Tuesday, 5 August 2014

Which Binoculars for Birding: Insights into Optical Design

Following up my post on the new Zeiss Victory SF binoculars, the most useful website for those seeking real information on the optical design of binoculars is that of Holger Merlitz who is Professor in the Department of Physics at Xiamen (Amoy to old China hands) University in China. His articles and papers are well worth reading and I have included links below to those of particular interest to this post in relation to the history of optical design, the introduction of intentional distortion and the characteristics of binoculars from different manufacturers.

The first major point to bear in mind is that the design of lenses for cameras differs (or should differ) from that for binoculars because the imaging system of binoculars includes the human eye which has its own distortions. The camera lens is aimed at the ideal of distortion free imaging; the binocular is aimed at the optimal image on the human retina, taking the binocular and eye as the integrated unit.

The history of the realisation that the unit to consider is binocular+eye is interesting and is outlined by Merlitz. Before 1950, optical designers tried to produce binoculars that, like camera lenses, were free of distortion (roughly defined as an absence of barrel or pincushion distortion). In 1949 Zeiss (Jena) picked up on the complaints of some army, presumably German, officers in two World Wars that when panned across the battlefield their binoculars or field glasses produced a strange effect that made them feel nauseous. As Merlitz puts it:

…appeared to display a rather strange kind of distortion, which became particularly obvious whenever that binocular was used for panning. The moving image appeared to roll over a curved, convex surface. This phenomenon, henceforth denoted globe effect, seemed to be absent with the static image, but it miraculously reappeared with the moving image each time the binocular was panned.

Koehler and Sonnefeld at Zeiss Jena, then in East Germany, suggested and demonstrated that this globe effect could be eliminated by introducing a degree of pincushion distortion into the binocular design. The human eye counteracts that pincushion bending of verticals and horizontals to send an image to the brain that is undistorted. Such a design of binocular would therefore be fine for both static spotting and panning. From the 1950s binocular manufacturers began introducing pincushion distortion. However, the degree of pincushion distortion employed can be noticeable and from about 2005 some manufacturers reverted to pre-1950 practice but in so doing exposed their customers to the globe effect and the feeling of nausea that it may induce.

More recently there has been renewed interest in the amount of pincushion distortion that should be added. Merlitz has tried to determine whether there is a point at which the globe effect is eliminated and noticeable pincushion distortion is minimised. I will not go into any detail of the geometry and trigonometry used to calculate theoretical levels of distortion here since they are fully described by Merlitz. suffice it to say that Sonnefeld, it seems, overestimated the degree of pincushion distortion required to overcome the globe effect. If k is the amount of pincushion distortion deliberately introduced and k = 1 is no distortion at all (termed the tangent condition and where the globe effect is evident), Sonnefeld suggested a value of 0 for k (the  angle condition). Other calculations from the work on human vision by another member of the Zeiss design team in the 1940s suggest a value of 0.5 (the circle condition).

More recent research by a group at Delft University in the Netherlands as well as that by Merlitz suggested that k should be between 0.6 and 0.8.

The more recent research brings out the second major point: there is variation between individuals on the value of k at which pincushion distortion can be perceived. For those interested, Merlitz shows Helmholtz checkerboards you can use to find your value of k (subject to variation in experimental conditions). Merlitz argues that the true average of k in the 56 people who responded to his request for help was around 0.7. Three of us here did the same study, finding values of 0.6, 0.7 and 0.8.

The major points throw up interesting challenges to the binocular manufacturer, as Merlitz points out:

Which consequences are to be drawn for the binocular manufacturer? With a choice of pincushion distortion near k=0.7, the majority of users would not complain about any globe effect. To be on the safe side, one might want to go a little lower, perhaps between k=0.6 and k=0.7, accepting a little bit of an extra pincushion distortion. In any case, the extremes should be avoided, namely values of k<0.5 (too much pincushion) or k>0.8 (too much of a globe effect).


It therefore appears that the ideal amount of distortion for handheld binoculars should be chosen between k = 0.6 and k = 0.8, a choice that would leave both the globe effect and the pincushion distortion (with the rolling eye) on a reasonably low level.

Merlitz also stated:

Binocular designers might also considering building oculars that would enable the user to modify the amount of distortion. In this way, the observer would be able to optimize the distortion characteristics of his instrument according to his own individual preferences and the particular mode of application.

As far as I know no manufacturer has yet done this and until one does, given the variation in different individuals, binoculars from one manufacturer may be more suitable for some individuals than those from another, depending on which k value is being incorporated in the optical design. If manufacturers stated the degree of pincushion distortion they have employed and retailers could test the k value of individual customers using Helmholtz checkerboards under proper test conditions, a better match might be achieved than by competitive birders buying binoculars for their brand badges—‘I’ve got to ‘ave Swarovskis ‘cos all my mates would laugh at me if I didn’t’, as I heard one checklist ticker say to another.

So what do we know of different manufacturers and their newer products. Well, here Merlitz helps again: From modern Nikons returning to pre-1950s undistorted optics and, therefore, the rolling ball effect when panning to the latest Zeiss Victory SF adopting a k value of 0.7, as recommended by Merlitz.

Of course there are many other optical and ergonomic factors in buying binoculars in a given price range, a sufficient number in fact to provide binocular nerds with hours and hours of discussion. But if you use binoculars to pan across the landscape, you need to read Merlitz and take note or you could end up with an the unpleasant rolling ball phenomenon and motion sickness if you choose a brand with undistorted optics.


1. These are all key pages in Holger Merlitz’s Website:

Merlitz, H. 2010. Distortion of binoculars revisited: Does the sweet spot exist? Journal of the Optical Society of America A 27, 50-57

Distortion of the new Zeiss Victory SF: A paradigmatic shift on the binocular market?

2. Globe effect

3. Oomes AH, Koenderink JJ, van Doorn AJ, de Ridder H. 2009. What are the uncurved lines in our visual field? A fresh look at Helmholtz's checkerboard. Perception 38, 1284-1294