# JWST mirrors each can be "positioned in tip, tilt, piston, horizontal & vertical decentering and clocking". What does this mean?

This interesting paper by Robert Warden 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)

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.

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.

• 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. Mar 16, 2022 at 5:39
• any insights regarding the last paragraph of the question? Mar 16, 2022 at 5:40
• @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! Mar 16, 2022 at 14:48
• 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
Mar 16, 2022 at 15:21
• 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 that might help. Btw., make sure to "tag" people if you want them to get a notification of your comments :)
– pela
Mar 16, 2022 at 22:46

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.

• Yes, I did mention that in the question Mar 1, 2022 at 18:21
• Roll helps cure astigmatism issues. Shaping helps some, but since there's only one DOF for shaping, it's not quite enough. Mar 1, 2022 at 18:24
• 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?) Mar 1, 2022 at 19:01
• "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
Mar 1, 2022 at 22:09
• @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. Mar 1, 2022 at 23:49