PHOTOSHOP 8.0 CS FOR SIGMA 8mm FISHEYE LENS

SUBJECT

I propose to discover the functional capability of the latest Adobe PS version (8.0 aca CS) in correcting two types of optical aberrations that some lenses (such as very wide angle and circular image fisheye) are prone to show.

Let's start with a lens that is now popular in the panoramist community : the 8mm f/4 EX SIGMA FishEye

The first error, chromatic aberration (both sagittal and longitudinal), would reduce dramatically the lens sharpness near the limit of the FOV and some color fringing be visible there at contrasty locations such as wall edges.

The second, illumination fall-off (including vignetting) may make blending of adjacent images difficult in the process of stiching panorama from multiple images. I have noticed that enblend, the new (and otherwise very good) tool for that purpose shall exagerate color saturation gradient in uniform areas (e.g. cloudless skies) at best, or shall exhibit ugly banding at the same location, at worse, when too strong illumination fall-off of the individual images is not corrected.

Adobe Photoshop 8.0 CS is recommanded to fully experiment what follows. Even without it, you should however be able to fully understand the matter...

ILLUSTRATION BY AN EXPERIMENT:

Here is a specially prepared Raw image. (Beware: 5.5MB CRW format) . To open it, you need a converter. Adobe  PS CS offers a nice one and for the next step, I shall assume that you have it available.

Technical data:

Here is the experimental set-up (*) that I used:

Enlarged view (*).

A circular end of my table of 1.1-meter diameter was used for the tests. Mounted on the circumference of the table was a printed checker board pattern with alternating black and white squares, each measuring 19.2-mm by 19.2-mm. These were designed to be 2° across. The checkerboard pattern was generated in PhotoShop and scaled to the circumference of the table. The nodal point of the camera lens was put at the middle of the diameter line of the semi-circular end of the table. The use of the round table considerably reduces the computational complexity of calculating data (such as fields-of-view, distorsion etc.) from image.

The output that was got from this experiment shall be used for other purposes. As an example calibration of a, b, c, d and e (PanoTools) can be cross checked with this material by simply mesuring the relative radial distorsion of the square blocks.

When the Raw image is opened with Photoshop CS Raw Converter:

You should then see something like this:

Here is a larger view of the screenshot.

The CS Raw converter applied settings are listed in the PS "File info" window inserted in the above figure: Everything set to ZERO but the colour temperature to 2700K

You should now see something like this:

Here is a larger view of this new screenshot:

No more Chromatic Aberration (CA) is visible and the light fall-off (and vignetting) is somewhat satisfactorily corrected as well.

SYNTHESIS

Similarily, chromatic aberration can be well corrected for all other apperture f-stop settings of the lens (f/4 to f/32).

Here is a larger view of this image.

This is a composite image that shows the Chromatic Aberration (obvious when the image is zoomed in) for all the apperture settings (shown from the center to the top of the picture). 

The result from application of PS CS correction is shown from the middle down to the bottom of the picture. Note that vignetting correction was not specifically applied. Even though, the natural light general level looks also much better due to some other corrections that were applied (See the list on the left of the figure or in the "File info" window).

On the contrary to light illumination natural fall-off (optical, not mechanical) that is less pronounced with smaller effective apperture, one can notice the variation of the (mechanical) vignetting that affects the effective usefull FOV: smaller is FOV(<180°) when smaller is the effective apperture (i.e. higher f stop setting number).

One can also see the expected increase of sharpness from f/4 to about f/16 and then the subsequent softness due to diffraction for smaller and smaller apperture (i.e. increasing f-stop numbers).

As a supplement it is possible to illustrate the compression that the lens does from the center to the edge of the circle image:

Click on the pict to enlarge.

The measured Angle of view as a function of the Distance from the center of the image frame (in pixels) is given on the chart.

I then compared to two theoretical results: following the Helmut Dersch Selected formula to modelise the real fisheye: Theta = 2 x ArcSin (distance /4 x focal length) or the linear ideal theoretical formula R= c x Theta.

The Excel spread sheet is here. A PDF version of the chart is here.

CONCLUSIONS:

I have experimentally verified that the lateral color of this fisheye is in fact quasi-linear in width with respect to the distance from the image center (With a -negligible- modulation by k x SIN Theta/2). More important, the colour aberration does not change in nature all along a radius of the circle. (no visible change from reddish to purple for exemple as it is commonly found in other wide lenses). In my opinion, this may be the basic reason why this fisheye may be compared favorably to some other (standard or fisheye) lenses for ease of CA correction.

Notes:

(*) Special thanks to Coastal Optics Systems for suggesting the clever and simple experimental aparatus in this paper. I have improved the set-up somehow by simply using a bare light bulb at the vertical of the "nodal" point of the lens in order to get uniform lighting of the cylindrical checkered target...

(**) Initially, I personnally found this fact so hard to believe that I decided to write this page so that anybody can check by themself! It was a very good surprise for me and other fellows before me (hello, John H)...This conclusion may be specific to the SIGMA lens considered. See for example this good study and tutorial and this followup about the same topic and which shows the complex nature of CA for another (Nikon FC-E8) lens.

(***) The correction was designed to occur starting from the corner of the image rectangle, where most of the light fall-off is supposed to be. This assumption is good for any type of lens with the exception of ...circular fisheye! In this case (as well as for quasi-circular image from APS sized CCD or CMOS sensors) these corners are void of any image pixel. The correction is then wrongly radially applied on the rest of the actual image on the central part. This problem is very similar to the one in previous topic (**) of this footnotes list

I have extensively also measured the illumination distribution of this SIGMA lens and reported it on an excel spread sheet. BTW, I have compared it with a typical standard wide angle lens.

Michel Thoby

July 26th, 2004

V2.1