Magomed A. Abdulkadyrov, Sergey P. Belousov, Alexandr N. Ignatov, Vladimir E. Patrikeev, Vitaliy V. Pridnya, Andrey V. Polyanchikov, Victor V. Rumyantsev, Anatoly V. Samuylov, Alexandr P. Semenov, Yury A. Sharov

JSC "LZOS" manufactures astronomical mirrors from the stage of blanks to finished astronomical mirrors. During 1997-2002 JSC "LZOS" has fabricated a number of astronomical mirrors under the contracts with Carl Zeiss Jena, Germany, up to 2.6m in diameter and up to 100m asphericity. Concave surfaces are tested with lens and lens-mirror wavefront correctors of special design. The Hindle test set-up is used for convex hyperbolic surfaces. For high-aperture hyperbolic surface, we use two Hindle spheres to test one mirror. At the present time, we have developed the test procedures for high-aperture surfaces of primary (diameter 4100 mm, asphericity about 881m) and secondary (diameter 1240 mm, asphericity about 364m) mirrors for the VISTA Project as well as the Fizeau test set-up for the LAMOST M_B sub-mirrors.

Keywords: telescopes, optical fabrication, optical testing, aspheres

* Correspondence: e-mail: lastro@comail.ru; Telefone: 007-095-552-15-47; Fax 007-095-552-15-86

The interferometric test methods for telescopic mirrors at their manufacturing and certification to define surface deviations and obtain a quantitative assessment of these deviations^1,2 have been used at LZOS for more than one decade. The testing of plane, spherical and aspherical (concave, convex) optical surfaces is carried out from the stage of grinding to the stage of final polishing. For each surface shape its own testing method is developed and fulfilled.

Since 1997 LZOS produced a number of primary mirrors for several projects, including primaries for the TTL, NOA and VST³ projects, of 2050 mm to 2650 mm⁴ in diameter. Today LZOS is contracted for the work on the manufacturing and testing of the primary mirror for the VISTA telescope (Visible and Infrared Survey Telescope for Astronomy)⁷ of 4100 mm diameter. The VISTA telescope is a 4m diameter wide field survey telescope designed to survey large areas of the southern sky both at visible and infrared spectrum. The telescope is equipped with an Alt-Azimuth mount and a Cessegrain focus.

The VST and VISTA primaries are the most complicated among the above-mentioned mirrors, since they have considerable asphericity for such diameters of the mirrors and high requirements for surface accuracy.

During the interferometric testing the primary mirrors are supported on the membrane-pneumatic manufacturing cells in the vertical test benches⁴. The membrane-pneumatic cell ensures stable position of an optical component in the course of tests. The support cell is equipped with an automatic system of mirror position stabilization throughout the cell when changing the ambient conditions (atmospheric pressure, humidity) during testing of surface shape and so secures steady state of the mirror surface with the required accuracy.

Specification	Mirror
	VST Primary Mirror	VISTA Primary Mirror
Material	Sitall CO-115M	Zerodur
Surface shape	concave , hyperbolic	concave , hyperbolic
Outer diameter	2650 mm	4100 mm
Inner diameter	600 mm	1200 mm
Thickness	140 mm (meniscus)	170 mm (meniscus)
Clear aperture	2600 mm	4020 mm
Radius of curvature	9509 ± 4 mm	8094 ± 20 mm
Conic constant	-1.139899	-1.129792
Asphericity from the best-fit sphere	105m	881m
Encircled energy (80%) with subtraction of regular errors	< 0.15 arc sec	-
RMS amplitude error of the wavefront	-	< 40 nm
RMS slope error of the wavefront	-	< 0.06 arc sec

In the course of the aspherization (by grinding) of the VST primary mirror surface an IR interferometer with a CO₂ laser ( = 10.6m) and a mirror wavefront corrector (Fig.1) were used. The mirror wavefront corrector consists of three mirrors and surfaces of all mirrors are spherical. The testing at the stage of the final polishing was carried out using lens wavefront correctors. A Twyman-Green interferometer was used for interferometry. Obtained interferograms are recorder by means of a CCD camera. In spite of large asphericity LZOS managed to design and produce a compact two-lens optical system with zero aperture of a wavefront corrector. A diameter of an input parallel beam is not more than 20 mm (Fig.2).

An encircled energy of the primary mirror of 80% in a dispersion spot of less than 0.15 arc sec diameter was obtained and rms wavefront error < 20 nm. To improve reliability of the test results a second corrector was manufactured taking into account previously measured actual vertex radius of the mirror. The final interferogram of the VST primary is shown in Fig.2.

As the VISTA specification indicates a hyperbolic surface deviation from a vertex sphere is almost 4 mm, that just defines specificity of the testing method. It was not possible to solve the task of testing with a two-lens corrector (like for the VST mirror). As a result of analysis a three-lens wavefront corrector system was calculated (Fig.3). To ensure testing at the stage of the aspherization by grinding and obtain more reliable information on a surface shape a mirror-lens wavefront corrector operating at both IR range ( = 10.6m) and =0.6328m was designed (Fig.3). All components of the lens and mirror-lens correctors have only flat and spherical surfaces. The components of the lens corrector also have property when some of them can be tested in pairs. This property allows additional check of the manufactured corrector lenses quality. Conversion from the IR range to the visible one in the mirror-lens corrector is fulfilled by change of a correcting lens.

A manufacturing error of both correctors is sufficient to achieve the specification requirements of an rms error < 40 nm.

Fig.3 Test setup with the lens and mirror-lens correctors.

The VST and VISTA secondary mirror were also the most complicated for the manufacturing.

Specification	Mirror
	VST Secondary Mirror	VISTA Secondary Mirror
Material	Sitall CO-115M	Sitall CO-115M
Surface shape	convex , hyperbolic	convex , hyperbolic
Outer diameter	938 mm	1241.5 mm
Inner diameter	176 mm	350 mm
Thickness	130 mm	156.6 mm
Clear aperture	2600 mm	1241 mm
Radius of curvature	4374.46 ± 2 mm	4018.81 ± 2 mm
Conic constant	-5.421864	-5.548792
Asphericity from the best-fit sphere	94m	364m
Encircled energy (80%) with subtraction of regular errors	< 0.15 arc sec	-
RMS amplitude error of the wavefront	-	< 40 nm
RMS slope error of the wavefront	-	< 0.15 arc sec

To test convex hyperbolic surfaces the Fizeau and Hindle setups are most popular. Realization of the Fezeau method requires an additional lens of a diameter some larger than a component tested with a reference aspherical surface. Manufacturing of a reference aspherical surface requires specific means and test setups, and optical quality of such surface shall not be worse than the required quality of a secondary mirror. Taking into consideration activities on the manufacturing of some secondary mirrors with similar parameters at the same time that solution was found technically laborious and expensive.

When the Hindle sphere is used to test secondary mirrors only one spherical mirror shall be manufactured and tested, besides during the testing only one reflection shall go from the Hindle sphere and two reflections from a surface tested. This feature of the method allows more detailed analysis of secondary mirrors. Wavefront errors can be subtracted from the total wavefront, if necessary.

In some cases a test sphere could have very large diameter. Therefore for each of the hyperboloids of the TTL, NOA and VST secondary mirrors the testing method with two Hindle⁵ spheres was elaborated.

The optical tests setup for the VST secondary mirror using two spheres of 1985 mm (R = 2708 mm) and 1640 mm (R=3995 mm) in diameter is presented in Fig.4. One sphere is used for the testing of external area of a component and other one for internal part. A common area of overlapping at the testing composes no less that 300 mm. Reconstruction of the surface topography was made with a special method⁵. To implement this optical setup a test bench was designed, manufactured and mounted (Fig.5). This test bench allows testing of a surface throughout the aperture at one mirror placement.

Subtraction of the spherical mirrors wavefronts was made to improve reliability of the test results, and the total wavefront twice reflected from the hyperbolic surface had an rms error about 0.15. In Fig.6 interferograms of the VST secondary mirror are shown. The VST secondary has a 13 nm rms error.

Fig.6 Interferograms of the VST secondary mirror.

The main features of the testing of the VISTA secondary hyperbolic mirror (Fig.7) are as follows:

• high aperture D/f₁ = 1/1;
• lightweighted structure of the mirror;
• insufficient area of overlapping at testing with Hindle spheres available at LZOS;
• testing in the standard cell with the working surface upwards.

Based on the requirements above LZOS with the VISTA project office took a decision to test the mirror surface in a vertical test bench with a Hindle sphere of 2420 mm (R = 2510 mm) in diameter. The Hindle sphere was calculated to ensure parameters for full aperture testing. The design of a test bench of the vertical Hindle setup was elaborated and is being manufactured now (see Fig.9). This test bench will be used for the testing of the secondary mirror and the Hindle sphere as well as R0 and Ê. The test bench mechanical parts ensure reliable attachment of the secondary mirror and necessary adjustment movements to coincide axis of the mirror, Hindle sphere and Twyman-Green interferometer. To check the operational integrity of the mirror cell an additional testing of the mirror central area in a horizontal test setup using the available Hindle sphere of 1985 mm diameter (Fig.8) will be also carried out.

Fig.9 Test bench for VISTA secondary mirror test setup.

At present LZOS is manufacturing finished segments of the primary mirror M_B for the LAMOST Project (The Large Sky Area Multi-Object Fiber Spectroscopic Telescope, Chine).

The LAMOST telescope is a reflecting Schmidt telescope. There are two large segmented mirrors in the LAMOST: one is the Schmidt plate M_A, and the other is the spherical primary mirror M_B. The dimension of M_B is about 6.7m x 6m. It is composed of 37 hexagonal sub-mirrors made of Zerodur supplied by Schott.

MB Sub-mirror Specification
Quantity	37 sub-mirrors
Material	Zerodur
Shape	hexagonal
Surface shape	concave, sphere
Diagonal dimension	1100 mm
Thickness	75 mm
Radius of curvature	40000 ± 20 mm
RMS error	20 nm
P-V	150m
Difference of sub-mirrors radius	< 1.5 mm

The main complexity of the spherical surface testing of the sub-mirrors of the segmented primary mirror M_B is a large radius (40 000 mm) and a tolerance of a radius deviation for all the sub-mirrors of ± 1.5 mm. The required specification is met only with using a vertical Fizeau test set-up (Fig.10). This method allows to reduce a test path to 10 m as well as to carry out the testing with respect to one reference surface. Defocusing of more than ±0.5 will be evidence of a radius deviation of more than ± 1.5 mm. The basic element of the optical test setup is a Fizeau lens one surface of which has a radius of curvature of 40 000 ± 20 mm and represents as a reference surface. The other surface of the lens is hyperbolic and serves to direct rays of a homocentric beam along the normal to the spherical surface.

A test bench was designed and fabricated to implement that technique (Fig.11). The test bench is used for testing of both the Fizeau lens and the spherical sub-mirrors of the segmented mirror. The lens is made of silica glass. To test the spherical lens a 1200 mm diameter a reference spherical mirror with a radius of curvature of 40 000 ± 7 mm was made of Sitall. The certification of the mirror was carried out in a special vertical test bench on the basis of the 70 m height vacuum chamber. Figure 12 shows the interferogram of the Fizeau lens tested using the spherical reference mirror.

Fig.10 The Fizeau test setup used for testing of the segmented mirror elements:
1 - sub-mirror to be tested; 2 - fizeau lens with reference surface;
5,6,8 - elements of interferometer 3; 4 - CCD camera; 7 - diagonal mirror.

Fig.11 Test bench for spherical segments.

Fig.12 Interferogram of reference surface of the Fizeau lens.

LZOS is manufacturing and testing the tertiary flat mirror of elliptical shape made of Zerodur for the GRANTECAN (Gran Telescopio Canarias, Spain)⁸ astronomical telescope. The overall dimensions of the mirror are 1520 mm x 1073 mm. To test the flat surface we designed and mounted a test bench of Ritchey-Common system with two incident angles of a principal ray. An angular position of an interferometer optical axis to the horizon plane is 60^o.

Fig.13 Vertical test bench.

1. Twyman-Green interferometer;
2. Adjustment table;
3. Optical shop metal constructions;
4. Floor - optical shop basis;
5. Carriage frame;
6. Platform with rotating unit;
7. Reference mirror axial displacement unit;
8. Flat mirror lateral displacement unit;
9. Carrying fork with flat mirror rotating unit;
10. Mirror in standard cell;
11. 1580 mm diameter reference mirror in standard cell.

The test bench (Fig. 13) was designed to make possible testing of two angular mirror positions (incident angles of a principal ray i₁ = 30^o and i₂ = 60^o) at one position of an interferometer. This property was achieved due to rotating movements of a platform (6) along high-precision guiding rails of a frame (5). An installation error of an upper base surface of the platform to the reference level is ± 12". An error of the guiding rails on a base diameter is ± 8". The platform (6) is designed to ensure the minimum deformation when rotating.

The mirror (11) is supported in a standard lever-type cell designed and manufactured by AMOS. A unit (8) ensures an accurate coincidence of the mirror optical axis in transverse direction. A unit (9) is used to rotate and fix the tertiary mirror for the testing positions. Rotation is implemented with respect to an axis passing near the mirror surface to minimize interferometer refocusing.

The mirror in a standard cell (10) is mounted on a special seats on a carrying fork (9) and is fastened by three bolted connections. The mirror is rotated and fixed in test position 1 for i₁ = 30^o by means of a rotating unit and then the mirror surface is tested interferometrically. With the help of a rotating unit (9) the mirror is rotated and fixed for the test incident angle i₂ = 60^o. Then the platform with the mirror are rotated at 180^o using a rotating unit (6) to test position 2, and the mirror surface is tested interferometrically.

Interferometric test data are processed for the two positions of the Ritchey-Common setup. Deviations of the mirror surface shape from the perfect shape are results of processing the data. Particular components of the total error such as spherical aberrations, astigmatism, coma etc., as well as sphericity and local error are mathematically subtracted.

In 2003 LZOS finished manufacturing of optics for two Schmidt systems with a spherical mirror of about 600mm diameter (1294 mm radius of curvature) and a Schmidt plate of 424 mm diameter. The Schmidt plate has asphericity of about 84m from the best-fit sphere of 19800 mm radius. The spherical mirror and compensating elements were manufactured separately, and the final testing and manufacturing of the Schmidt plate were implemented in an optical setup using a large size objective (see Fig. 14). The main advantage of this test setup is the possibility to test the telescope assembly as a whole.

Fig.14 Interferometric test setup for the Schmidt telescope elements.

1. He-Ne laser;
2. Beam splitter;
3. Rotational mirror;
4. Rotational mirror + micro-objective (A=0.4);
5. Compensative plate;
6. Schmidt telescope mirror;
7. Schmidt plate;
8. ÎCollimator objective (D=500, D/F'=1/6);
9. Interferometer (set in collimator objective focus);
10. CCD camera;
11. Laser beam of interferometer operating track;
12. Laser beam of interferometer reference track;
13. Plane wavefront (interferometer is set with respect to flat test mirror).

The production capabilities and development works in the field of the optical interferometric testing allowed LZOS to manufacture the primary and secondary mirrors of the TTL, NOA and VST projects with the required quality and according to the specifications. In particular a set of the mirrors for the VLT Survey Telescope (Osservatorio Astronomico di Capodimonte Napoli), the primary of 2650 mm diameter (F/1.8) and the secondary of 938 mm diameter (F/2.3), has an encircled energy of 80% on axis of two mirror system in a spot of less than 0.20 arc sec after taking away of constant coefficients, tilt refocusing and decentring come, and an encircled energy of 80% on axis of the two mirror system in a spot of 0.12 arc sec after additional subtraction of spherical aberration coefficients, astigmatism, triangular coma and quadratic astigmatism.

We developed optical test method for the VISTA primary mirror of 4100mm diameter (881m asphericity) and secondary mirror of 1240 mm diameter (364m asphericity).

The test setup was designed for the 40 sub-mirrors of the LAMOST segmented mirror M_B (radius of curvature of 40 m and difference between radii < 1.5 mm). The test bench and the Fizeau lens were produced.

For the tertiary mirror of the GRANTECAN project LZOS developed the optical test setup and produced the test bench. Now we are carrying out the final polishing of the mirror optical surface.

The test setup for the optical set of the telescope with the Schmidt plate was developed at LZOS. The test bench was installed and the testing of two sets of the Schmidt telescopes was carried out.

ACKNOWLEDGEMENTS

The authors express their thanks to Prof. D.T. Puryayev (N.E. Bauman Moscow State Technical University, Russia) for the optical test setups calculations, W. Heilemann (Carl Zeiss, Germany) and P. Gloesener (AMOS, Belgium) for joint work on the GRANTECAN M3, team of the VISTA project office (UK) and especially Eli Atad - Ettedgui for the opportunity to take part in the VISTA project and critical analysis of the materials.

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