Convergence vs. Convergence

(or struggling to find meaning in the world of stereoscopic filmmaking) 

One of the most confusing and misused terms in the field of stereoscopic cinematography is the word convergence.  In common usage the word means a coming together. Marketing people in consumer electronics like to use it to refer to the coming together of PC and TV technology. It’s also a technical term that is used in the jargon of displays.  For example, for projection of displays that use three image engines–red, blue and green–the term is used to describe how well the three optical paths are combined into one image.  If they don’t combine nicely you’ll get color fringing.

We have to draw the line when using the term convergence or we will wind up with everything coming together in a reverse of the big bang, and then where would we be?  Everything in the world would be the same thing and there would be no difference between Haagen Dazs and De Beers.

In stereoscopic filmmaking, the term convergence can mean different things leading to even more confusion in a world already rife with mind numbing farragoes.  Human beings have a visual system that uses two eyes to see the world and our eyes’ optical axes cross or converge on the object on which we are concentrating.  The eyes need to verge either inward or outward.  If they verge inward the term is called convergence, and if they verge outward the term is called divergence.  Depending upon where you are looking in space–if you’re looking at something that is farther or closer to your point of convergence–your eyes will have to either converge of diverge. 

The purpose of vergence for your eyes and your eye-brain in the visual world is to place the image of greatest interest–what you’re concentrating on–on your fovea centralis.  This is the part of the fovea that has most of the cones.  It is where the eye-brain provides high definition and where fusion is brought about; that’s the ability of the eye-brain to turn these two views of the world with a single point of convergence into the stereoscopic depth sense. 

The term convergence, or vergence, means something to visual scientists and it means something else to stereographers.  For stereoscopic displays the meaning is different enough to be worth talking about.  If portions of left and right projected images superimpose perfectly they can be said to be converged, and have zero parallax.  They appear to be (more or less) in the plane of the screen.  The term convergence is also used to refer to the rotation of camera heads to achieve that end, because if the optical axes of the left and right heads’ lenses cross on a point in space, that point will have zero parallax upon projection. 

Some workers talk about converging the cameras (or camera heads), but others talk about toe-in to mean the same thing.  Toe-in refers to the inward rotation of the cameras to achieve a zero parallax setting.  (Sometimes one would have to toe-out to achieve the zero parallax condition.) 

People who are doing CGI animation don’t have to use toe-in or its geometric equivalent rotation.  Toe-in is not required because these workers can use cameras that have parallel lens axes, and these parallel lens axes look straight ahead at the world and the “convergence” can be achieved by horizontally shifting the left and right images with respect to the lens axes to achieve zero parallax.  Without any toe-in one can achieve zero parallax without distortion.

I’m talking about trapezoidal distortion, which is sometimes referred to as keystoning.  Rotation to achieve the zero condition will produce trapezoidal distortion because the two images have, in effect, placed one portion of the object closer to the camera sensor than another resulting in differential magnification across the image field.  One way to beat this with real-world photography is to horizontally shift the lenses or the sensors to achieve so-called convergence. I call that HIT for horizontal image trnalation. The term convergence is confusing in these contexts because it can relate to both the zero parallax condition and the means to achieve it during photography by toe-in or horizontal lens axis shifting. Because of this confusion I call this the zero parallax setting (ZPS). I don’t like the term convergence when I am talking about this idea. 

From the get-go stereographers have been arguing about convergence.  They say: It’s okay to toe-in the cameras because the eyes toe in. But eyes and the brain are not the same as cameras and projectors.

Toe-in, not convergence, should be the terminology used for the inward or outward rotation of cameras to achieve a zero parallax condition.  Although it’s undesirable to use toe-in because of the design of some camera rigs, it’s expedient and its resultant trapezoid distortion, which leads to vertical parallax in projection.  However, in this the age of digital post trapezoidal distortion can be successfully countered in post using image distortion tools. Although I can’t kick about toe-in for features because or the rectification possible in post, for live camera feeds to theaters, for example, toe-in would probably create some real problems.

In a nut shell:  Don’t use the term convergence when you are talking about setting the zero parallax point (or plane) especially if you are doing CG because it could mean toe-in.  Note: Toe-in cannot produce a zero parallax plane.  A plane of zero parallax can only be achieved by means of horizontal translation of the lenses’ axes with respect to the image sensors.  Toe-in can only produce a warped surface with a zero parallax locus.

Make a distinction when using the term convergence between projected superimposed image points and the act of toeing-in the cameras heads.

As the poet said:  A rose by any other name smells as sweet but please don’t smell my feet.


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