The first telescope with a shaped-back, center pull, micro-flex mirror

A six inch diameter, 29.125 inch focus plate glass sphere - pulled to perfection.

What is a micro- flex mirror? In 1990, Bill Kelley conceived the idea of pulling a sphere into a paraboloid by simply epoxying a bolt to the back or a mirror and applying tension with a wing nut. He made almost 200 6 inch f/5 mirrors this way, turning unuseable surplus aluminized spheres into rough parabolas that yielded serviceable images (See Sky & Telescope June 1992). Later I performed analysis and measurement that showed that using this simple method, a mirror=s figure could be improved over a sphere by a factor of about 5. Thus the above - mentioned sphere could be improved from 1.2 waves of spherical aberration (peak to valley wavefront error) to about 1/4 wave. For small mirrors this works fine, but
for larger or faster mirrors, the method does not give enough improvement to be practical - the simple method tends to pull a relative hole in the center of the mirror, while the outer parts are pretty parabolic.

The formula used above for the peak to valley wavefront error of a sphere used to form images of a distant object is : Error = 22.2* D^4/F^3, so the residual spherical aberration of a simple center - pull mirror is about 1/5 of this, or Error = 4.4*D^4/F^3. Thus you can apply this formula to see if the simple center - pull method will yield a wavefront error acceptable to you for a given mirror.

Enter Annular pull. For more correction, Alan Adler conceived the idea of gluing a flexible sponge - like annular plate on the back of the mirror and pulling from there. This yielded almost perfect parabolas, but required a much more complex mounting system and in addition required much more pulling tension than the center - pull method. (See Sky & Telescope November 2000.)

The shaped - back, center pull mirror. Of course, if one were to shape the back of the mirror, making it thicker at the center and thus more resistant to deformation, it should be possible to get the perfect correction of the annular pull mirror and still have the simplicity and convenience of the center - pull concept of Kelley. Thus, a macroscopic surface profile on the back of the mirror yields a microscopic optical parabola on the front of the sphere by applying tension on the back.

Bill and I both thought that, for every spherical surface, there exists a back profile that yields a perfect parabola on the front surface with the proper amount of applied tension - just like every block of marble contains a great work of art!


This is precisely what the present mirror accomplishes - Alan Adler provided a computer program which calculates the surface accuracy and provides the back surface profile and required tension in order to reach perfection. Bill Kelley and myself purchased 50 six inch diameter mirror blanks from Newport Glass with a rough curve molded on the front and back.  Inspection showed that the curves were not precise enough on the back, and that there was far too much wedge between the front and back surfaces. A machinist was able to generate a more precise curve on the back and we de-wedged the mirrors by hand. Thus we made a simple sphere on the front and turned it into a parabola with a wing nut, as before.

The resulting telescope provides proof of concept - the mirror yields super images of the planets, with intricate belt structure visible on Jupiter and the circular shape of the shadow of Europa on the ball was clearly evident. Relaxing the tension on the mirror caused the detail to vanish, leaving a circular mushy blob with a bare hint of belts. (Using the mirror at various stages of correction provides an excellent education in the effects of residual spherical aberration!)

Extra and- Intra focal Star images approach perfection. Also very gratifying, a Foucault analysis showed a peak to valley wavefront error of 1/11th wave (the sphere was not perfect) and a peak to valley RMS wavefront error of 1/48th wave. 

Equally gratifying, a rough measurement of the tension necessary to provide the parabolic correction gave 19 pounds, in very good agreement with the FLEXCP.EXE calculation of 22 pound


Howard Moore