Mirror math

Is it possible to calculate the accuracy of a spherical mirror in waves given the following parameters:
Diameter=59.00"
R=314.00" +- 1%
Smallest blur circle size =.06"
light source diameter=.03"


What can be expected in terms of spherical accuracy of either slope error or waves. I haven't been able to find a formula to answer this question. Your assistance is greatly appreciated!

Is it possible to calculate the accuracy of a spherical mirror in waves given the following parameters:
Diameter=59.00"
R=314.00" +- 1%
Smallest blur circle size =.06"
light source diameter=.03"


What can be expected in terms of spherical accuracy of either slope error or waves.

This makes it 59" f/2.66 sphere. The smallest blur diameter for point source is:

B=D/128F^2 for D in mm

which gives 1.65mm. The blur is twice as large, 3.3mm, at best (diffraction) focus. The PV wavefront error of lower order spherical is:

W=D/2048F^3

or 0.0389mm. In units of 0.00055mm (550nm, 0.55 micron) wavelength it is a bit over 70 waves.

The surface PV error is twice the best focus error (half the paraxial focus error), or 0.0778mm.

Vla