Circular 180° Fisheye Lens

Mapping of the in-focus zone in the object space

Foreword

The article is about In-focus and Out-of-focus images or part of images. Please remember that Aperture Stop setting is a factor that changes considerably the depth of field of the lens. In the whole article, the aperture is set at the widest opened Aperture Stop. Completely different results would have been found and presented with less opened diaphragm settings.

Subject

Similarly to standard rectilinear lenses, when the hemispherical fisheye lens is set at full aperture (e.g. Nikkor 10.5mm @ f/2.8 or Sigma 8mm @ f/3.5, etc.), the image shall generally not be evenly sharp over the entire circle. Part of the image frame might be affected by de-focusing but this can be also compounded with the softness of the lens that increases with the distance from center. This effect shall depend on the distance of the object and on the distance setting that is selected for the focusing of the lens. This setting can be commanded and controlled from the camera or (in manual control mode of the lens) with the ring for setting the focus distance that may be around the barrel of the objective. Note that certain lenses are deprived of this distance setting ring: they can be of the fixed focus/ fixed aperture kind (e.g. Sunex 5.6 mm f5.6; Coastal Optical-IPIX 4.88 mm f5.2, etc.) for example.

The aim of this paper is to determine and drawing up a 2D map describing the in-focus (i.e. sharp) zone in the object space of a fisheye lens. The first step is purely experimental and involves a lot of shooting images with a camera on a tripod. The second step shall be empirical as it needs to peer to these dozens of images in order to rate them all with a grade mark. The last stage is to draw the 2D map by using the results from the precedent stage.

The way how to proceed shall be given step by step and an example shall be shown.

A 2D map detailed case study: the Nikkor 10.5 mm f2.8 @ f/2.8

 

About 0.4 m is set on the distance setting scale:

The experiment final result: the 2D map!

Color keys:

BAD
 
GOOD
       
Blurred
Too soft
Slightly soft
Crisp
Ugly bokeh
Misty
Un-sharp
Sharp
Badly out-of-focus
Out-of-focus
If need be only
In-focus

The camera is at the bottom of the map aiming vertically toward the top. The distance in the object space is shown along the circles that are all centered at the front of the fisheye lens. Oblique angle measured from the lens axis are shown from 0 deg. to 90 deg. on both left and right sides of the axis. This map could represent a large room limited by surrounding walls: 8.8 meters long and 4.4 meters wide and the observer views from the top the middle horizontal section . Rotating the whole graph by 90 deg. and the camera would then be aiming horizontally...

Let's now explain how to get the 2D map.

The experiment (first distance of focus setting = 0.4 m)

This shall concern the 2D map shown above. Some of the steps and test conditions may vary with other constraints.

A- Shooting the test images

Typical set-up:

A reflex camera is placed in landscape mode on top of a stiff tripod. It is set to shoot with locked-up mirror function activated. It is fitted with a 180° fisheye lens. A rotator should be installed between the camera and the tripod to allow successive shootings separated by e.g. 10 degrees intervals. The vertical column of the tripod should be set vertically and the lens axis should be horizontal.

We have used a Canon EOS 5D full frame DSLR and a Nikkor 10.5 mm lens (set at f/2.8). On a Canon camera, this is a manual controlled fisheye lens. A Nodal Ninja R-D161 was used on top of a Manfrotto tripod for support.ired remote control and mirror up-locked helped for quiet shutter release. The lens was set at the fully open aperture and this setting was locked with masking tape to lock the stop setting ring.

The prime parameter selected for this experiment is the distance of focus setting

The distance of focus is set on the ring at one of the distance listed above and this setting is locked with masking tape to lock the lens setting ring. We have selected 0.4 meter in this example..

Target

A suitable and well lit target is fixed vertically for instance on a wall with its center at the same level as the horizontal optical axis of the lens. It should be selected to give both low contrast elements and high contrast elements on it. We have used a cible de jeu de fléchettes! Oh, I have been tought to call this thing a "Dartboard"...

Distance for shooting images

The tripod shall be displaced to temporarily put the camera in front of the target and at a given distance (shooting sequence), then at another distance (shooting sequence), then etc.

Marks can be chalk-drawn on the floor at certain discrete value of distances from the wall: for instance 0.5 meter, 0.75 m, 1 meter, 1,5 meter, 2 meters, 3 meters and 4 meters. These are the distances from the target approximately to the Non Parallax Point of the lens (i.e. near the front element) and may be re-used for experiments further to this single case study.

But for this specific parameter setting (i.e. 0.4 m) that is exceptionally short, supplementary shorter shooting distances have been used: 0.13 meter, 0.20 meter, 0.30 meter and 0.40 meter. This was done in order to record data with better "map resolution" for "close-up photography" or near macro range (claustro)-panoramas.

Shooting

At a given distance from the target, eleven photographs were shot: one separated from the next by 10 deg. by rotation of the camera on the NN R-D16 rotator: from 0 deg to 90 deg.

The same sequence (each yielding 11 images) was repeated at each of the selected shooting distances from the target. This means 11 * 11 = 121 images were recorded on photographs in full RAW mode.

B- Preparing the 121 photographs

Results from a typical shooting sequence (at 1.5 m from the target which is one location amongst eleven for shooting) are presented on an overview in the following image:

The result of the subjective empirical analysis is also shown below each cropped image.

The 11 sets of 11 images each had been developed, chromatic aberration and vignetting corrected and then severely cropped in ACR 5.6: only the center part of the target was intentionally kept for the rest of the analysis.

C- Analyzing the 121 cropped image

As shown above, each of the small cropped images was peered to and subjectively affected with a grade mark. Then this was optionally confirmed and then converted to a color coded mark (from red to blue, see above). Important: this was done by peering at 100% zoom-in only. But to be able to possibly differentiate one image IQ from a similar other image, zooming-in at 200% would be done. This specific process should not be used for overall analyzing and comparison of the whole set of images.

D- Final stage: drawing up the map

We have virtually "pin-pointed" the color coded data on a graph grid template with prepared distance circle scales and angle indication to get the following result:

On a layer overlaid above this preliminary chart we have painted the final map that was shown on the top of this page.

 

A second distance of focus setting (2 meters):

A similar sequence was used to get this other map:

Approximately 2.0 m is set on the distance setting scale:

As this second distance of focus setting is not adapted for close range or macrophotography, the shooting sequence from very short distance was suppressed to start at 0.5 m only.

The scale that is engraved on the Nikkor lens is awfully difficult to use to accurately set a given distance. One can guess that the actual set distance was here closer to 1.5 meter than the expected 2 meters!

 

 

Illustration and correlation with some other actual photographs

Hans Nyberg had shown us some excellent and inspirational test images that he had shot to demonstrate the complex shape of the focus zone in the object space:

Pay attention to the white metering stick. We would like to quote Hans:

<<Check the white measuring stick (...) You can see that even if that one is straight 90 degree vertical it is sharp at the bottom but very un-sharp at the centre.
This means that the focus plane is not flat but actually bowed "the wrong way"

Hans >>

We also have played with a meter rule by hanging it on a wire that was fixed parallel to the ceiling! The rule was then shot at different distance from the lens front: 13 cm, 20 cm, 30 cm, 40 cm, 50 cm and 60 cm. Layer stacking in Photoshop was performed to show all six meter rules on the same image.

Nikkor 10.5 mm f2.8 @ f/2.8 and focus distance locked at about 0.4 meter:

Vertical section view from side showing the location of the rules

The general scene with six meter rules:

Composite from 6 images stacked with Photoshop CS4

Horizontal section viewed from top showing the location of the rules

The composite image of the scene IMHO matches very well with the map despite the very limited ability to repeat and set manually and accurately the focus distance with that pitiful scale on the Nikkor lens.

 

Information provided by the lens maker

Nikon provides an Instruction Manual sheet to the end customer: one should find it in the box when the lens is delivered.

As if this specialty (fisheye) lens was a standard (rectilinear) lenss, a simple Depth-of-Field table is given. Obviously applicable only for paraxial conditions and measured from the sensor (focal) plane, none of these two important conditions are said anywhere at all!

Furthermore, the user is not informed about focusing constraints and performance near the edge of the field. Despite so many conflicting opinions and presomptuous statements on the web about this, they sadly cannot be straighten out by reading this official document.

By the way, this table reflects also the poor practical resolution of the focus distance setting scale on thye lens by showing parameters value only for 0.14 m, 0.17 m, 0.20 m, 0.30 m, 0.50 m and... infinity!

In green here we can read the limits of the depth of field determined by Nikon: they are obviously very much narower than our own findings. The determination depends of course on some basic assumptions and principally the cercle of confusion.

Conclusion: for normal photography and for panorama photography (and especially to post VR on the internet), the information provided by Nikon are simply deceptive and ... useless:-(

 

Testing the whole range of focus distance setting of the Nikkor?

As we have repeatly said, the manual focus distance ring and scale are poorly designed on this lens that BTW with f 2.8, is the "fastest" of all commercially available fisheyes at the time of writting this paper.

With a Canon EOS 5D, there is no way to insure the correctness of even approximative manual setting of the distance beyond 0.5 m. An adapter ring with auto-focus confirmation may have helped a bit but I haven't one. No live view mode was implemented on our "older" Canon DSLR yet:-(

The best would be if someone with a Nikon made camera could complete the test that we have begun above. Anyone?

 

 

Further experiment: the Samyang 8 mm fisheye

With the new Samyang lens on the same camera as before we have then drawn a more complete set of maps that encompasses a range of distance of focus settings from 0.5 m up to... infinity.

The following presentation is illustrated with a flash animated object movie (beware: 1.2 MB) . Please click on the thumbnail:

 

Michel Thoby

September 4th, 2009

Slightly edited 9 Sept 2009