Lightweight primary mirrors are increasingly applied both in
ground-based and space-based telescopes. Because the absolute
stiffness of the lightweight mirror is much lower than that of the
solid one, the design of lateral support becomes more difficult. Based
on parallel push-pull support, we have proposed a multi-class variable
F
−
θ
optimization approach (MVFOA), where
F
denotes the magnitude of the support
force and
θ
denotes the support position.
Compared with conventional optimization approaches, which have
only one class of design variables,
F
or
θ
, MVFOA considers the impact of
F
and
θ
simultaneously. In addition, we also
study push-pull-shear lateral support and propose an unequal-angle
push-pull-shear support optimization approach (UPSOA). To verify the
advancement of above approaches by means of finite element
calculation, the lateral support optimization of a 2.5 m ultra-low
expansion honeycomb sandwich mirror is described in this paper. For
parallel push-pull support with 24 forces, three optimization
approaches with different variables, including single-class variable
F
, single-class variable
θ
, and multi-class variable
F
−
θ
, are compared, and the RMSs of
surface deformations are 17.60 nm, 15.93 nm, and 14.81 nm,
respectively. For push-pull-shear support with 24 forces, the optimal
result by UPSOA occurs when
β
equals to 0.84 and the RMS of surface
deformations is 10.83 nm. UPSOA also solves the problem that the
forces in the region
x
≈
±
R
are much larger than the ones in the
region
x
≈
0
in the equal-angle push-pull-shear
support optimization approach (EPSOA). Through the analysis of
results, we find that optimal
β
of the honeycomb sandwich mirror is
greater than that of the meniscus mirror in push-pull-shear support.
In addition, both in parallel push-pull support and push-pull-shear
support, it also can be concluded that the position and the magnitude
of optimal lateral support forces depend on the stiffness distribution
of the mirror along the altitude axis rather than the mass
distribution.
