Title: Canon RF 5.2mm f/2.8L Dual Fisheye lens

Alternative title: The VR180 fallacy

Written by Paul Bourke
December 2021


The following discusses an initial evaluation of the new (at the time of writing) pair of fisheye lenses, the "Canon RF 5.2mm f/2.8L Dual Fisheye" mounted on the Canon EOS R5. The target for this lens is predominantly the so called "VR180" market, that is, a stereoscopic viewing environment that fills our entire peripheral vision. The main desirable features of this photographic solution over many others are:

  • The images are recorded onto a single sensor so perfectly genlocked.

  • Since there is only one sensor each of the pairs is assured to have the same colour, exposure, white balance, focus ... etc.

  • The sensor is 8K pixels wide (more precisely: 8192x4320, for video) and therefore results in each fisheye having close to a 4K circle.

  • Generates a wide field of view stereoscpic image with the issues of blending multiple cameras together.

Of course, like everything in optics, photography and video, there have been similar splitting mirror designs in the past. The main difference here is the introduction of fisheye lenses.


Stitz SA-1, Made by Itzuki (Japan), circa 1970

First observation, the fisheyes are not centered. An easy fix and a common trait of all dual fisheye 360 cameras. But given the price point of this lens and camera surely the two fisheyes could be factory aligned. It means of course that one needs to correct the horizontal offset to align the image pairs and the vertical offset to remove any vertical parallax. It also means that every camera will be slightly different, requiring a different fisheye circle center and radius value.

The fisheye circle is about 4010 pixels, rated as 190 degrees at that circle. Interocular is 6cm. The image below illustrates the vertical offset as well as the manual method for determining the fisheye centers and radii.

The lens does have a higher light fall off towards the rim than most other similar fisheye lenses, and still exhibits some fall-off at the 180 degree mark. The following are two 180 degree fisheyes extracted after determining the horizontal position, correcting for the vertical offset and flipping the left and right half of the frame. These are now perfectly centered in each half of the frame.

It will be left up to the reader to work out why the left eye image appears on the right hand side of the image. This is obviously so since the left and image should "see" the bulging fisheye lens from the right hand camera. So after processing the two bulging lenses should appear in the center of the combined frame.

The next correction that needs to occur is linearising the fisheye, that is, a radial correction such that the field angle is a linear function of distance from the fisheye center. This is discussed here in more detail. It is a shame that Canon does not publish this information and even finds it necessary to refuse requests for it, unlike most other fisheye lens producers. This is as much a key attribute of the lens as the field of view or f number. Indeed, this curve is necessary for anyone who wishes to use the images correctly in almost any VR environment. Almost any downstream usage of the footage is going to assume a linear relationship, not doing this will result in errors in perceived scale in, for example, VR headsets. It is possible to measure it oneself and the results are given below but Canons attitude with respect to such basic information is unforgivable.

As it happens this lens is extremely linear. The graph below is normalised radius vs field angle. Field angle phi = r / (0.5*190*pi/180) = 0.6031 r where r is normalised radius of the fisheye circle. For the vast majority of applications no further correction would be required.

Unlike many of the comments from Canon, it is not necessary to use their paid tools to edit this footage. Whether the pipeline uses fisheye (see extracted image pairs above) or pair of 180 degree longitude equirectangulars shown below, there are lots of conversions options.


The VR 180 fallacy

There is a fallacy in much of the marketing of this lens, typical are statements like the following that appear multiple times on the Canon web site, and regurgitated by reviewers.

"Viewers will be able to take in the scene with a vivid, wide field of view by simply moving their heads".

or

"... allowing the viewer to immerse themselves in the content — by simply moving their head to provide a vivid, incredibly wide view".

In reality the view one experiences is only strictly correct if one is looking directly forward. Only in this situation are the two fisheye views presenting a reasonable model of the the human visual system. There are two obvious situations to illustrate why the above statements are not true, or at best misleading.

  • If the viewer looks directly to the left or right then there is decreasing parallax and therefore decreasing (and incorrect) depth perception. At +-90 degrees there is no parallax with which to convey depth information. Indeed one sees a scene object in one eye being larger than in the other eye on account of the object being closer to one camera. This lack of parallax and scale is not an issue if one looks directly ahead because that effect is close to what occurs in real life.

  • When looking away from the vertical and horizontal axes of the view (eg: diagonals), there is vertical parallax introduced, something that should not occur in correctly created stereoscopic views.

The effects described above are not due to imperfect fisheye optics in a physical lens but are fundamental to any single shot dual fisheye camera. For example, one can recreate the perfect case with computer graphics, the following is a simulation of the two Canon RF 5.2mm f/2.8L dual fisheye lenses but with perfect optics (190 degrees FOV). The scene is a simple latitude/longitude grid a fixed distance from the center between the two lenses. The two fisheye images have been overlaid, the left eye in blue and the right eye in red.

All the effects discussed can be observed in this image. Noting that the lenses are parallel as expected for VR headset style viewing, so zero parallax is at infinity and the relative location of scene elements should exhibit negative parallax. In other words the blue lines (left eye) should always be to the right of the red lines (right eye). Along the horizontal axis this separation decreases towards the edges, in the extreme case there is no depth perception. The vertical parallax is clear along the four diagonals, and in different directions depending on the quadrant being considered. Again, note that these effects are the correct behaviour for a forward looking observer, but they make the statements above about being able to turn ones head, incorrect, at least for correct stereoscopic viewing. Turning ones head away from the central direction will result in incorrect depth percpetion and increased eye strain as the human visual system is presented with "unexpected" stereoscopic pairs and tries to compensate.

These effects do not "go away" when converting to equirectangular, the issues just get revealed in different parts of the image. The following is the equirectangular corresponding to the simulated image above, this is also 190 degrees FOV.

These stereo pairs can also be viewed, in pieces, by perspective views. In the following each perspective camera is 100 degrees horizontal field of view, the adverse effects discussed above are visible in this representation also.


Looking directly forward

Looking 40 degrees to the right

Looking 40 degrees upwards

Looking along the top-right diagonal

Screen based stereo and the convergence problem

In order to understand the effects of projecting onto a screen based stereoscopic system, for example, the iDome display, a simulation of the Canon and fisheye lenses will be used along with some simple scene elements. The coordinate system and geometry is as shown, the L and R are the location of the fisheye lenses and three small spheres will be placed at the distances as shown. These three spheres will also be rotated by +/-45 degrees and +/-80 degrees so as to lie along the horizontal plane, +/-45 and +/-80 degrees so as to lie along the vertical axis. A further 4 instances of the 3 spheres will be positioned so as to be located in each quadrant.

As earlier, the resulting images will be overlaid with the spheres in the left eye image being blue and the spheres in the right eye image being red. The fisheye rendering using a 190 degree ideal fisheye is as follows.

Most effects have already observed with the latitude/longitude grid earlier.

  • The horizontal plane looks as expected except the parallax decreases to 0 at the extremes.

  • Vertical parallax is increasing introduced as an object moves away from the horizontal and vertical axis.

  • The 10m (infinity for all practical purposes) spheres coincide as expected for zero parallax.

  • Since we are using parallel cameras, all scene objects exhibit negative parallax, that is, the blue (left) sphere is always on the right of the red (right) sphere.

While it may seen risky to make observations from the fisheye images, one can readily extract perspective views. This will be left as an exercise for the reader, but while the details change slightly, the conclusions are the same. The 180 degree longitude equirectangular representation of the above is shown below.

For screen based stereoscopic systems one needs to choose a zero parallax distance, this is the distance at which scene objects will appear to be at the screen depth. For dimensional correctness (if that is required) the zero parallax distance as determined by the distance of the viewer to the display surface would match the distance of objects in the recorded scene.

For flat wall stereoscopic displays the matching of zero parallax distance can be made exactly, this is performed by horizontally sliding the left and right images with respect to each other and trimming off the excesses. This process mimics the asymmetric frustum used in realtime computer graphics head tracking systems. Essentially matching the view frustum of the camera with the projection pyramid from the projector. The equivalent for fisheye images is to rotate the fisheye image about the vertical axis. For the simulated test scene described above the angle to rotate the fisheye image by in order to set the zero parallax point can be exactly calculated. The result is shown below for both overlaid fisheyes and overlaid partial equirectangulars after the image has been rotated to place the 1m sphere at the screen depth.

Observations.

  • In the center the goal of setting the 1m sphere to zero parallax has been achieved. Across the center horizontal plane the apparent depth of objects is being increased towards the edge, rather than going to zero as before. Relative positive and negative parallax is at least being preserved out to +-45 degrees.

  • Similarly along the vertical relative positive and negative parallax is being preserved out to +-45 degrees. Otherwise scene objects are being brought closer to the viewer.

  • As with the zero at infinity case, along the diagonals the relationships are more complicated with both vertical parallax being introduced and a distortion of the depth relationships.


The general conclusion is the same, specifically, that while 180 degree stereoscopic captured with dual parallel fisheye lenses can give acceptable viewing, it only occurs for a viewer looking "forward".

There are alternatives, these are generally known as omnidirectional stereoscopic methods and they exist for both 360 cylindrical displays as well as hemispherical dome displays. They allow a viewer to look left and right and the stereoscopic depth percpetion remains correct along a horizontal view direction, the price is incorrect depth perception in the periphery but that is widely accepted as less important. Unfortunately (at the time of writing) there are no "perfect" omnidirectional cameras for video, but they do exist for still images. So called 3D 360 video cameras create approximations to the omnidirectional stereoscopic ideal but still exhibit depth perception errors as well as the inevitable issues across stitching zones.