Gimbal Lock and Derotation in FLIR/ATFLIR systems

[Mick West]

Source: https://www.youtube.com/watch?v=4X1PRDbtiF0


The above video is an attempt to demonstrate how a system mounted like the ATFLIR targeting pod:
A) requires a derotation mechanism
B) require major camera movements around 0°

It's a tricky thing to explain, and I anticipate this thread getting somewhat detailed and technical, but unless Raytheon wants to weigh in then some digging will be required to figure out exactly what is going on with this rotating glare.

What I'd like to do is collect as many references as possible that address this issue, to help paint a better picture.

One interesting patent I found is US9121758 - "Four-axis gimbaled airborne sensor having a second coelostat mirror to rotate about a third axis substantially perpendicular to both first and second axes" held by Raytheon, which has this interesting discussion on the need for derotation:
https://patents.google.com/patent/US9121758

However, due to this rotation around the roll axis 242, the image from the far field object or scene is also rotated. In order to correct for the rotation of the image, the derotation device 330 is configured to counter-rotate so that the image output by the derotation device is in the same direction independent of the rotation of roll gimbal around the roll axis 242 or the rotation of the first coelostat minor 220 around axis 244 or the rotation of the second coelostat minor 230 around axis 248. In one embodiment, the derotation device 330 is an optical prism. In other embodiments, the derotation device 330 may include reflective optical elements (e.g., minors) and can be, for example, an all-reflective derotation device. However, as it will be appreciated by those skilled in the art that other types of derotation devices can also be used. Furthermore, the derotation device 330 can be omitted, and the derotation function may be accomplished electronically or through image data processing.

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And also the issue near the 0° position, referred to to as "gimbal lock" or "gimbal singularity"

As discussed above, when the orientation of the first coelostat minor 220 is such that the sensor line of sight direction is precisely parallel to the roll axis 242, rotation of the gimbal-mounted optics about the roll axis does not change the line of sight direction. This situation where the roll axis cannot steer the line of sight is referred to as a gimbal singularity or gimbal lock. In certain circumstances where the gimbal singularity cannot be avoided, for example because the gimbal singularity is within the desired field of regard (FOR), a fourth gimbal axis 246 may be provided within the plane of the first coelostat mirror 220 and perpendicular to the first rotation axis 244. In one embodiment, the fourth gimbal axis 246 resides on the first rotation axis 244 of the first coelostat minor 220 in that a rotation of the first coelostat minor 220 around the first rotation axis 244 produces a rotation of axis 246. The fourth gimbal axis 246 may be of small angular travel (for example, less than or equal to 5 degrees). As a result, axis 246 travels around the roll axis 242 and avoids the gimbal singularity.

For example, referring again to FIG. 3, when an object being continuously tracked by moving the first coelostat minor 220 in various directions by rotating around the first rotation axis 244 and/or around roll axis 242and/or optional fourth axis 246 using control system 390 is projected to go close to or through the gimbal singularity, and optional fourth gimbal axis 246 is provided with a range of angles (for example, ±3 degrees), the roll axis 242 is no longer used for tracking the object within the ±3 degree range that surrounds the gimbal singularity. Instead, the first rotation axis 244 and fourth gimbal axis 246 are used to continue to track the object within the ±3 degree angular range. When, on the other hand, the object location exceeds, for example, the ±3 degree singularity, the roll axis 242 is used by control system 390 in the tracking motion. In this case, the fourth axis 246 may be gradually returned to 0 degrees and no longer has involvement in the tracking motion. In other words, control system 390controls the tracking by rotating the first coelostat mirror 220 around the fourth gimbal axis 246 when an object is located closely around the singularity (e.g., within the ±3 degree range). Otherwise, when the object is outside the ±3 degree range around the singularity, control system 390controls the tracking by rotating the roll axis 242 and leaving the fourth axis 246 fixed or returning the third axis to 0 degrees.

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The mention of +/- 3° is particularly interesting, as all the major apparent motion of the object happens between -3° and +4°

 

[jarlrmai]

Is it worth mentioning that the jet can also rotate and the the camera has to adjust for that as well?

 

[Mick West]

Copied this from my post here: https://www.metabunk.org/posts/217222/


Another source of info for the ATFLIR obsessed is Raytheon's patents.
https://patents.google.com/?q=gimbal&q=IR&q=rotation&q=visible&assignee=raytheon


https://patents.google.com/patent/US6288381B1/

Ideally, a high resolution imaging and laser designation system in a highly dynamic disturbance environment would typically have, at least, a four gimbal set, with two outer coarse gimbals attenuating most of the platform and aerodynamic loads and the two inner most, flexure suspended gimbals providing fine stabilization, with the inertial measurement unit (IMU), IR and visible imaging sensors, and a designating/ranging laser located on the inner most inertially stabilized gimbal.

To reduce gimbal size, weight and cost, the assignee of the present invention has developed a pseudo inner gimbal set for use on various tactical airborne and airborne surveillance systems. This pseudo inner gimbal set uses miniature two-axis flexure suspended mirrors mounted on the inner gimbal together with the IMU and IR sensor, in a residual inertial position error feedforward scheme. The pseudo inner gimbal set replaces the two innermost fine gimbals, while maintaining equivalent performance. With increasing aperture size and constraints required to maintain the size of existing fielded systems, some tactical airborne IR systems are forced to locate the IR and visible sensors and laser off the gimbals using an optical relay path.

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The following diagram is a schematic of an ATFLIR, with the nose (and hence the windows) on the left. It explains that the image is "derotated" by "a reflective derotation mechanism 25" (and another for the visible light at 35).

 

[Mick West]

An interesting analysis along these lines on YCombinator from colanderman, who discusses the gimbal lock issue, and hypothesizes it's some warm bird poop on the camera

https://news.ycombinator.com/item?id=20019375

It's appropriate that the first video is called "gimbal", because that's exactly what it is.

Watch the angle readout at the top of the video. The rotation of the object happens exactly around the time that the angle passes 0°. Why is this?

Have you ever watched a PTZ security camera rotate up and over the vertical axis and down the other side? It will tilt up until it nears the vertical axis, at which point it will rotate around that axis, and then tilt back down, now facing the other way. It does this to avoid gimbal lock [1], a state in which it would lose a degree of freedom of rotation. (In this case, it's not the vertical axis, but the forward axis.)

Why doesn't the image rotate then? [shallow speculation] The video software keeps it oriented so that it matches the plane's orientation. (Note that the feed is square, making it easier to make full use of the sensor regardless of rotation.)

Why does the object rotate? This should give you a clue where the object is. If the background is not rotating while the camera is rotating, but the object is, the object is on the camera. It will appearto rotate as the video software rotates the image to compensate for the camera rotation about the forward axis.

So why is the object moving? Well, it's not moving, not if it's on the camera. But whenever the camera moves, it would look like it's moving relative to the background.

So why is the camera moving? It's tracking the object. But the object isn't moving! Well, the camera doesn't track movement. It tracks position. The object is slightly offset from the center of the frame, so the tracking software slightly moves the camera to compensate. This of course does not change the situation, so the tracking software repeats its compensation. This constant camera movement in a single direction gives the appearance that the object is moving.

Why does the object show up on an infrared camera in the first place? It must be warm.

So… what is this warm object, which is stuck on the camera, slightly off-center, causing the tracking software to follow it, through and around the camera's axis, giving the appearance that the object is moving and then rotating?

Well, it's the same thing as this article in the NY Times, which, in service of securing funding from the UFO & Hitler Channel (as @floatrock astutely noted), decided to lend its gravitas to an easily-explainable video glitch which has been paraded by conspiracy theorists as incontrovertible validation of their deepest-held beliefs that extraterrestrials, against all probability, regularly visit Earth.

Bird shit.

Why am I paying for a NY Times subscription again?

[1] https://en.wikipedia.org/wiki/Gimbal_lock

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While the gimbal lock analysis is fine, the bird poop explanation does not really hold up, as there's a distinct size change, which seems to indicate the object is getting closer and/or brighter

 

[Agent K]

I demonstrate gimbal lock by making a "thumbs up" gesture and showing how I can "pan" left and right and roll the first, but not tilt up and down. To point it down, I'd have to roll 90 degrees first.

 

[Mick West]

I demonstrate gimbal lock by making a "thumbs up" gesture and showing how I can "pan" left and right and roll the first, but not tilt up and down. To point it down, I'd have to roll 90 degrees first.

I don't follow, where's the lock?

 

[Mick West]

The mention of +/- 3° is particularly interesting, as all the major apparent motion of the object happens between -3° and +4°

An interesting thing with that range is that it's a good chunk of range that the Nimitz/FLIR/Tic-Tac goes over, from 4° right to 6° Left, and as it goes past 2° left there's a fairly distinct rotation of a light area in the background, then a slightly less distinct one at

Which all is very consistent with the idea of a glare being rotated by the camera.

 

[Agent K]

I don't follow, where's the lock?

It's the same thing you show in the video, just using a fist instead of sticks.

 

[Mick West]

It's the same thing you show in the video, just using a fist instead of sticks.

But a fist has more degrees of freedom. With the thumb up I can rotate around all three axes. The gimbal setup can only rotate around two.

 

[Agent K]

But a fist has more degrees of freedom. With the thumb up I can rotate around all three axes. The gimbal setup can only rotate around two.
View attachment 37557

I know, but pretend it can't tilt up and down.
I also demonstrate the North-East-Down axes with the left hand by extending the index finger forward (North), thumb to the right (East), and middle finger down. Then, I can show the yaw-pitch-roll rotation from NED into image coordinates Depth-Column-Row.

 

[Candy-O]

How would FLIR footage of a disc shaped craft that rotates on it's side DIFFER from what we see in the gimball video? Or an actual tic-tac shaped object differ from what we see on the Nimitz footage? I'm not going down any logical path here, I'm just curious how you feel footage of objects as described would differ from what we see.

 

[Mick West]

How would FLIR footage of a disc shaped craft that rotates on it's side DIFFER from what we see in the gimball video?

I'd expect it to remain the same profile through the video, whereas it actually changes shape quite a lot.

Or an actual tic-tac shaped object differ from what we see on the Nimitz footage?

Similar here, the shape of the "object" changes in both visible light and infrared. which suggests something more like an irregular object.

 

[Gerard]

Similar here, the shape of the "object" changes in both visible light and infrared. which suggests something more like an irregular object.

Can you describe what this image is showing. Is the upper image visible and the lower IR ? If so why aren't the engines showing as hot spots ?

 

[Mick West]

Can you describe what this image is showing. Is the upper image visible and the lower IR ? If so why aren't the engines showing as hot spots ?

It's a simulated back-lit image of a plane, where the lower one is more blurred. See 1:54 here:
Source: https://youtu.be/s1oTg0kxzDs?t=114

 

[Mick West]

This patent is interesting, in that it focuses largely on derotation, and discusses the corrections for gimbal lock.
https://patents.google.com/patent/EP2525235B1/



Discussing different methods of derotation:

However, due to the rotation of portion 11A mounted on roll gimbal and thus to the rotation of c-mirror 12 around axis BB, the image from the far field object or scene is also rotated. In order to correct for the rotation of the image, derotation device 20 is configured to counter-rotate so that the image output by the derotation device is in the same direction independent of the rotation of roll gimbal around axis BB or the rotation of c-mirror around axis AA. In one embodiment, derotation device 20 is an optical prism. In another embodiment, derotation device 20 may include reflective optical elements (e.g., mirrors) and can be, for example, an all-reflective derotation device. However, as it can be appreciated other types of derotation devices can also be used. Furthermore, in one embodiment, derotation device 20 can be omitted. In this case, the derotation function can be accomplished electronically or through image data processing.

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Discussing gimbal lock

• In one embodiment, whenever the orientation of c-mirror 12 is such that the sensor line-of-sight direction (LOS) is precisely parallel to roll axis BB, for example as shown in FIG. 4B or as shown schematically in FIG. 1, a rotation of the gimbal or portion 11A of optical system 10 around roll axis BB would not change the LOS direction. On the other hand, when c-mirror 12 is oriented such that the LOS direction is at a certain angle α relative to roll axis BB (α is the angle between roll axis BB and LOS direction), for example as shown in FIGS. 3A-3C, 4A, 4C, 5A-5C (e.g., α equal to about 45 deg, about 60 deg., or about 90 deg.), a rotation of the gimbal or portion 11A of optical system 10 around roll axis BB causes the LOS direction to sweep out a cone centered about roll axis BB (e.g., with an angular diameter equal to about 2x45 deg., about 2x60, or about 2x90). The situation where the LOS is precisely parallel to roll axis BB and thus causing the roll axis BB to not steer the LOS [Line of Sight] is called a "gimbal singularity" or "gimbal lock." A control gain of roll axis BB is proportional to 1/sinα. Hence, the gain of roll axis BB can go to infinity when α is equal to 0, i.e., when the LOS is precisely parallel to roll axis BB. From the standpoint of an automated control system 90 (shown in FIG. 1) for controlling the orientation of c-mirror 12, i.e., controlling the rotation around roll axis BB and rotation around axis AA, this gimbal singularity may be problematic because no amount of rotation around roll axis BB produces any desired effect of steering the LOS.
• [0037]
  As a result, in certain applications, the gimbal singularity is to be avoided. However, in an embodiment, where the gimbal singularity cannot be avoided, for example because the gimbal singularity is within the desired field of regard (FOR), then it may be desirable to provide a third gimbal axis TT (shown in FIG. 1). In one embodiment, third gimbal axis TT is within the plane of c-mirror 12 and is perpendicular to rotation axis AA. In one embodiment, the third gimbal axis TT resides on rotation axis AA of c-mirror 12 in that a rotation of c-mirror 12 around axis AA produces a rotation of axis TT. The third gimbal axis TT can be of small angular travel (for example, less than or equal to 5 deg.). As a result, axis TT travels around roll axis BB and avoids the gimbal singularity.
• [0038]
  For example, when an object being continuously tracked by moving c-mirror 12 in various directions by rotating around rotation axis AA and/or around roll axis BB and/or optional third axis TT using control system 90 is projected to go close to or through the gimbal singularity, and optional third gimbal axis TT is provided with a range of angles α, for example, ±3 deg, roll axis BB is no longer used for tracking the object within the ±3 deg. range that surrounds the gimbal singularity. Instead, rotation axis AA and third gimbal axis TT are used to continue to track the object within the ±3 deg. angular range. When, on the other hand, the object location exceeds, for example, the 3 deg. singularity, roll axis BB is used by control system 90 in the tracking motion. In this case, the third axis can be gradually returned to 0 deg. and no longer has involvement in the tracking motion. In other words, control system 90 controls the tracking by rotating c-mirror 12 around third gimbal axis TT when an object is located closely around the singularity (e.g., within the ±3 deg. range). Otherwise, when the object is outside the ±3 deg. range around the singularity, control system 90 controls the tracking by rotating roll axis BB and leaving the third axis TT fixed or returning third axis TT to 0 deg.

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[Mick West]

This A10 targetting pod footage is interesting.
Source: https://youtu.be/If53pV3ibo0?t=130


It shows derotation, possibly in software, and you can actually see the frame rotate - i.e. there are dark areas of no image that rotate around.


There's also a display that pops up "GIMB ROLL" just before it does a major gimbal roll. Unfortunately, the video fades to a different shot at the same time.

 

[Ravi]

It shows derotation, possibly in software, and you can actually see the frame rotate

I think it actually is caused by the vignetting occurring at the de-rotator part. A square mirror design of this part would result in a square (blocking) frame.

It could of course be software, but I doubt it as it, is prone to errors etc. A hardware solution is likely preferred.

Here is a link to a similar de-rotator design, but for an instrument used on a large telescopes (VLT). VLT telescope design (altazimuth mount) causes the FoV to rotate as Earth rotates.

https://www.researchgate.net/figure/Optical-concept-for-the-ESO-MCAO-Demonstrator_fig1_41194920

As can be seen it involves 3 mirrors, that rotate radially along the optical axis.

 

[Mick West]

It could of course be software, but I doubt it as it is prone to errors etc

Rotating an image isn't really a complex bit of software, so long as the hardware can supply the correct angle, there would be zero problems.

 

[Ravi]

Rotating an image isn't really a complex bit of software, so long as the hardware can supply the correct angle, there would be zero problems.

True, I can imagine..

But, why then have a de-rotator in the design... hmm...

 

[Max Phalange]

It shows derotation, possibly in software, and you can actually see the frame rotate - i.e. there are dark areas of no image that rotate around.

There's some quite noticeable circular blur around 0:39, which suggests that the sensor is static relative to the gimbal rotation. If the de-rotation happened optically before hitting the sensor, this shouldn't happen.

 

[Amber Robot]

I think it actually is caused by the vignetting occurring at the de-rotator part. A square mirror design of this part would result in a square (blocking) frame.

It could of course be software, but I doubt it as it, is prone to errors etc. A hardware solution is likely preferred.

Here is a link to a similar de-rotator design, but for an instrument used on a large telescopes (VLT). VLT telescope design (altazimuth mount) causes the FoV to rotate as Earth rotates.

https://www.researchgate.net/figure/Optical-concept-for-the-ESO-MCAO-Demonstrator_fig1_41194920

As can be seen it involves 3 mirrors, that rotate radially along the optical axis.

In astronomy, I have heard this called a "K Mirror". I gave a presentation once on how a telescope might be retrofitted with a K Mirror and had to look into this a bit.

Also, a similar situation to the "gimbal lock" happens with alt-az telescopes when tracking objects that pass through or near the zenith. This is usually not allowed because the azimuth speed wants to go to infinity when an object passes directly overhead.

 

[Ravi]

In astronomy, I have heard this called a "K Mirror". I gave a presentation once on how a telescope might be retrofitted with a K Mirror and had to look into this a bit.

Indeed! I forgot about this term. I worked for ESO in the past, on adaptive optics instruments.

 

[gtoffo]

Source: https://www.youtube.com/watch?v=4X1PRDbtiF0

I think this theory makes a lot of sense. But I have a couple of questions:

1. If I understand this correctly we are assuming the rotation is caused by the gimbal crossing the centerline and having to make a rotation to keep tracking the object without locking correct?
2. Shouldn't then the rotation be a full 180° rotation given the flat plane (-2 degrees vertical) as your video shows? The rotation seems to be much less.
3. Also the movement does not seem in a uniform single motion contrary to the "GIMB ROLL" videos posted (although the systems are different and in different modes). Is this expected? I see intermittent rotation at 13°L, 6°L, 3°L, 0, 4°R
   
   Thanks

 

[Mick West]

1. If I understand this correctly we are assuming the rotation is caused by the gimbal crossing the centerline and having to make a rotation to keep tracking the object without locking correct?
2. Shouldn't then the rotation be a full 180° rotation given the flat plane (-2 degrees vertical) as your video shows? The rotation seems to be much less.
3. Also the movement does not seem in a uniform single motion contrary to the "GIMB ROLL" videos posted (although the systems are different and in different modes). Is this expected? I see intermittent rotation at 13°L, 6°L, 3°L, 0, 4°R

The gimbal roll is an adjustment to allow for continued tracking using the internal mirrors and possibly the azimuth rotation. The system will seek to minimize such movements, as they are coarse, and can result in jitter and/or loss of lock. The algorithm it uses to decide when to rotate and by how much is unclear.

In the older 2004 FLIR1 footage, you see two gimbal rolls. In the larger roll tracking is lost.

So it might be that newer systems try to apply the gimbal roll corrections in a more intelligent way to minimize this.

 

[gtoffo]

The gimbal roll is an adjustment to allow for continued tracking using the internal mirrors and possibly the azimuth rotation. The system will seek to minimize such movements, as they are coarse, and can result in jitter and/or loss of lock. The algorithm it uses to decide when to rotate and by how much is unclear.

In the older 2004 FLIR1 footage, you see two gimbal rolls. In the larger roll tracking is lost.

So it might be that newer systems try to apply the gimbal roll corrections in a more intelligent way to minimize this.

FLIR1 shows exactly what I would expect. A rapid full 180° rotation if I'm not mistaken. That is not what gimbal shows.

From what we know of the physical structure of the ATFLIR (a head that swivels ~90° mounted on a platform that can rotate 360°. That's also what I see you reproduced in the video above also) the 180° rotation of the external window is necessary to track the object across the horizon or isn't it?

Nothing I can think of can prevent this unless the head can swivel more than 90° and that would negate gimbal lock across the 0° and the whole theory that what we are looking at is the ATFLIR rotating to avoid lock. Maybe the new versions have a head that is able to do this and gimbal lock is a non issue?

Or am I missing something? Thanks

 

[Mick West]

FLIR1 shows exactly what I would expect. A rapid full 180° rotation if I'm not mistaken. That is not what gimbal shows.

That difference is what I was explaining. FLIR1 nearly fails to reacquire tracking with its single big roll. The newer GIMBAL video does smaller rolls, and very little recentering is required.

It's 11 years later, seems entirely reasonable that the algorithm and maybe the hardware had improved.

 

[gtoffo]

That difference is what I was explaining. FLIR1 nearly fails to reacquire tracking with its single big roll. The newer GIMBAL video does smaller rolls, and very little recentering is required.

It's 11 years later, seems entirely reasonable that the algorithm and maybe the hardware had improved.

Yes but it can't "make smaller rolls". The full 180° roll is required given the physical constraints of a 90° swivelling head. Or NO rotation is needed if the head swivels 180°.

There is no way of getting past this limit that I am aware of. Do you have any ideas to get past this problem?

 

[Mick West]

There is no way of getting past this limit that I am aware of. Do you have any ideas to get past this problem?

Sure, if you combine it with a pointing system inside the head (the mirrors), you get much more leeway regarding how much you need to roll and when. It's not just a 2-axis camera + derotation. It's 2 coarse axes, and 1-3 fine mirror axes, plus derotation.

 

[gtoffo]

Sure, if you combine it with a pointing system inside the head (the mirrors), you get much more leeway regarding how much you need to roll and when. It's not just a 2-axis camera + derotation. It's 2 coarse axes, and 1-3 fine mirror axes, plus derotation.

You mean within the system there are mirrors that "point" the camera without moving the external window? So for example it may stay fixed externally but internally move and track an object making small movements (that would make sense)? I wasn't aware of that. Even so with large movements across the centerline the full 180° rotation is still always needed as the external structure must also move. Right?

I might have missed something here but I'm asking those questions because aren't we theorising that the glare is generated by the external window and follows its rotation? Or is there something else that might cause the glare+rotation within the internal components? Or do we just don't know exactly what might cause this.

Thanks

 

[Mick West]

You mean within the system there are mirrors that "point" the camera without moving the external window?

Yes, this patent describes them as "coelostat mirrors", also discusses not wanting to use the main roll axis.
https://patents.google.com/patent/US9121758

Conventional airborne sensor systems generally have ability to maintain a desired pointing direction as the aircraft rolls and changes forward direction in azimuth. However, conventional systems generally cope poorly with significant changes in aircraft pitch. One approach to compensating for aircraft pitch uses the roll axis. However, as illustrated schematically in FIGS. 1A and 1B, there is typically significant hardware, including the complete afocal telescope 110, mounted on the roll axis. As a result, compensating for aircraft pitch by rotating the roll axis may require significant power to move the large associated mass, and also is not fast (or agile) and may not be particularly accurate. The problem is particularly challenging in the case of a multi-function airborne sensor, such as that discussed in U.S. PG Publication No. 2012/0292482, where alignment and pointing accuracy must be maintained for several different optical sub-systems performing different functions.

Aspects and embodiments are directed to an optical configuration for an airborne sensor that allows for agile compensation of platform pitch while also maintaining all the functionality and advantages of the multi-function airborne sensor disclosed in U.S. PG Publication No. 2012/0292482. In particular, aspects and embodiments include a dual coelostat airborne sensor configuration that enables level horizon pointing when the platform is pitched at large angles. Referring to FIGS. 2A and 2B, a gimbaled optical portion 310 a of an airborne sensor system according to one embodiment includes afocal foreoptics 110 optically coupled to a fold minor 210, a first coelostat mirror 220, and a second coelostat mirror 230. The first coelostat minor 220 corresponds to the coelostat minor 120 discussed above as used in a similar system. The afocal foreoptics 110, fold mirror 210, and first and second coelostat minors 220, 230 are mounted on a roll gimbal that rotates about an outermost roll axis 242 (first gimbal axis) that is generally parallel to the beam of electromagnetic radiation output by the afocal foreoptics 110. The first coelostat minor 220 rotates around a first rotation axis 244 (second gimbal axis) that is parallel to the beam of radiation 250 a reflected by the first coelostat minor 220, and perpendicular to the roll axis 242, as discussed above. The second coelostat mirror 230 rotates around a second rotation axis 248 (third gimbal axis) that is parallel to the beam of radiation 250 b reflected by the second coelostat mirror 220 and substantially perpendicular to the first rotation axis 244. This rotation of the second coelostat mirror 230 is used to compensate for pitching motion of the platform, thereby allowing the line of sight of the system to be maintained in a desired direction (determined by rotation of the first coelostat mirror 220 to a desired angle) even as the platform pitches over a relatively large angular range, as discussed further below. Rotation of the first coelostat minor 220 about a fourth gimbal axis 246 is used to compensate for a gimbal singularity, as also discussed above and further below.

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Or do we just don't know exactly what might cause this.

This, basically, because the patent are both not easy to read, and often have various possible embodiments.