Aspherisation by Elasticity of a 50cm Plate for the Lyon Observatory Schmidt Telescope
Abstract
Aspherisation by Elasticity of a 50cm Plate for the Lyon Observatory Schmidt Telescope Summary. We describe the development of what we have called the dioptric elasticity method for making aspherics. The method was applied to the construction of the BSC B Schmidt corrector plate. The oversize disk is supported on a narrow metal ring which divides the plate into two concentric zones. On each side of the ring the air underneath is partially evacuated and the loadratio of the inner and outer zones is fixed at a constant value during the grinding and polishing. The elastically deformed disk is worked flat with a fullsize tool. When the loads are removed, the disk takes on an excellent, smooth Kerber profile over the giO within the supporting ring. The elasticity theory used to calculate the flexure of the plate is given, first for the old method invented and used empirically by Schmidt, and then for the flat polishing method used here. If we denote the radius of the ring support as r1, and that of the disk as r2, and the loads applied on the inner and outer zones of the plate as Pi and P2' respectively, the form of the resulting profile depends on three parameters: V (Poissons's ratio), Q2 (radius ratio = r2/r1), and (load ratio =P2/Pl). Since Poisson's ratio is fixed by the nature of the glass, there is an infinity of pairs (Q2"1) which formally satisfy the equation of the Kerber profile for the inner zone. By working the surface flat, one eliminates the inconvenience of the Schmidt method in which a spherical surface has to be made. The geometrical figure obtained is always a Kerber profile no matter what the thickness. In fact, by choosing different thicknesses, one can make correctors for different fratio mirrors without changing the apparatus or the tools. (However, it is always preferable to make the plate first and then to redetermine the appropriate curvature of the mirror by carefully measuring the asphericity of the completed plate). A search for (Q2' ii) pairs giving Kerber profiles has been made for 0< V <1/2. We note that for `i= 1, the surface area of the outer zone (which is not useful) is a maximum. For ,i> 1, the area of the outer zone decreases and the limiting casefor which is infinite requires a plate of zero thickness, and so is not Thus, a fortiori, we chose the compromise 4 =<,i < 8 for large diameter correcting plates. The Schmidt plate for the Observatoire de Lyon has a 50cm optical aperture (2r1) with ratios v=0.2, 2= 1.254 and =4. Both faces are aspherical; this reduces the risk of rupture. During the experiment, the amplitude of the aspherical quantities was controlled by adjusting the intensities of the loads Pi and P2 while keeping their ratio, , constant. The table of the polishing machine floated on an oil pressure bearing with the imperative condition that the supporting ring define a plane to within 50nm. A Fizeau interferometric test with a HeNe Laser allows inspection of the fringes of constant thickness between the front and back surfaces of the plate. This test is very precise, since one fringe represents a deformation of the refracted (wavefront) of value (n  1)/2n 46. In the spectral interval from 3509 A to 7000 A, the wedge of the plate, which is superimposed on the Kerber profile, introduces a spectrum of length 0.05". This is negligeable compared to the blurring due to atmospheric turbulence. The interferogram was reduced with a high precision spectrocomparator used generally for the measure of stellar radial velocities. The ideal radius of curvature for the mirror 270.7 cm  was calculated for the central wavelength of 4100 A. For this wavelength, the axial blur circle has a diameter of 1 1 m. The effective focal length is 133.8cm and the effective aperture ratio is f/2.675. Whenever possible, this principle should be applied more generally to the figuring of aspherical surfaces. The use of this method requires, of course, a fairly elaborate apparatus, but this is a small price to pay in return for gain improvements in detection, and for future, more compact, astronomical instruments of greater performance for which the optical components will necessarily require greater asphericity. Key words: geometrical optics elasticity Schmidt telescopes aspherical surlaces useful.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1975
 Bibcode:
 1975A&A....44..305L