<p>Can I assume that &quot;piston, horizontal &amp; vertical decentering&quot; correspond to 3D positioning in space and &quot;tip, tilt, and clocking&quot; correspond to attitude? Could someone help translate these into more explicit terminology?</p>
<p>How explicit??</p>
<p>To answer your direct question, yes, you've got the concept.  There is &quot;Translation&quot; or just X,Y,Z motion followed by &quot;Rotation&quot; about X,Y axis. Clocking is rotation about Z. (assuming Z is normal to mirror surface)</p>
<p>Simply put, imagine a tabletop with a plate on it. &quot;Piston&quot; is lifting the plate flat upwards off the table. &quot;Horizontal and vertical&quot; is analogous to  simply pushing the plate around on the surface of the table. &quot;Tip and tilt&quot; amount to lifting one edge of the plate. Finally, &quot;clocking&quot; is turning the plate so what you want to get to easily is right in front of you. (or what you dislike is away!)</p>
<p>As a side note... in January I did a calculation based on Warden's gearing numbers and believe each hexapod actuator went thru 50 fine cycles at mirror deployment.</p>
<p>edit to add:</p>
<p>because of the way the actuator uses a single motor to drive both coarse and fine modes an interesting coupler was devised. (fig 5 in Warden's paper) When the mirror segments were being moved 12mm from stowed location the fine mode was also being driven at same time. Since fine mode is driven by a cam the mirror flexed its focus shaping to full extents 50 times. When segments reached deployed position the drive motor reverses and the coupler 'backs away' from coarse drive, leaving just the fine mechanism driven.</p>

CC BY-SA 4.0
2022-03-16T05:39:25.800Z
Yes, I think you're right. 'Clocking' was the one that had me a bit puzzled. When I google 'clocking' and 'telescope' it refers to mechanisms  for tracking stars across the night sky.  I'm sure, as you say, 'tip, tilt, and clocking' refers to 'pitch, yaw, and roll' along the z-axis.
Roger Wood
CC BY-SA 4.0
2022-03-16T05:40:25.983Z
any insights regarding the last paragraph of the question?
Roger Wood
CC BY-SA 4.0
2022-03-16T14:48:06.823Z
@Roger Wood I will be the first to admit that I am not by any means an expert on these types of optics. However, I spent my youth in photography and in college worked semiprofessionally with view cameras in which the front lensplate and rear filmplate could be independently tilted and rotated. I 'was' knowledgeable. AND SO... about the need for mirror segment clocking. I believe this relates to the fact that the mirror is parabolic and the segment surface is not symmetrical about the Z axis. I welcome feedback on this!
BradV
CC BY-SA 4.0
2022-03-16T15:21:36.227Z
Each segment's edge have three different directions, resulting in a diffraction pattern with spikes in three directions. If the segments are not "clocked" equally, i.e. if their edges are in more than three directions, the diffraction pattern will be more complex, which is not desired.
pela
CC BY-SA 4.0
2022-03-16T15:30:59.163Z
THX! I was wondering about what kind of effects needed to be considered with a segmented mirror. Was any edge 'softening' (for lack of a better term) employed?    Also, was any part of my understanding significantly flawed?  I believe @David Hammen commented much earlier "Roll helps cure astigmatism issues." Is this kind of the same thing?
BradV
CC BY-SA 4.0
2022-03-16T22:46:11.700Z
No, your answer is great :)  But I'm unsure what you mean by "edge softening"? Wrt. how roll would cure astigmatism, I don't know, I'd think that astigmatism would be caused by the segments having different heights/shapes and hence different foci. But I think it has to do with the mirror's asymmetry causing the wavefront to be… hmm… "asymmetric" for lack of a better word. There a document [here](https://www.telescope-optics.net/astigmatism1.htm) that might help. Btw., make sure to "tag" people if you want them to get a notification of your comments :)
pela
CC BY-SA 4.0
2022-03-16T04:07:06.397Z
2022-03-16T15:15:35.607Z
2022-03-16T15:15:35.607Z
BradV
<p>Each of the primary mirrors has seven degrees of freedom, not six. It's just the secondary mirror that only has six degrees of freedom. The six degrees of freedom for the eighteen primary mirrors and the one secondary mirror are for positioning and attitude. The seventh degree of freedom in each of the eighteen primary mirrors applies to shaping.</p>

CC BY-SA 4.0
2022-03-01T18:21:46.350Z
Yes, I did mention that in the question
Roger Wood
CC BY-SA 4.0
2022-03-01T18:24:16.627Z
Roll helps cure astigmatism issues. Shaping helps some, but since there's only one DOF for shaping, it's not quite enough.
David Hammen
CC BY-SA 4.0
2022-03-01T19:01:09.857Z
good point. there's a deliberate cylindrical component to the mirror surface but any additional cylindrical error could potentially be corrected by a roll adjustment.   (does "clocking" refer to roll?)
Roger Wood
CC BY-SA 4.0
2022-03-01T22:09:28.920Z
"The six degrees of freedom... are for positioning and attitude." I thought that many are used for adjusting the *shape* of the primary mirror segments not just their rigid-body attitude, am I wrong? Of course changing the shape of a fixed-position mirror and changing the position of a fixed-shape mirror can have some overlapping optical optimization functionality, but I thought that they really bend the mirrors with the actuators.
uhoh
CC BY-SA 4.0
2022-03-01T23:49:56.467Z
@uhoh yes, I was under the same impression, but , apparently, only one is for spherical correction (focal length), the other six are for rigid body position and attitude.  Wikipedia JWST says much the same thing "Six positional actuators with a further ROC (radius of curvature) actuator at the center to adjust curvature".  They must be very confident that the mirrors will change shape in a small predictable manner between fabrication at room temperature and final operating temperature.
Roger Wood
CC BY-SA 4.0
2022-03-02T03:47:32.380Z
@RogerWood *Interesting!* Thanks
uhoh
CC BY-SA 4.0
2022-03-02T16:26:55.940Z
@RogerWood  since there's no atmospheric turbulence to deal with, there's no need to adjust the shape of each segment at greater spatial frequencies.  Next, given the overall design curvature of the primary assembly, I suspect the difference between spherical and aspherical curvature or, at least, the deformation caused by the 7th actuator) of each segment is too small to be controllable in any sensible way.
Carl Witthoft
CC BY-SA 4.0
2022-03-16T03:37:29.483Z
@RogerWood I'm guessing that by now you've checked out the various "hexapod" videos.  Is the term "clocking" of mirror clear now? Since primary mirror as a whole is roughly parabolic, each individual segment must have the ability to be rotated to to achieve best performance.
BradV
CC BY-SA 4.0
2022-03-16T04:13:49.613Z
@Roger Wood I suspect that the machining of each segment (three  different 'types' in primary mirror) and location of anchor points for the 7th actuator were tuned so that each segment deformation tuning would be consistent with overall parabolic mirror performance.
BradV
CC BY-SA 4.0
2022-03-01T18:19:39.270Z
2022-03-01T18:19:39.270Z
David Hammen
<p>This <a href="https://www.esmats.eu/amspapers/pastpapers/pdfs/2006/warden.pdf" rel="noreferrer">interesting paper by Robert Warden</a> refers to each mirror segment on JWST as having six actuators providing six degrees of freedom in positioning (plus one more to tweak the curvature). These degrees of freedom are described as &quot;tip, tilt, piston, horizontal &amp; vertical decentering and clocking&quot;. Can I assume that &quot;piston, horizontal &amp; vertical decentering&quot; correspond to 3D positioning in space and &quot;tip, tilt, and clocking&quot;  correspond to attitude?  Could someone help translate these into more explicit terminology?</p>
<p>Also, requiring a full six degrees of freedom sounds like overkill.  I imagine that three degrees of freedom would cater for almost all the required correction: motion along the z-axis and pitch and yaw with respect to the z-axis. As long as these first three corrections are available, does it matter very much where exactly the mirror is in the x-y plane or whether it's slightly rotated around its z-axis (roll)?  (here the z-axis is taken to be perpendicular to the plane of the mirror segment)</p>

<telescope><james-webb-space-telescope><adaptive-optics><mirror>
JWST mirrors each can be "positioned in tip, tilt, piston, horizontal & vertical decentering and clocking". What does this mean?
Roger Wood
# JWST mirrors each can be "positioned in tip, tilt, piston, horizontal & vertical decentering and clocking". What does this mean?

(Asked by: username_0 on 2022-03-01)

This [interesting paper by Robert Warden](https://www.esmats.eu/amspapers/pastpapers/pdfs/2006/warden.pdf) refers to each mirror segment on JWST as having six actuators providing six degrees of freedom in positioning (plus one more to tweak the curvature). These degrees of freedom are described as "tip, tilt, piston, horizontal & vertical decentering and clocking". Can I assume that "piston, horizontal & vertical decentering" correspond to 3D positioning in space and "tip, tilt, and clocking" correspond to attitude? Could someone help translate these into more explicit terminology?

Also, requiring a full six degrees of freedom sounds like overkill. I imagine that three degrees of freedom would cater for almost all the required correction: motion along the z-axis and pitch and yaw with respect to the z-axis. As long as these first three corrections are available, does it matter very much where exactly the mirror is in the x-y plane or whether it's slightly rotated around its z-axis (roll)? (here the z-axis is taken to be perpendicular to the plane of the mirror segment)

**Tags:** telescope, james-webb-space-telescope, adaptive-optics, mirror

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## 2 answers

### Answer by username_1 on 2022-03-16. Score: 4 | Accepted answer

Can I assume that "piston, horizontal & vertical decentering" correspond to 3D positioning in space and "tip, tilt, and clocking" correspond to attitude? Could someone help translate these into more explicit terminology?

How explicit??

To answer your direct question, yes, you've got the concept. There is "Translation" or just X,Y,Z motion followed by "Rotation" about X,Y axis. Clocking is rotation about Z. (assuming Z is normal to mirror surface)

Simply put, imagine a tabletop with a plate on it. "Piston" is lifting the plate flat upwards off the table. "Horizontal and vertical" is analogous to simply pushing the plate around on the surface of the table. "Tip and tilt" amount to lifting one edge of the plate. Finally, "clocking" is turning the plate so what you want to get to easily is right in front of you. (or what you dislike is away!)

As a side note... in January I did a calculation based on Warden's gearing numbers and believe each hexapod actuator went thru 50 fine cycles at mirror deployment.

edit to add:

because of the way the actuator uses a single motor to drive both coarse and fine modes an interesting coupler was devised. (fig 5 in Warden's paper) When the mirror segments were being moved 12mm from stowed location the fine mode was also being driven at same time. Since fine mode is driven by a cam the mirror flexed its focus shaping to full extents 50 times. When segments reached deployed position the drive motor reverses and the coupler 'backs away' from coarse drive, leaving just the fine mechanism driven.

> **Comments:**
> **username_0**: Yes, I think you're right. 'Clocking' was the one that had me a bit puzzled. When I google 'clocking' and 'telescope' it refers to mechanisms  for tracking stars across the night sky.  I'm sure, as you say, 'tip, tilt, and clocking' refers to 'pitch, yaw, and roll' along the z-axis.  
> **username_0**: any insights regarding the last paragraph of the question?  
> **username_1**: @Roger Wood I will be the first to admit that I am not by any means an expert on these types of optics. However, I spent my youth in photography and in college worked semiprofessionally with view cameras in which the front lensplate and rear filmplate could be independently tilted and rotated. I 'was' knowledgeable. AND SO... about the need for mirror segment clocking. I believe this relates to the fact that the mirror is parabolic and the segment surface is not symmetrical about the Z axis. I welcome feedback on this!  
> **username_2**: Each segment's edge have three different directions, resulting in a diffraction pattern with spikes in three directions. If the segments are not "clocked" equally, i.e. if their edges are in more than three directions, the diffraction pattern will be more complex, which is not desired.  
> **username_1**: THX! I was wondering about what kind of effects needed to be considered with a segmented mirror. Was any edge 'softening' (for lack of a better term) employed?    Also, was any part of my understanding significantly flawed?  I believe @David Hammen commented much earlier "Roll helps cure astigmatism issues." Is this kind of the same thing?  
> **username_2**: No, your answer is great :)  But I'm unsure what you mean by "edge softening"? Wrt. how roll would cure astigmatism, I don't know, I'd think that astigmatism would be caused by the segments having different heights/shapes and hence different foci. But I think it has to do with the mirror's asymmetry causing the wavefront to be… hmm… "asymmetric" for lack of a better word. There a document [here](https://www.telescope-optics.net/astigmatism1.htm) that might help. Btw., make sure to "tag" people if you want them to get a notification of your comments :)  

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### Answer by username_3 on 2022-03-01. Score: 3

Each of the primary mirrors has seven degrees of freedom, not six. It's just the secondary mirror that only has six degrees of freedom. The six degrees of freedom for the eighteen primary mirrors and the one secondary mirror are for positioning and attitude. The seventh degree of freedom in each of the eighteen primary mirrors applies to shaping.

> **Comments:**
> **username_0**: Yes, I did mention that in the question  
> **username_3**: Roll helps cure astigmatism issues. Shaping helps some, but since there's only one DOF for shaping, it's not quite enough.  
> **username_0**: good point. there's a deliberate cylindrical component to the mirror surface but any additional cylindrical error could potentially be corrected by a roll adjustment.   (does "clocking" refer to roll?)  
> **username_4**: "The six degrees of freedom... are for positioning and attitude." I thought that many are used for adjusting the *shape* of the primary mirror segments not just their rigid-body attitude, am I wrong? Of course changing the shape of a fixed-position mirror and changing the position of a fixed-shape mirror can have some overlapping optical optimization functionality, but I thought that they really bend the mirrors with the actuators.  
> **username_0**: @uhoh yes, I was under the same impression, but , apparently, only one is for spherical correction (focal length), the other six are for rigid body position and attitude.  Wikipedia JWST says much the same thing "Six positional actuators with a further ROC (radius of curvature) actuator at the center to adjust curvature".  They must be very confident that the mirrors will change shape in a small predictable manner between fabrication at room temperature and final operating temperature.  
> **username_4**: @RogerWood *Interesting!* Thanks  
> **username_5**: @RogerWood  since there's no atmospheric turbulence to deal with, there's no need to adjust the shape of each segment at greater spatial frequencies.  Next, given the overall design curvature of the primary assembly, I suspect the difference between spherical and aspherical curvature or, at least, the deformation caused by the 7th actuator) of each segment is too small to be controllable in any sensible way.  
> **username_1**: @RogerWood I'm guessing that by now you've checked out the various "hexapod" videos.  Is the term "clocking" of mirror clear now? Since primary mirror as a whole is roughly parabolic, each individual segment must have the ability to be rotated to to achieve best performance.  
> **username_1**: @Roger Wood I suspect that the machining of each segment (three  different 'types' in primary mirror) and location of anchor points for the 7th actuator were tuned so that each segment deformation tuning would be consistent with overall parabolic mirror performance.  

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