Magomed A. Abdulkadyrov*, Sergey P. Belousov, Alexander N. Ignatov, Victor V. Rumyantsev

* Correspondence: e-mail: bcrubin@glasnet.ru; Telefone: 007-095-552-15-47; Fax 007-095-552-17-90

In the performance of tasks of the high-resolving optical systems manufacturing, the significant funds are required. This fact can be a reason limiting further development of astronomical research. The aim of this paper is demonstration of the ways to reduce the fabrication cost of astronomical instrument mirrors.

The following requirements to large-size mirrors, which are conditioned by tight tolerances (in the order of 0.01m) to meet the designed shape of a mirror surface and to keep this shape in time, are stated:

• high weather resistance (combination of physical properties, which ensures small mechanical and temperature deforma-tions);
• dimensional and properties stability in time;
• high quality of the polished surface ensuring quite good reflectivity of a mirror coating;
• small density.

There has been no such astronomical mirror material, which meet all the above requirements, as yet. However, owing to properties such as high isotropic stability, susceptibility to polishing and, the main thing, the thermal coefficient of expansion, which is close to zero, glass ceramics is the best material to manufacture substrates for large-size mirrors.

A disadvantage of this material is low thermal conductivity, small mechanical strength and comparatively high density.

Before I go on to the analysis of the ways of reducing an effect of the above mentioned disadvantages on a mirror performance, apparently, it is advisable to give some glass ceramic data characteristics.

The most well-known glass ceramic at present is Zerodur of Schott company (Germany).

Table 1. Properties of Zerodur and Sitall CO-115M produced by JSC LZOS (Russia)

Property	Sitall CO-115M	Zerodur
Average coefficient of linear thermal expansionat a temperature range of -60oC to +60oC, (K-1)	±1.5 x 10-7	(-2±1) x 10-7
Refractive index (ND)	1.536	1.542
Density (g/cm3)	2.46	2.35
Young's modulus (MPa)	9.2x104	9.3x104
Poisson's ratio	0.28	0.24
Specific heat (J/g x K)	0.92	0.80
Heat conduction (W/m x K)	1.18	1.46

As it was already mentioned, the disadvantage of glass ceramic is comparatively high density. The most effective method to avoid this disadvantage is the manufac-turing mirrors of lightweighted structure.

Different types of lightweighted mirrors produced at LZOS are shown in Fig. 1,2,3.

Fig.1 The lightweighted mirror design with perforated back side.

A monolithic mirror design in which a lightweighted structure is made with light-weighting hollows on a mirror back side is shown in Fig.1. A disadvantage of this design is a long manufacturing cycle and dissymmetrical design, that decreases stiffness and mirror shape stability.

Fig.2 The sandwich-type lightweighted mirror design.

Figure 2 shows a mirror design according which parts of a multilayer mirror from optical Sitall is connected each to other with electric-adhesive method. A disadvantage of this method is a long period of lightweighting hexahedral cells manufacture, as well as an absence of principles and criteria of selection of the parts to be connected does not provide stability of the mirror optical surface.

Fig.3 The sandwich-type lightweighted mirror design of optimal lightweighting structure.

It appears that the most promising in the context of adaptability to the manufacture process, deformation minimization and obtaining the necessary lightweighting level is the design given in Fig.3.

The lightweighted mirror consists of three plates 1,2,3. In the middle plate (2), the cylindrical holes (4) of a radius r, the holes (5) of a radius ro and the walls (6) of thickness b are made. In order to increase the lightweighting level, centers of the large diameter holes are placed in vertexes of equilateral triangles, and smaller diameter holes - in a center of these triangles, at that radii of the larger and the smaller (r₀ and r) diameter holes are coupled with the relationship as follows:

where b is a thickness of a wall between holes.

The results of evaluation of a lightweighting level of the design and a labor-content of the manufacture process for the mirror shown in Fig. 2 and 3, when their stiffness parameters are equal, are rated by Table 2.

Table 2.

Mirror Substrate	Lightweighting Level	Manufacture Labor-Content
Option 2 (Fig. 2)	65 %	A
Option 3 (Fig. 3)	83 %	0.7 A/TD>

Fig.4 A movement plan of the plates during the assembling procedure of the mirror.

On purpose of enhancement of mirror optical surface stability , the composing plates are cut from a monolithic substrate and are assembled with a displacement of the layers with respect to their location in the parent substrate both axially and according to an angular arrangement, as described by Fig.4. The connection of the tree plates as a unit is fulfilled using the electric-adhesive method. The principle of the electric-adhesive connection of components made from Sitall CO-115M is that the electrical conductivity is generated in Sitall, when it is heated considerably, and this allows to use the electrical field to activate the process of diffusion between high precision polished plates. Such technological solution is used to connect substrates of an astronomical mirror , which consists of a supporting lightweighted structure covered with a metal coating applied on the planes to be bound and two cover-plates.

The process of a mirror assembly is shown in Fig. 5,6,7.

Fig.7 Handling of the middle plate.		Fig.5 Installation of the middle plate.
		Fig.6 "Sandwich" ready for adhesive joint.

Fig.6 The 1500mm diameter lightweighted mirror.

By means of displacement of the layers with respect to their initial location, an averaging of physic-mechanical properties of the mirror substrate are achieved, that enhances considerably isotropy of Sitall material. And a closed design of the mirror allows to increase largely stiffness of the structure. Thereby we can conclude that the mirror manufacture process according to the design shown in Fig.3 allows to avoid the disadvantages of glass ceramic. In Fig.8 a sandwich-type lightweighted mirror of 1500mm in diameter made from glass ceramic Sitall CO-115M are shown.

An essential reduction of the manufacturing cost for aspherical surfaces can be reached with an optimal distribution of machining allowances at aspherization process.

Fig.9 A layout of the segmented mirror.

Fig.10 The one-side cut element.

As an illustration we will consider the manufacture of a segmented aspherical mirror consisting of 36 hexagonal elements, a sketch of which is shown in Fig.9. The mirror is formed by 6 types of segments. A number of aspherization and finishing variations for this mirror can be done.

Fig.11 The joining points of the segments.

Our opinion the most effective is the following one:

• Manufacturing of a central auxiliary element of the primary mirror necessary to test off-axial 1^st type segments (shaded in Fig.9);
• Manufacturing of spherical blanks for the 1^st type segments; a radius of curvature on the spherical blanks is equal to an outer radius of curvature on an axial element in the field of joining of the axial and off-axial elements;
• Aspherization of the 1^st type segment surface with gradual expansion of material to be removed to the field of joining of the 1^st and 2^nd type segments; please, note, that on this stage all 1^st type segments have an outside periphery as shown in Fig.10; after aspherization the blanks shall be cut to a hexagonal shape, and the surface finishing shall be made;
• The next type segments shall be made initially spherical with radii of curvature equal to an outer radius of curvature of an aspherical segment of the previous type (Fig.11); for the 1^st type with a radius equal to an aspherical surface radius in point A, for the 2^nd type in point B, for the 3^rd type in point C, for the 4^th type in point D, for the 5^th in point E, and for the 6^th in point F;
• Final certification of the segments shall be made on a vertical test bench in accordance with the arrangement as per Fig.12.

This distribution of the machining allowances allows: to manufacture all the segments of the segmented mirror with the required radii; to except the need to build expensive equipment for testing radii of curvature; to fulfil the polishing and testing of each segment of the mirror without using a standard mount.

Fig.12 The layout for testing.

The aspherical surfaces unlike the spherical ones are incomparable more multivarious on their types, properties, parameters, requirements to the manufacturing accuracy, operation conditions, therefore it is practically impossible to make a universal method or set-up for aspherical surfaces testing. Each aspherical surface is a unique one and its test method is an unique too.

There are test methods (unaberration points method), which have become classics, using auxiliary optical elements, in particular the Hindle test-up with a spherical mirror.

However, as often happens, the direct application of these methods to test high-aperture mirrors is or impossible at large or extremely expansive. Such a problem was highlighted when analysing the possible test set-up for secondary mirrors with the following dimensions:

1. Hyperbolic convex mirror of the VST telescope:

• Clear aperture: 900 mm;
• Radius of vertex sphere 4374.46 mm;
• Central shielding 112 mm.

2. Hyperbolic convex mirror of the NOA telescope:

• Clear aperture: 740 mm;
• Radius of vertex sphere: 4602.2 mm;
• Central shielding: 128 mm.

The above mirrors are being manufactured at LZOS under subcontracts of Carl Zeiss Jena.

Several variations of test set-ups were examined, and due to their difficult realizability and, accordingly, the high cost, there was impossible to use here one of the classical methods. In particular, it would be needed to manufacture the Hindle sphere of diameter 2800mm to test these secondary mirrors. A difficulty in designing was that it was necessary to test high-aperture mirrors with different parameters and small central shielding. Figures 13 and 14 shows the accepted test set-ups for the mirrors with using the two additional mirrors M1 of a diameter 1950mm and M2 of a diameter 1640mm. The secondary mirrors are set at the test set-up by turns and tested in conjunction with each of the additional mirrors. At that when testing with M1 a zone of 900/268mm is illuminated for the secondary mirror of the VST telescope a zone of 740.6/307mm - for the secondary mirror of the NOA telescope, and accordingly when testing with M2 we have zones 465/112mm and 533/128mm.

Fig.13 A test set-up of the secondary mirror for the VST telescope.

In both cases we have an overlapping zone (a zone which is tested both with M1 and M2) 200mm and larger. This overlapping zone allows to make a joint of the topographies received after interferometric testing using M1 and M2 mirrors to plot a total topography of the secondary mirror to be test.

Fig.14 A test set-up of the secondary mirror for the NOA telescope.

The secondary mirror of the 2m TTL telescope (our common project with Carl Zeiss Jena) shall be tested in the same set-up (Fig.15) and using the same spherical mirrors.

Fig.15 Testing of the secondary mirror for the TTL telescope.

The hyperbolic mirror has the following parameters:

• Clear aperture: 617 mm;
• Radius of vertex sphere: 4813.19 mm;
• Central shielding: 59 mm.

The implementation of this test method cheapens appreciably the testing process and decreases manufacturing time for the above mentioned secondary mirrors.