

With the first hypothesis, where the subject is a dome-shaped object plane, a solution in terms of aberration is easily deduced with a normal focusing system. However, does this really make for a fisheye lens with good rendering? As a photographic lens, shouldn't it be based on a flat object? No matter how much I considered this question at the time, I could not reach a clear decision about which was correct. I asked my boss, Mr. Aono, to investigate with trial production of both types. This was the beginning of development of a fisheye lens with which performance at close distances was emphasized more than with any previous lens.

First, a fisheye lens that performed very well at infinity was designed. Then we came up with the new close-range correction system ("floating element" design) that supported consideration of the relationship between object images as a flat plane to a flat plane. We then evaluated two solutions, the design solution and the solution that ensured curvature of field with the dome-shaped photographic subject, with trial production of both. With this trial production, we considered a design that thoroughly eliminated differences other than the close-range correction mechanism. We used these two trial products in tests and to take pictures, that were then analyzed. The pictures taken with those trials remain. Let's take a look at them.

Images A and B are photos of the right half of a flat resolution chart captured at a distance of 0.3 m. Portions at center left in each represent the center of the lens. The right corners represent the maximum angle of view. Image A was captured with the trial product equipped with the close-range correction mechanism.

Image B was captured with the trial product not equipped with the close-range correction mechanism, and offering flatter curvature of field. Which image do you think is better? The difference was clear. Consideration of flat plane to flat plane wins.

It was at that moment that a fisheye lens with which emphasis was placed on performance at close distances was born.

VI. Actual performance with sample images

Next let's look at some actual results. Details regarding performance at various aperture settings are noted.

f/2.8 (maximum aperture)

While resolution is relatively good at the center of the frame, sharpness gradually drops as image height increases. However, even at the extreme edges of the frame, image quality appears sufficient for practical use. In addition, colors are sharp with little bleed.

f/4 to f/5.6

When the aperture is stopped down to f/4-5.6, sharpness increases from the center of the frame to the edges. With the exception of extreme edges, a satisfactory level of sharpness is achieved throughout the frame.

f/8 to f/11

Resolution at the edges of the frame is increased. A satisfactory level of sharpness is achieved throughout nearly the entire frame. This range of aperture settings seems best for regular use.

f/16 to f/22

Consistent rendering is achieved throughout the entire frame, but the effects of diffraction cause resolution to appear somewhat reduced.

If sharpness is the goal, better results would likely be achieved at an aperture setting of f/8 to f/11.

If slightly softer rendering is desired at the frame peripheries, users should probably try an aperture setting of f/2.8 to f/4.

Let's confirm these rendering characteristics with sample photos.

Sample 1 is a photo of the dome at Tokyo Station. Please note that as this image was captured at a high sensitivity setting, it does contain some of the noise common with such settings. However, I think you can see just how pleasing sharpness and color reproduction are. In addition, the image is also pleasing in that it exhibits no noticeable color shift. Sample 2 is a snapshot of a city street. Though focus was acquired on a relatively close subject, you can see how the image exhibits sufficient sharpness from close distances to far. Sample 3 is a photo of the Tokyo Metropolitan Government buildings. It is structured so that portions at the center of the frame are more distant than those at the edges. The image clearly exhibits no degradation in sharpness. Sample 4 is a photo that is fully backlit. The sun is positioned just outside of the frame at the top of the image. Normally, these are conditions in which ghost and flare are common, but the image exhibits no noticeable ghost at all. When fisheye lenses are used, the sun is often included in images captured on clear, sunny days. The fact that ghost and flare occurs so rarely makes these lenses very convenient. I think that after looking at these sample images, you will agree that even the relatively old design of this lens stands up well to practical use even today.

VII. The fisheye lens with the largest angle of view

Sample 1
Nikon Df with Ai AF Fisheye-Nikkor 16mm f/2.8D
Aperture: f/11, Shutter speed: 1/80 s
ISO 5000
Image quality: RAW
White balance: Auto
D-Lighting: Auto
Picture Control: Standard
Captured in April 2014
Sample 2
Nikon Df with Ai AF Fisheye-Nikkor 16mm f/2.8D
Aperture: f/11, Shutter speed: 1/320 s
ISO 800
Image quality: RAW
White balance: Auto
D-Lighting: Auto
Picture Control: Standard
Captured in April 2014

Now let's consider angle of view for a moment. You may be interested in knowing just how wide a photographic lens's angle of view can extend. As the subject interested me very much, I examined records and patents. I discovered the answer in a book titled, Kameraman no tameno shashin renzu no kagaku (in English, The Science of Photographic Lenses for Photographers), by Shotaro Yoshida. Records show that the widest angle of view was achieved with a 12.3mm f/10 medium-format fisheye lens invented by three people including A. C. S. V. Heel from The Netherlands' National Defense Research Committee (NDRC). It offered an incredible 2ω = 270° angle of view. We do not know whether this lens was actually made, or whether it was simply invented on paper, but it seems to be the lens with the world's widest angle of view.

Next let's find the lens with the widest angle of view that was actually manufactured. Which do you think it was?

Sample 3
Nikon Df with Ai AF Fisheye-Nikkor 16mm f/2.8D
Aperture: f/11, Shutter speed: 1/800 s
ISO 400
Image quality: RAW
White balance: Auto
D-Lighting: Auto
Picture Control: Standard
Captured in April 2014
Sample 4
Nikon Df with Ai AF Fisheye-Nikkor 16mm f/2.8D
Aperture: f/11, Shutter speed: 1/1000 s
ISO 400
Image quality: RAW
White balance: Auto
D-Lighting: Auto
Picture Control: Standard
Captured in April 2014

The correct answer is the SAP Fisheye-Nikkor 6.2mm f/5.6 manufactured in 1969. Also requested by university professors, a few of these lenses were manufactured. It was a fisheye lens with a solid-angle projection system that covered 230° and utilized an aspherical lens element. Though the lens was never mass-produced, a few are still in existence. Why was a 230° angle of view necessary? The reason lies in the fact that field of view of the human eye is 220-230°. A fisheye lens with a 230° angle of view was developed to contain the entire maximum field of view of the human eye in a single photo. SAP in the name of this lens is taken from its solid-angle projection system. In order to correctly achieve solid-angle projection, an aspherical surface was adopted.

It is clear that, at that time, Nippon Kogaku K. K. (now Nikon) put a lot of time and effort into its research into fisheye lenses, whether orthographic projection (OP) or SAP fisheye lenses. Incidentally, the designer of the SAP Fisheye-Nikkor was Masaki Isshiki, who worked in the research department at that time. Mr. Isshiki not only designed optics, but also developed optics software. After retiring, he took a teaching position at a university, and remains active in the field of optics.

I recently saw this SAP Fisheye-Nikkor lens for myself. It is a precious piece in a collection maintained by a Japanese person now living in the U.S. It will surely be handed down to future generations.