The ESO requirements asked for the VCM during operation are tight. The
main one is to limit the
surface deviation from a sphere to less than one wave peak-to-valley (PTV)
for 
= 632.8 nm , but the clear aperture concerned varies during the operation.
The deviation has to be minimized on two different diameters according
to successive ranges of curvatures. To radii of curvature between [2800 and 230 mm]
and those between [230 and 84 mm] correspond respectively a 14 mm and a 6 mm
clear aperture.
The important result deduced from surface measurements is that the central part of
the mirror fulfils the requirements: deviation from a sphere is lower than
PTV on a 6 mm diameter. The analysis shows that on a 6 mm diameter the deviation
remains below during the whole curvature range (LOOM 1994),
as proved
by the interferogramms in Fig. 6 (click here) taken at radius of curvature equal
to 2800 mm and 84 mm. A large curvature variation can be
achieved with a reasonable good optical quality on the central part of
the surface. Unfortunately, the analysis also shows that this good quality
is not achieved on the full aperture. For radii from 2800 m to
230 mm the outer part of the mirror surface is out of quality requirements, due to an
excessive amount of spherical aberration.
Figure 6: Interferograms of the optical surface of a VCM sample
(#5): The radii of curvature are 2800 mm (up) and 84 mm (down). The diameters on
which the deviation from a sphere is lower than PTV are 15 mm and
7 mm respectively
This problem comes from two different parts:
- 1 - The collar at the edge of the active meniscus produces a "semi built-in'' effect, equivalent to a rigidity increase, depending to the ratio between the collar and the meniscus thicknesses.
The bending moments distributed along the outer edge of the meniscus modify the deflection shape which is then different to the calculated spherical one.
- 2 - The linearisation of the strains in the mirror substrate during the pre-stressing
stage, also called "Ewing-Muir'' effect, changed the curvature of the mirror.
This added convexity (about 15
m sag) produces a deviation from the theoretical
deflection just at the outer part of the meniscus where the residual spherical
aberration is observed.
A second set of mirrors was realized with an added "lens profile'' which provides
a 15m overthickness at the center, and a 15m under-thickness at
the edge, that compensate for the rigidity increase introduced by the collar.
The results obtained with this modified profile show that the spherical aberration
is reduced by more than a factor of two on the tested samples (LOOM & Von
der Lühe 1996).
| P | R | a | Wave Fronf Error () | ||
| [bar] | [mm] | [mm] | Sph. Abb | rms | PTV |
| 0.233 | 2800 | 7 | 0.492 | 0.439 | 2.271 |
| 1.013 | 420 | 7 | 8.098 | 0.929 | 4.713 |
| 1.815 | 230 | 7 | 16.170 | 1.481 | 7.118 |
| 1.798 | 230 | 3 | 0.270 | 0.111 | 0.588 |
| 3.341 | 140 | 3 | 0.219 | 0.130 | 0.679 |
| 5.082 | 105 | 3 | 0.027 | 0.146 | 0.755 |
| 7.561 | 84 | 3 | 0.460 | 0.202 | 0.849 |
Table 1 (click here) presents the optical quality (rms and PTV) achieved with one of the VCM samples on the whole curvature range, the spherical aberration amount is also indicated.
For radii of curvature from 2800 mm to 230 mm the Wave Front Error (WFE) is
evaluated on a 14 mm diameter. The spherical aberration becomes rapidly
important leading to an out of requirement quality but, as already mentioned,
the best results are obtained for a 6 mm diameter. At the 230 mm radius, the
spherical aberration is divided by 60 when we reduce the clear aperture from
14 to 6 mm. This amount of spherical aberration remains low within the range
[230 - 84 mm], and the WFE (PTV) is slowly increasing from 0.59
for 230 mm to 0.85 at 84 mm. This proves that the largest deviations come
from the outer part of the mirror. Although the spherical aberration amount has
been divided by two this is still the major problem encountered.