J. E. Gunn, 23 Jan 1999
The pneumatic astigmatism corrector has been installed on the 2.5-meter telescope. It consists at the moment of a set of twelve precision manually adjusted pressure regulators operating twelve low-friciton Airpel air cylinders which apply forces at twelve approximately equally spaced intervals along the circumference of the mirror. These pressures are monitored and displayed by a controller resident with the regulators on the 'North' fork arm of the telescope.
This note describes the parameters of that system in some detail and describes the use of a small program which calculates the settings of the regulators.
The actuators are arrayed in two groups of 6, each with 60-degree spacings. Both are located on a circle of radius 49 inches centered on the mirror. The first group has angular locations
theta1(i) = 12 + 30*((i-1)/2) i odd, i=1,3,...11
and the second
theta2(i) = 9 + 30*((i-1)/2) i even, i=2,4,...12
To sufficient accuracy for present purposes, they may be considered to be located on an equally spaced angular grid with 30-degree spacing:
theta(i) = 10.5 + 30*((i-1)/2)
Where the angles are measured CLOCKWISE from the vertical with the telescope stowed, and looking from the back of the mirror, i.e. AT THE SKY.
Thus the pattern may be considered to be equally spaced and rotated 10.5 degrees clockwise from the vertical, or, if you like the mathematically nicer pattern 15 deg, 30 deg, .....30 deg, 15 deg from the origin, 4.5 degrees counterclockwise from the vertical.
The pressure meter on the controller is calibrated in a more-or-less arbitrary fashion and may be recalibrated in the future, but as of now the setup is as follows.
For NO forces on the mirror, all the regulators are set at a pressure of 100 units; the REFERENCE pressure, which is applied to the other side of the double-acting air cylinders, is set to 88.3 (this is because the air cylinders generate different forces for a given pressure on the top and bottom because of the area occluded by the cylinder shaft on the top of the piston, and the calibration of the reference channel is identical to the others.
A reading of 100 on the meter corresponds to a pressure of 198 kPa, 28.6 PSI. With the geometry of the cylinders, this corresponds to a force of 11.8 newtons, 2.66 pounds. This active pressure is applied to the TOPS of the air cylinders (shaft side) and pulls the mirror DOWN. The reference pressure of 88.3 units = 25.3 PSI is applied to the bottoms and pushes up with an equal force when the active pressure is set to 100 units. For each unit the minimum force is at 0, which is an UPWARD force of 11.8 N, and the maximum is 200, a DOWNWARD force of 11.8 N.
The range of forces with this setup is larger but perilously close to that calculated to be required by Walter some time ago; there was a slip of a factor of two somewhere along the line. This is fixable if necessary, but until a need is demonstrated for more range we will live with it this way.
To set a pressure, press the button adjacent to the number for the desired channel. The LED immediately to the right of the pushbutton lights, indicated that the metering circuit for that channel is active. With a small screwdriver adjust the corresponding regulator until the desired pressure reading is achieved on the digital panel meter. The settings may be made to about 0.1 units, and are stable to about 1 unit over time and reasonable temperature changes.
To calculate the pressures required, I have written a little C program, astigcor. The source (astigcor.c), a make script (makeastigcor), a Sun executable (astigcor), and an MSDOS/Windoze executable (astigcor.exe) can be found in ~jeg/Astigcor/ on galileo, along with all the documentation on the astigmatism corrector and a file (astigcor.readme) which describes what is present. To use the program, say
astigcor astig_ampl_in_nm pos_ang_in_deg
where astig_ampl_in_nm is the (educated guessed) amplitude of the astigmatism and the pos_ang_in_deg is the (measured) position angle of the MAJOR AXIS of the astigmatism measured COUNTERCLOCKWISE from the vertical (i.e. the direction of increasing ELEVATION) on an image INSIDE OF FOCUS--ie with the secondary piston GREATER than its in-focus value or the detector moved UP with respect to the focal surface. The mirror surface is described by
s = -A*cos(2*(phi-PA))(r/r_M)^2
where A is the amplitude, PA the postion angle, r the radius on the mirror and r_M the outer radius of the mirror, and phi the angular coordinate on the mirror, here measured in the same sense as PA; i.e. couterclockwise from the vertical. Note the overall minus sign--the radius of curvature of the mirror
is LONG along the major axis of an inside-of-focus astigmatic image. One thus wants to push UP on the ends of this axis, and so the pressures are LOW on this axis, high perpendicular.
Thus
your_prompt> astigcor 230 19.5
produces
Meter settings for astigmatism amplitude 230 nm, PA 19.5 degrees
chan
pos ang
setting
1
349.5
53.1
2
319.5
146.9
3
289.5
193.8
4
259.5
5
229.5
6
199.5
6.2
7
169.5
8
139.5
9
109.5
10
79.5
11
49.5
12
19.5
Simple enough. How do you guess the amplitude? One way is trial and error; the OSC report says there is about 230 nm of astigmatism, so the amplitude given above is likely to be near correct, if the FEA connecting forces to deflections is correct and there are no further complications.
It can also be measured. Suppose one has a surface error described by the simple astigmatism expression above. The the edge ray along the major axis has an emergent angle error of
dgamma = 4 * A / r_M = .066 arcsec * A100
Where A100 is the amplitude in hundreds of nanometers. The difference in major and minor diameter of the elliptical image is 4 times that, or
a-b = .26 arcsec * A100
At the scale of the 2.5 meter, this corresponds to
a-b = 15.8 microns * A100.
Thus if one measures an ellipticity for which a-b is 40 microns (.66 arcsec) the amplitude is 40/15.8 * 100 = 253 nm. If one measures a position angle of 5 degrees for this image, one says
your_prompt> astigcor 253 5
and gets
Meter settings for astigmatism amplitude 253 nm, PA 5.0 degrees
11.5
101.8
190.3
188.5
5)
98.2
9.7
back to top
1. Install the pushrods.
The Ultem pushrods LOOK symmetrical but are not. The bottom is marked with a black band, the top with a lettered 'UP' label. Place the bottom end in the swagelok handling fixture and tighten. Insert the top into the actuator mounting hole and carefully feel for the ball fitting on the back of the mirror. Fit the upper cup in the pushrod over the ball and push UP firmly, until the ball snaps into the cup (the required force is about 10-12 pounds). Loosen and remove the handling fixture.
2. Fit the insertion fixture to the actuator.
Turn the actuator over so that the cylinder shaft extends fully under gravity. Place the insertion fixture (two rectangular plates of 1/16" aluminum--be sure that it is CLEAN) through one of the slots in the brass mount so that it straddles the cylinder shaft. Insert it as far as it will go, and then push down on the ball so that the fixture is captured between the bottom of the slot and the skirt on the ball.
3. Fit the actuator to the pushrod
The shaft of the cylinder is now captured and cannot retract. Place the lower cup of the pushrod over the ball and push up firmly, so that the cup snaps onto the ball. Remove the insertion fixture, being careful not to stress the shaft of the cylinder.
4. Install the actuator into the mirror cell.
Push the actuator up into the hole until it snaps into place, compressing the wave spring.
5. Setup conditions
Set the mirror at its nominal height and (if possible) the telescope to the zenith. The translation of the primary should be the nominal observing setting--ie about +1000 microns in x, +200 microns in y, or -8000 on the transverse galil (D), 26000 on the lateral galils (E&F) with the setup as of Jan 99; the setmir locations are safer, since the galils might change with some mechanical change. This positions the upper actuator ball mounts exactly over the mounting holes in the cell.
6. Disengage the actuators from the cell.
Use the actuator removal tool. This device compresses the four fork tines of the brass actuator mount so that they can be pulled free of the cell. This is a somewhat tricky operation; the rollers must have the correct azimuth with respect to the tines, clearly, and one must use EXTREME caution not to put sideways stresses on the actuator shaft, since the actuators are still attached to the pushrods. Let the actuator hang from the pushrod. and remove the pushrod before going on to the next actuator.
7. Disengage the lower ends of the pushrods from the actuators.
Using the L-shaped pushrod disengagment tool, snap the actuator balls out of the lower ends of the pushrods. To do this, insert the thin blade of the tool into one of the slots in the pushrod above the ball and pull out on the long handle, levering the ball out of the cup. BE VERY CAREFUL when doing this. It may be necessary to gently rotate the pushrod in order to get a pushrod slot aligned with the slots in the actuator holder, and it may be slightly difficult to insert the tool. DO NOT APPLY excessive side forces on the actuator shaft; if the shaft bends the actuator will not work properly.
8. Put the actuator out of harm's way
The actuator is now attached only by its hoses, and one does not want to take them loose, so be sure that the actuator is physically safe; it can be taped to the cell if necessary. It is necessary to use extreme caution to keep the cylinder shaft clean; the actuators will not work properly if the shaft is dirty.
9. Remove the pushrods.
DO NOT attempt to pull the pushrods off; the pads carrying the upper balls are RTVd to the mirror and may pull loose. Use the provided pushrod removal tool. Fit the tube over the pushrod, making sure the recessed receptacle fits over the base of the ball glued to the mirror. It is this recessed surface which receives the removal force. Insert the screw into the bottom of the receptacle and screw into the pushrod using the small handle. When it bottoms, spin the large nut up until it is snug, and then continue to screw it on until the pushrod snaps loose. This should take about 5 turns after it is snug. When it comes loose, spin the large nut all the way down and remove the screw from the pushrod.
Figure 1: Drawing of astigmatism actuator
Figure 2: Diagram of hose connections on mirror cell
Figure 3: Diagram of actuator geometry from back
