Defished fisheye compared with ultra-wide

I have previously looked at how to defish the images from the Samyang 7.5mm f/3.5 fisheye lens. Even with a generic fisheye lens profile, it is easy to defish the output images so that they appear rectilinear. But my example image does not show how wide the output image really is. To illustrate that, I will present the same image taken with an ultra-wide lens.

But first, let's compare the specs:

Lens	Focal length	Diagonal field of view
Samyang 7.5mm f/3.5 fisheye lens	7.5mm	180°
Lumix G 7-14mm f/4	7mm	114°
Olympus 9-18mm f/4-5.6	9mm	100°

As is apparent from this table, the fisheye lens has a vastly wider diagonal field of view. However, we also know that the fisheye lens has a more compresses field of view the further we get from the centre. Hence, not all of the 180° diagonal field of view can be used when defishing the image.

This can be illustrated by looking at the defishing process. Here are the same images taken with the Samyang 7.5mm fisheye lens, defished, and taken with the Olympus 9-18mm lens at 9mm:

Original fisheye image	Defished, not cropped
Defished and cropped	Olympus 9-18mm @ 9mm

The defishing process was done with Hugin, and is described in this article. In this example, I used the "orthographic" lens type, rather than the "fisheye" lens type.

We clearly see that a lot of the fisheye corner image is lost in the transformation process.

Letting the Hugin program calculate the optimal resolution yields a defished and cropped image of 11385 times 4750 pixels.  This reflects the true resolution only in the centre of the image, while the resolution is less the further from the centre one gets.

Hence, to compare the wideness of the lenses, it is better to look at the horizontal and vertical field of view:

Lens	Focal length	Horizontal field of view	Vertical field of view	Diagonal field of view	Aspect ratio
Samyang 7.5mm f/3.5 fisheye lens	7.5mm	132°	86°	180°	4/3=1.33
Samyang 7.5mm f/3.5 fisheye lens defished	7.5mm	132°	86°	135°	2.40
Lumix G 7-14mm f/4	7mm	102°	85°	114°	4/3=1.33
Olympus 9-18mm f/4-5.6	9mm	87°	71°	100°	4/3=1.33

When given the diagonal field of view, the horizontal field of view can be calculated as:

2*DEGREES(ATAN(TAN(RADIANS(114/2))*COS(ATAN(3/4))))

with the diagonal field of view being 114° in the example formula above.

From the table, we can see that the fisheye lens loses a lot of diagonal field of view when defishing. This is not surprising, since the image must be stretched into the corners. The image also loses resolution in the corners due to this.

The Panasonic Lumix G 7-14mm f/4 is a very wide lens, and it is also very expensive. But using a fisheye lens, we get a resulting defished image which is still far wider in terms of horizontal field of view, and only marginally wider horizontally. This can be further illustrated by showing what crops I would have gotten if I used the two ultra wide zooms to take the same picture:

However, the flip side of the coin is of course that due to stretching out the image into the corners, the resolution suffers. Here is a 100% crop from both the original and defished images from the corner:

If I had used the Lumix G 7-14mm lens at 7mm, this would have been in the extreme corner of the image frame. Now, I don't have this lens, but I think it would have achieved somewhat better sharpness than the defished example above.

Conclusion

When defishing images from the Samyang 7.5mm f/3.5 fisheye lens, the resulting image becomes much wider than that from the widest rectilinear lens for the Micro Four Thirds system, the Lumix G 7-14mm f/4. However, you also lose some resolution in the corners.

Note: After having published this article, I have take actual comparison images using the Lumix G 7-14mm f/4 ultra wide lens and the Samyang 7.5mm f/3.5 fisheye lens.