Last month I photographed the distortion characteristics of four expensive roof prism binoculars: The new "Swarovision" 8.5x42, Nikon 8x42 EDG, Zeiss 4x42 FL and Leica 8x42 Ultravid. I'm just now getting around to making slides that demonstrate the differences among them.
I used two targets that were handy in the store; a round suction cup to show the effect on shapes of angular magnification distortion and and a straight window frame to show the curving of lines caused by the pincushion form of rectilinear distortion used in binoculars. What you can see from the photos is that none of the binoculars is distortion free. In fact that is impossible. If rectilinear distortion is reduced to zero that creates angular magnification distortion. Achieving relative freedom from angular magnification distortion is only possible by the application of pincushion distortion. The problem is similar to what map makers face in trying to produce a flat map of the sphere of the earth.
The left slide shows the angular magnification distortion of a circular shape at the edge of the field. Swaro is upper left, Nikon is upper right, Zeiss is lower left and Leica lower right. The Zeiss is the most nearly distortion free which in this case means a perfect circle with the horizontal and vertical diameters equal. The Swaro has the highest angular magnification distortion because it has virtually no pincushion distortion, so the circle appears as if it were seen from an oblique angle. The Leica has a little too much pincushion for exact compensation so that the horizontal diameter of the circle is wider than the vertical diameter, essentially reverse angular magnification distortion.
The right slide (Sorry, that slide is in post # 2) shows the rectilinear distortion of the window frame. Swaro is on the far left, then moving right Nikon, Zeiss and Leica. The Swaro has virtually no rectilinear distortion and the Nikon has a very little pincushion. The Zeiss and Leica show increasing amounts of pincushion which is more obvious in viewing through the Leica because its apparent field is smaller.
The designers of these binoculars made different decisions about distortion. The Swarovski designers made an unusual choice of zero pincushion which leads to considerable angular magnification distortion. The Nikon designers applied slight pincushion which leaves a little angular magnification distortion, but doesn't cause lines to curve very much. Zeiss applied more pincushion which mostly correct angular magnification distortion but causes lines to visibly curve and Leica, for reasons I don't understand, applied a little more pincushion than is really needed.
Sorry, I wasn't able to include the window frame slide that shows rectilinear distortion in the first post so here it is.
Thanks Henry, accurate and well presented.
I might offer some guesses as to the curvature choices, only guesses mind you, based on experience with both Zeiss and Leica photogrametry lenses. This is were we measure the angle from two known focal points and measure the angles, horizontally and vertically from the optical axis of each of the two images and project them to intersection at a known 3D point in space. These lenses are designed to, very accurately, reproduce the image angle from the principal point / optical axis. These usually scale accurately for focal length. Binoculars have eyepieces that allow for some correction of the curvature at the expense of other parameters, say astigmatism or other parameter. I suspect that these do not scale for focal length or apparent angle as well as the objective because of the shorter, more divergent factors. This could lead to two different sources, one, the eyepiece was designed for a different configuration and scaled or, two, that the tolerance of the focal length is critical enough to show the error, i.e. magnification times tolerance.
And, then again, the designer might just think more curvature is aesthetically appealing.
I have been doing some experimenting along the same lines and after seeing your examples, I think I will add concentric rings to my test target.
I find it really helps understand some edge problems. Notice the edges of attached. The red grid is computer generated for reference against a constant distance/angular offset.
Best
Ron