Image Stabilization and Bokeh

How does IS/VR/SSS/OIS affect bokeh?
I have lately run across several conversations about image stabilization and its effect on bokeh.  Several people with long stabilized lenses have been reporting strange artifacts in foreground and background blurred objects.  Thin lines appear as double lines, like Nisen Bokeh, but they are only present when using the image stabilization, and NOT when using a tripod and IS/VR turned off.  I first heard of it at this link:

Since then I have been trying to understand why this would happen, and again, for me visualization is the key to understanding this.  Anyone who has done any panorama work knows about parallax error.  If your camera does not rotate exactly around the entry pupil of the lens (not the nodal point, as is often incorrectly asserted), your images won’t line up from one shot to the next.  This is essentially the same thing that causes these defects in stabilized lenses (and also in sensor shift technology).

IS and bokeh smaller

The above diagram demonstrates parallax in an image stabilized lens.  The central spot is kept sharply in focus, as it is “set” in the lens as the location which must be kept stable.  But the other spots will move depending on which direction you rotate the lens.  If however, the lens can be rotated exactly at its entry pupil, I believe that this effect should be virtually eliminated.  Why do you get a double line instead of just a straight smear?  When you are shaking the lens, you move it one direction and then another.  When you turn from one direction to the other, you have to go through a point of deceleration, then a full stop, followed by acceleration.  Therefore, more time is spent at and near the place where you switch from one direction to the other, therefore more exposure happens there.  So the question remains, is this effect mitigated when you have a lens with superb Bokeh, or does it affect mirror lenses and lenses with excellent bokeh equally?

Parallax and SA small

Despite the fact that the diagrams only show how this happens in lenses with in-lens image stabilization, exactly the same principle works for those with in body stabilization. 

How much movement do you need to reproduce the effect (updated 11/10/09)?
I have recently been thinking a bit more about this problem in a more abstract way.  Lenses can experience shake in both a rotary motion, as well as lateral motion.  From a non-stabilized lens perspective these are very different.  A slight lateral motion of the lens (if there is no rotary component) is no big deal, especially on far off subjects.  But when rotation is involved, one can get significant blurring of the image, even far away objects.   Here is a diagram of 1 mm of horizontal displacement and the angular movement of objects at different distances.

lens shift

As you can see, there is a VERY small a angular change from a 1mm horizontal displacement when taking a picture.  To the right I put the angular horizontal field of view of a full frame 35mm camera with lenses of different focal length.  If you divide this number by the number of pixels horizontally on your imaging sensor, you can get an idea of what horizontal angle every pixel images.  In my case, with a sony A900, with 6048 horizontal pixels, we divide the angular FOV of a lens by 6048.  Since I shoot portraits at around 135mm often, I get 15.2˚/6048.... every pixel images a horizontal angle of 0.00251˚.  That’s pretty small but even this horizontal motion should be detectable on objects closer than 10 meters.  That represents a 2 pixel blur at 10 meters and a 22 pixel blur at 1 meter.  That could certainly be noticeable.  With a 600 mm lens, a single mm of motion laterally with no rotation should cause a single pixel blur even at 100 meters.  Clearly parallax matters, and more so at close distances.

Adding in rotation makes it much more complex.  The reason we need fast shutter speeds is exactly because of rotary shake.  If anyone can hold a camera so incredibly still for a second that they do not even have an angle aberrancy of >0.00251˚ (one pixel) I would be very impressed.  If you can notice a shake when looking through the viewfinder, you are shaking orders of magnitude more than this.  This is what IS/VR was designed for.  While taking a picture, one might shake as much as 0.05 to 0.1 degrees on a longer exposure, which could be a 40 pixel blur!  VR/IS stabilizes an image by counteracting rotary blur in the focal plane.  While the workings actually use a small lens inside the camera to divert the light beam, its effect can be thought of as translating your rotary shift into a horizontal shift, and then rotating the entire camera to aim at the point on which you were focussing.  The amount of horizontal shift is actually quite complex-  it is zero if you happen to be shaking your camera exactly around the entrance pupil.  But most shaking doesn’t act so nicely, and the shaking you do will introduce some parallax error, which IS/VR/SSS can NOT correct for.

The next illustration shows what I mean.  While in a “real” rotary shake, the front of the lens element may move a millimeter up or down or side to side, and the little internal lens will deflect the light such that the in focus plane stays at the same place on the sensor.  This can be thought of as moving the lens down 1 millimeter and then rotating the whole camera to aim at the focal point, in this case Dc (10 meters away)

lens shift2

From the calculations, you can see that parallax error still comes into play when VR/IS is on, and it in fact AMPLIFIES the effect on more distant objects over mere horizontal non-rotary motion alone.  If you look at the above example, in a IS/VR corrected lens, if your shake introduces a small parallax error (which it essentially always will) of 1 mm, you can get a blur even on the more distant 100m object of  2 pixels (in my example with a sony A900 and a 135mm lens).  If a 600mm lens were used, it would have been a 10 pixel blur.

The reason I got interested in this in the first place was someone’s comments about their Canon 100-400 f/4 L. They claimed to get bad bokeh when the IS was turned on, and having no bokeh problems with IS turned off.  Others noted it on the 600mm L lens as well.  I think it is relevant that the reports like this were from owners of VERY LONG lenses.  I doubt there is much of an effect on a 24 mm lens.

If anyone has corrections, comments or mathematical genius to impart on me, I would appreciate it!  Has anybody done any testing on exactly how much shaking occurs when handholding a lens, both angular and translational?