Analysis of David Davis's ultra thin 16 x 3/8 F3.5 plate glass slumped mirror.

Analysis was done using my Bath interferometer. Confirmation of the spherical correction was also done using Ronchi and Foucault tests. The analysis method used techniques to try and remove deformation caused by the test stand. A test stand can add a lot of deformation to a mirror this thin. A lot of the effort of measuring this mirror was used to separate the stand errors from the mirror errors.

The mirror has almost no correction so this is an image of the gross error. The white box is 1 wave high. This image is wave front error. The surface error would be of this value. The PV wave front error is 7 waves. The rms is 2 waves.

There is somewhat of a mystery about why the correction is so small. The mirror was tested in a telescope at the Table Mountain Star Party in Washington. While there it was deemed to have acceptable medium power view by Mel Bartels, the owneer and others. Afterwards David did a little more figuring to improve the figure. He believed he did so. He used several Ronchi tests to help him. I volunteered to measure it with my interferometer. He sent it to me and I found it to be only about 20% corrected. This mirror is very thin and we thought that perhaps his mirror cell added the extra correction needed. He sent me the mirror cell to use for testing. I found it made little difference. The correction increased to about 25%. However the mirror cell created much worse astigmatism. See Mirror cell section below.

From this I conclude that since it had acceptable views before more figuring, then David must have removed what correction it did have. I am not satisfied with that answer either but I don't know David's expertise. David will get the mirror back soon and will test it again himself. He will let us know what he finds.

There is the possibility that all three of my systems fail to measure accurately on fast mirrors. This one is F3.5. I have measured mirrors as fast as F4 that match others measurements.

Part of the reason for testing this mirror is to demonstrate what happens to the surface when it is not supported well. We also wanted measure the astigmatism and higher order errors that can plague thin mirror manufacturing. It is still possible to that because my interferometer software can ignore spherical aberration and display only the other terms. It can turn off any or all error terms thus isolating errors of interest.

Next is the mirror with the correction error removed.

The error box is again 1 wave. The PV error is 1.5 waves and rms is .4 waves. The major contributor to the error is astigmatism. You can see one diameter is high (red) and the other is low (blue) at the edge. Any astigmatism induced by the test stand has already been removed.

Next, turn off astigmatism errors to see what is left.

Now the box is wave. Everything that is colored grey also meets the wave limit. The PV is 1 wave and rms is 1/5.6 wave. Again, these are wave front errors.


For those of you that understand Zernike numbers here is a contour plot showing all the Zernike values. Spherical, Astigmatism, and coma terms have all been disabled for the image and the error report.

Below is an image of the mirror rotated every 22.5 deg. These were computed by Steve Koehler from my interferograms taken at each rotation. Steve's software removed the test stand errors. You can see a similar surface to the above image that rotates with each mirror rotation. We used this to verify that what we measured on the surface was indeed on the surface.

Mirror Cell Analysis

David sent me his mirror cell to use with the mirror. He found that it worked well with the mirror. I found that it added a large amount of astigmatism. First I used the same lateral support that David does. The cell has two lateral support pegs about 30 deg apart at the edge. The back board of the cell has been made bowl shaped on a lathe to match the shape of the slumped mirror. To that David glued foam rubber tubes at support points calculated by the mirror cell analysis program PLOP.

Below is the analysis of the mirror and cell combination. (I removed the pliers before placing the mirror J )

The box is 8 waves!

I had done other testing that showed lateral support of this type can generate larges amounts of astig on mirrors this thin.


For better lateral support I found that a piece of tape attached to the back of the mirror and to the top of the mirror cell induces little astigmatism. So I used that to pull the mirror off of the 2 peg lateral supports about 1/16 of an inch.

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Above is the mirror in David's mirror cell on the left. The box is 1 wave. The image on the right is the mirror with all test stand errors removed as best I can. You can see that David's mirror cell introduces a lot of astigmatism. So much so that it completely over powers what is already on the mirror and rotates it 90 degrees. I think the reason the cell does not perform is that its surface needs to be almost as accurate as the mirror it is trying to control. It is hard to make and keep a wooden surface accurate to even 100 wave lengths (about .002 inches). I found the mirror would sag several wave lengths when supports were not spaced at the correct positions. If one of those correctly spaced supports is 100 waves too short then it stands to reason the mirror will sag several waves there as well.

Conclusion

I have enjoyed testing this mirror and how it responds to different conditions. A mirror this thin is very difficult to support properly. I can create over 8 waves of astigmatism with only a few ounces of force in the wrong place.

I also found that PLOP predicts the deformation very well once you tell it that there is no sagitta. Anyone wondering how a thin mirror will behave can use PLOP to simulate it.

There is still an issue I don't understand. How can a mirror and cell that tests so badly here in my basement be considered much better by actual use. Has it changed or are my test systems flawed?

Acknowledgments

I would like thank Steve Koehler who supplied the software and time to sort out test stand error from the mirror error. Also, Richard Schwartz for pointing out the tape support solution and how to configure PLOP to best simulate a slumped mirror. Most of all David Davis for supplying the mirror in the first place.