What is a "diagonal/circumferential fisheye lens"?

New lens FISH-EYE 220 from tokyo grapher. Boasting an amazing 220° angle of view, this fisheye lens was designed as a "diagonal fisheye lens" for the iPhone.
This time, what is a "diagonal fisheye lens"? What other types of fisheye lenses are there? We will discuss the characteristics of each.

Fisheye lenses, which are characterized by taking advantage of large distortion, can be divided into two types: "diagonal fisheye lens" and "circumferential fisheye lens (or circular fisheye lens)."

Looking at the difference between the images taken, the image taken with the "circumferential fisheye lens" was recorded in a circular shape or with a part of the circle left (so-called vignetting left), and the image taken with the "diagonal fisheye lens". The difference is that the image is recorded on the full screen.

The light that forms an image through a lens is originally circular, and is captured as a square by a sensor (image pickup device) or film, and is recorded in the photographs and images we often see. The circular light imaged through this lens before being clipped is called the "image circle". (Fig. 1)
There is a difference between the two types of fisheye lenses that is closely related to this structure.

As shown in Fig. 2, a diagonal fisheye lens records images with an image circle larger than the screen diagonal and no vignetting.
Since the image is recorded exactly as you see it on the screen, there is no need for trimming, making it easy to imagine the finished product when shooting.
Especially when shooting with a camera like the iPhone that is easy to use and you want to avoid cropping as much as possible, a diagonal fisheye lens may be suitable.

As shown in Fig. 3, the angle of view of a diagonal fisheye lens is the range that can be captured on the diagonal line of the screen.

As shown in Fig. 4, a lens whose image circle fits entirely within the screen or whose image circle is smaller than the width of the screen is called a circular fisheye lens.
Circumferential fisheye lenses are recorded with a circle or a part of the circle left as they are taken, so trimming is necessary to use as a photo without vignetting.

In the case of a circular fisheye lens, in which the entire image circle is contained within the screen, photographs and images taken are recorded with the entire angle of view (Fig. 5). A characteristic of circular fisheye lenses is that it is difficult to envision the final shape when shooting until you get used to the area that will be trimmed.

The first fisheye lens released by tokyo grapher, the FISH-EYE LENS, was designed using this circular fisheye.

With two types of fisheye lenses from tokyo grapher, you can easily and actively enjoy nature, cities, portraits, extreme sports, and other images that have never been possible with an iPhone.