Mirror Sag vs. Mounting Method – Part 1

Background

We recently tested a 20” diameter x 2” thick F/5 mirror made from fine anneal Pyrex utilizing three methods for holding the mirror: a chain sling, a V-stand (two support points) and standing the mirror on it’s edge (one support point). Our intent was to measure and compare the self-weight deflection (sag) in the mirror for these three mounting methods. The primary aberrations due to mounting a mirror in the vertical position, regardless of method, are third order astigmatism (saddle shape) and a higher order astigmatism called trefoil (three sided astigmatism).

In analyzing the interferograms I did find the two forms of astigmatism mentioned above but the relative amounts of third order astigmatism did not agree with theory. Theory predicts that the chain sling will have the least sag with the V-stand a close second. The mirror should have the most astigmatism when tested standing on it’s edge. I found that the chain and V-stand had the most astigmatism while the last test with the mirror on it’s edge had the least. From these results I have concluded that great care must be exercised in applying any of the three methods of mounting in order to obtain good results. I plan to make further tests of this mirror, after it returns from coating, to measure the effects of chain or contact point location on mirror sag.

Following are surface and contour plots along with the usual interferometer test output for the three mounting methods.

# Chain Sling – Astigmatism On

P-V = 0.712

RMS = 0.133

Strehl = 0.500

Astigmatism = 0.627 @ -89.0 degrees

Spherical Aberration = 0.098

The above results were obtained with the mirror hanging in a 180-degree chain sling. The results show the expected saddle astigmatism, however the value is quite a bit higher than normal. Occasionally we get what we call a “bad hang” where the chain sling isn’t properly positioned under the center of mass of the mirror. When we see results like this we adjust the chain and re-shoot the mirror. Note that the astigmatism is in the vertical axis as expected.

# Chain Sling – Astigmatism Off

P-V = 0.174

RMS = 0.026

Strehl = 0.974

Spherical Aberration = 0.098

The above graphics and output show the same set of test results but the third order saddle astigmatism is subtracted out. You can see that there is a small amount of trefoil with one lobe near the bottom of the mirror. The form and orientation of the trefoil agrees with theory except that it is rotated slightly counter-clockwise with respect to the vertical axis.

# V-Stand – Astigmatism On

P-V = 0.796

RMS = 0.143

Strehl = 0.444

Astigmatism = .654 @ 49.7 degrees

Spherical Aberration = 0.252

The above graphics show the test results with the mirror mounted in the V-stand. [It is important to note that the edge of the mirror is marked so that it can be mounted in the same orientation in all of the tests.] The difference in the direction of the astigmatism in this test is striking. It is now oriented at about 45 degrees with respect to the vertical axis. The V-stand contacts the mirror at +/- 45 degrees. The form and direction of the astigmatism in this test indicate the two-point equivalent of the “bad hang” mentioned above. In this case, the mirror is not square to the rig. It is contacting at one point near the mirror’s front edge (right in the graphics above)  and at a second point near the mirror’s back edge (left).

# V-Stand – Astigmatism Off

P-V = 0.317

RMS = 0.046

Strehl = 0.921

Spherical Aberration = 0.252

Here’s the V-stand data again but with the third order astigmatism subtracted out. You can see the residual trefoil in the results.

# Mirror on Edge – Astigmatism On

P-V = 0.373

RMS = 0.064

Strehl = 0.851

Astigmatism = 0.260 @ 82.6 degrees

Spherical Aberration = 0.106

The above test results were obtained with the mirror standing on it’s edge. You can see the strong deflection at the bottom of the mirror where it is contacting the support. Oddly enough, this test exhibits only one half to one third of the astigmatism in the two “superior” support methods above. As I mentioned above, a logical explanation for this unusual result is that the sling and V-stand tests were not set up properly.

# Mirror on Edge – Astigmatism Off

P-V = 0.249

RMS = 0.034

Strehl = 0.954

Spherical Aberration = 0.106

Above are the on-edge test results with the astigmatism subtracted out. Again, you can see the residual trefoil astigmatism.

### Conclusion

Though I set out to compare the sag in a thin mirror using different support methods, I only managed to show that the amount of self-weight deflection in a thin mirror on its edge depends very strongly on the accuracy of the set up. Regardless which method is used, it seems critical that the support points be located as close as practical to the mirror’s center of mass. I will conduct further tests soon to verify this hypothesis. Then I will redo the above experiment with greater care to make a more informative comparison of the three mounting techniques.

PS. This is 20-31-061802 You can view other test images for this mirror at http://www.ProSpecMirrors.com

E-mail me on the Yahoo! groups or at jcmulherin@opticalmechanics.com if you have questions or comments.