# Earth’s Rotation Limits IBIS Performance to 6.3 Stops

In 2016, Olympus Camera made some buzz in the photo world when they claimed that their new camera was capable of an impressive 6.5 stops of stabilization and that the limiting factor was in fact the rotation of the Earth.  This was rather surprising given the slow and steady improvement since the first such stabilization systems were introduced in lenses in the 1990s.  These only provided a couple stops of benefit.  Since then the technology has improved dramatically and the move from film to silicon has allowed it to be incorporated into the camera itself as IBIS.

A major driver of this increase in stabilization performance has been in the gyroscopic sensors used to measure the vibration and control electronics used to correct it.  For these types of applications, the accuracy of the zero offset of the gyro sensor is often the limiting factor.  Even when perfectly still, noise will cause the sensor to read a small but non-zero value, which will in turn cause the stabilization system to drift.  The smaller the drift, the longer the stabilization system can hold an image steady.  If there were no noise on the gyro sensor and the stabilization system worked perfectly, it should in theory be able to provide an infinite number of stops of benefit.  However, at somewhere around 6 stops of shutter speed increase, the limiting factor stops becoming the electronics, and instead becomes the rotational motion of the Earth!

To illustrate , lets imagine that you are somewhere on the Earth’s surface, pointing the camera due East or West.  For simplicity, lets assume you are on the equator, but your latitude doesn’t actually matter for this analysis.  There are 86,400 seconds in a day, so Earth rotates at a rate of 2π/86400 radians/second, or 7.27*10^-5 rad/s.  That means that your subject, which is presumably stationary on Earth’s surface as well, is rotating at this rate.  Your camera, which is using its IBIS system to attempt to keep everything as still as possible, may not realize that you are rotating with your subject and will instead try to zero out any rotation of the camera, including that of the Earth.  More technically, the camera is trying to maintain stability with respect to an inertial reference frame, which by virtue of the Earth’s rotation, you and your subject are not.

The camera will of course move with the Earth and your subject, but will rotate relative to the subject.  If the camera is pointed east as shown in the figure above, it will rotate up relative to the subject.

Lets say that you have an exposure time given by the variable T.  IBIS will therefore cause the image to move by a distance on the sensor given by:

$FocalLength \times T \times 7.27*10^-5$

Using our typical standard for the maximum allowable blur to be 1 pixel width, we get the maximum allowable shutter time to be

$T = \frac{1}{Focal Length}\frac{PixelWidth}{7.27e^{-5}}$

A 24 megapixel full frame camera will have pixels that are 0.0059mm wide.  Plugging this into the above equation, we get

$T = \frac{81}{Focal Length}$

If we take 1/Focal Length as the standard advice for the maximum shutter speed you can use to achieve sharp images, this equation says we can use shutter speeds 81 times as long with stabilization before Earth’s rotation blurs the image by one pixel.  In more familiar terms:

$log_{2}(81) = 6.3$ Stops

Neat.  Of course not all cameras have the same 0.0059mm pixel pitch, but the rule for the maximum hand-held shutter speed will vary accordingly, so this 6.3 stops will be consistent across most cameras.  We can turn this around and say that in order to provide 6.3 stops of stabilization, the system must be able to measure and compensate for rotations of the camera as slow as the Earth’s, or 360 degrees per day.  That’s pretty impressive.

Presumably, a calculation like the one above or very similar was the inspiration for the claim by Olympus Camera:

“6.5 stops is actually a theoretical limitation at the moment due to rotation of the earth interfering with gyro sensors”

Since then the plot has thickened.  Olympus has released the OM-D E-M1X which claims to have 7.5 stops of stabilization, and Panasonic claims their new 70-200 f/2.8 has 7 stops of stabilization.  How could this be?  Without access to the data used to perform the CIPA stabilization rating test for these pieces of equipment, it’s difficult to say for sure.  In theory though, there are some possible ways to work around the limitations placed be Earth’s rotation:

1.   Use the camera’s GPS, accelerometer, and compass to calculate exactly where it is pointed and its latitude.  With this information you could calculate the necessary offset and program your stabilization system to compensate accordingly.
2.   Use a high pass filter on your stabilization system.  The rotation of the Earth is very constant, so if your gyro sensor should measure a small but constant rotation.  In comparison, your hands shake the camera all over the place, so an engineer could tell the sensor to only compensate for this later kind of motion.

The first isn’t a good solution for many reasons.  Don’t have GPS signal?  Shooting next to a magnet?  Your system won’t work.  The second solution is much more plausible, but still very difficult.  The user would have to be pointing the camera at the subject for long enough such that the drift in their aim at the subject is smaller than the drift from the rotation of the earth.  This is also implausible.  What is concerning though, is that this second method is one that could work very well to cancel out Earth’s rotation on the CIPA specified stabilization test apparatus.

For the CIPA stabilization test, the camera is mounted to a vibration platform.  The camera is then moved by the platform in a way that is determined by a CIPA provided waveform designed to mimic the motions from hand-holding a camera.  The setup is shown below:

In this test setup, the camera is mounted to a very stable platform and held there for a long time before and after the test images are being taken.  In theory, this could make it much easier to for the camera to identify and filter out any effects from Earth’s rotation.  If the waveform has no very low frequency components, it would be easy to identify any low frequency motion as Earth’s rotation.  Without knowing exactly what waveform is given to camera manufacturers to perform this test though, it’s impossible to draw any meaningful conclusions.  It would be great if we could get some independent verification of the stated stabilization values, but CIPA seems to make that deliberately difficult.  As quoted on their application guide:

• The applicant must be a corporate organization.
• The applicant must understand that the standard and measurement kit cannot be provided to individuals, universities, or any other parties for research purposes.

This seems unnecessarily restrictive to me and makes independent verification and analysis of the test impossible.

This has been a long way of saying that I don’t know if Olympus and Panasonic have found a way to compensate for the Earth’s rotation in their stabilization systems, breaking through the 6.3 stop limit, or if they are achieving 7+ stops through oddities of the CIPA rating test.  If anyone has one of these cameras with 7+ stops of stabilization and some time on their hands, it would be really cool to show the camera breaking through the Earth rotation barrier.  If the cameras can’t, and you could show that Earth’s rotation is actually the limiting factor on the stabilization system, well that would be pretty cool too.

## 19 thoughts on “Earth’s Rotation Limits IBIS Performance to 6.3 Stops”

1. Austin says:

Interesting! Explanation 2 does seem more likely than 1. But I also don’t think 1 would be too hard to make work
reliably in the real world. I imagine it’s not that sensitive to exact latitude, so you only need coarse GPS
coordinates and a lazy cache. And magnetic interference is uncommon enough that you could just let it fail in
that case, especially if you can detect the interference and fail gracefully. But the real reason 2 seems more
likely is that I think if camera makers were doing this they would brag about it in their marketing.

1. David Berryrieser says:

Totally agree. Also, explanation 2 is pretty close to the methods that are already built in to the electronic gyros for correction zero bias. Not exactly the same as those usually want the chip to be stationary for calibration, but after calibration the offset bias noise is spec’d far lower than Earth’s rotation rate.

2. For what it’s worth, this is the “vibration apparatus” – https://www.physikinstrumente.com/en/products/parallel-kinematic-hexapods/h-840-6-axis-hexapod-700810/

I would imagine “gen 2” of the standards will use the gen 2 of this hexapod, but its payload is too small in this incarnation – https://www.physikinstrumente.com/en/products/parallel-kinematic-hexapods/h-860-high-dynamics-motion-hexapod-700891/

If you have 75k burning a hole in your pocket, I see no reason why PI wouldn’t sell you a unit of the 840 with controller. You could inquire with them about vibration simulation, I’m sure they won’t disclose anything CIPA proprietary, but I’m also sure CIPA hasn’t implemented much more vis-a-vis trajectories than the ones PI provides out of the box as demos.

1. David Berryrieser says:

Thanks, that’s very useful. But yeah, wouldn’t say I had that kind of cash sitting around to throw at this kind of thing. Agreed, I don’t think the CIPA waveforms for the vibrations are particularly sophisticated. I could also easily make my own with simple gyro chip attached to the camera.

3. Piotr says:

Wait. Imagine you’ve a perfectly stable tripod. The accelerometer inside the IBIS will happily report a constant acceleration (gravity + inertial rotation of the Earth), during all the exposure time, even if it is 1 hour, and IBIS will not move (ok, in reality, the accelerometer will be noisy and the IBIS will introduce some random motion, but that’s not the point). The point is the the rotation of the Earth has nothing to do with the stabilization.

1. David Berryrieser says:

Its not the accelerometer that is principally involved in making IBIS work, it is the Gyroscope. So if the camera is on a tripod, the gyro will report the camera as rotating due to the rotation of the earth. A simple, perfectly working IBIS system would then try to compensate for that rotation.

1. Piotr says:

Ah, ok, thanks for the info. Then indeed the problem arises. They use a gyro because it is more accurate?

1. David Berryrieser says:

Well, a gyro is used because the accelerometer can’t detect rotation. And rotation of the camera is principally the cause of image softness. Small lateral or vertical movements don’t matter much at normal shooting distances. In lens stabilization systems only compensate for pitch and yaw rotations, not the other 3 axes (roll, left/right, up/down).

2. So does all this have any bearing on the “turn off IBIS while on tripod” argument?

1. David Berryrieser says:

Unclear. It depends on the specific implementation of IBIS. Most IBIS systems these days have a tripod detection mode which automatically turns IBIS off. Also, if there is a high pass filter implemented, being on a tripod wouldn’t matter. In principle though, yes, Earth’s rotation could cause IBIS to make the image soft during long exposures.

3. julia deiuliis says:

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4. Thanks Dave for writing this up. It’s a very cool calculation!

1. David Berryrieser says:

Thanks for posting this, it is an interesting interview in this context. It still isn’t totally clear to me what algorithms they are referring to with the Gyro. But yeah, it isn’t approach 1.

5. Great article. This page and the LensRentals blog are my happy places on the internet because they present actual data instead of stupid fanboy “this lens renders beautifully!” arguments.

1. David Berryrieser says:

Thanks! The lens rentals guys do great work, and I will happily be thrown in the same bucket with them.

6. Felix G says:

I see two problems with this theoretical limit of 6.3 stops:

– The 1/focal length rule comes from an age of analoge film printing to something like 8×10 inch. With the current high resolution sensors it is nearly impossible to consistently get pixel sharp images with those times. I personally would go at least a stop faster, better 2 if i want to ensure a very sharp image.
– The situation changes even more if you the photographer has no stable platform to stand on. In a moving car, on a rocking boat, you name it. This reduces the maximum exposure time you can use for sharp images even further, given stablization systems a loot more room than 6.3 stops before they run into any problems with earth rotation.

1. David Berryrieser says:

This is why we assume a modest 24MP sensor. Also, loss of sharpness in an image is noticeable well before we get to 1 pixels worth of blur.