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DOI: 10.21122/22209506201893234242
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Introduction
In recent years, the largest terrestrial telescopes
operating in a wide spectral range of wavelengths
use the technology of segmented composite mirrors
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[1–4]
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. A typical representative of this class is
the Keck Observatory of two telescopes (Keck
Telescope) Mauna Kea, Hawaii (1996), in which two
10 meter mirrors consist of 36 segments.
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A typical representative of this class is
the Keck Observatory of two telescopes (Keck
Telescope) Mauna Kea, Hawaii (1996), in which two
10 meter mirrors consist of 36 segments.
The most wellknown method of aligning
segmented mirrors is described in the works of
Mast and Nelson
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and found practical application
in the alignment of Keck telescopes. According to
this method, each individual segment is described
as a local curve of an aspherical surface, and all
together they form a common curve of the aspherical
surface.
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Segments have different geometric dimensions and a distorted hexagonal shape, i. e. elongate
in the radial direction to ensure minimization
of the intersegment gap area.
The exact mutual position of the mirror segments relative to the base surface is established
in two steps
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.
The first stage involves geometrical positioning,
during which the plane segments are displaced
along three linear directions (along the coordinate
axes OX, OY and OZ in the base coordinate system)
and the maximum reduction of all optical rays in the
central region close to the center of the curvature
of the mirror is achieved.
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respect to the top of the mirror segment (two
slopes with respect to the optical axis and rotation
around it) and minimization of the wave front
difference (aberrations) at the working wavelength
of the telescope (Figure 1). The error in positioning
and relative positioning of individual segments
should not exceed the dimensions of the working
wavelength
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.
Figure 1 – Diagram of geometric and optotechnical positioning of mirror segments
The comparison method involves the process
relative to a common reference surface by means
of actuators (eg piezo drives).
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segment is performed under the condition that
the normal vectors constructed from the center
of the flat surface of each segment must intersect
at one calculated point on the axis OZ coinciding with
the center of curvature of the base spherical surface.
The tangent plane in space is determined by three
Cartesian or spherical coordinates (Figure 1)
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.
However, in practice it is impossible to realize
completely identical mirror segments, and their
normals do not converge at the point of the double
focal length of the mirror spheroid, but in some region
of this point.
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The optimization problem usually
reduces to minimizing this region of convergence,
as well as to reducing the difference between the
real and calculated wavefronts, both for the entire
composite mirror, and for each segment separately
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.
In [6], the efficiency of using the method of
geometric computer positioning of 20 controllable
hexagonal mirror segments forming a 500 mm
composite mirror for 1 hour with an error of not
more than 0.01 mm is shown in [6].
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The optimization problem usually
reduces to minimizing this region of convergence,
as well as to reducing the difference between the
real and calculated wavefronts, both for the entire
composite mirror, and for each segment separately [9].
In
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[6]
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, the efficiency of using the method of
geometric computer positioning of 20 controllable
hexagonal mirror segments forming a 500 mm
composite mirror for 1 hour with an error of not
more than 0.01 mm is shown in [6].
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In [6], the efficiency of using the method of
geometric computer positioning of 20 controllable
hexagonal mirror segments forming a 500 mm
composite mirror for 1 hour with an error of not
more than 0.01 mm is shown in
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[6]
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. In the classical
scheme of alignment of similar elements using an
autocollimator, it takes about 20 hours. It should be
noted that the complexity of the alignment increases
exponentially, so it took 1 year to set up a composite
of positioning each individual mirror segment
236
telescope mirror Gran Telescopio CANARIAS with
Segmented mirrors with regular hexagon
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In addition, when mounting segments on supports,
convenient placement of actuators and sensors
at the edge points is provided for their subsequent
positioning and optimal position control
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.
3) The projection of segments and the coordinate
system OXYZ.
The segmented mirror is described in such
a way that when projecting onto the XOY plane,
the individual segments are a circular array of regular
and evenly spaced hexagons relative to the main
optical axis collinear with the geometric axis OZ [11].
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The segmented mirror is described in such
a way that when projecting onto the XOY plane,
the individual segments are a circular array of regular
and evenly spaced hexagons relative to the main
optical axis collinear with the geometric axis OZ
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.
In the plane of the optical axis, two parameters
determine the geometry of the projection of segments: the length of the side of the segment and
the intersegment gap. The length of the side of the
segment is determined by the distance between two
adjacent vertices of the projected segment, while
the intersegment gap is determined by the distance
b
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Intersegment gaps allow avoiding contact
between adjacent segments and are assigned taking
into account processing tolerances, in addition they
allow compensation of gravitational and thermal
deformations of the mirror cell
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. The geometric
size of the gap should be as small and uniform
as possible across the entire width [13].
5) Segmentation approach.
In order to minimize the distortion of segments
caused by the curvature of the aspherical mirror
surface, two possible approaches to segmentation
are proposed:
a) Consider the case of a mosaic with regular
hexagons and equal
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Intersegment gaps allow avoiding contact
between adjacent segments and are assigned taking
into account processing tolerances, in addition they
allow compensation of gravitational and thermal
deformations of the mirror cell [12]. The geometric
size of the gap should be as small and uniform
as possible across the entire width
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[13]
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.
5) Segmentation approach.
In order to minimize the distortion of segments
caused by the curvature of the aspherical mirror
surface, two possible approaches to segmentation
are proposed:
a) Consider the case of a mosaic with regular
hexagons and equal gaps across the surface.
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In order to minimize the distortion of segments
caused by the curvature of the aspherical mirror
surface, two possible approaches to segmentation
are proposed:
a) Consider the case of a mosaic with regular
hexagons and equal gaps across the surface.
According to Dan Curley's method
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, we make
the assumption that all segments are identical
flat hexagons, with the best relative position
relative to the common aspherical surface. In the
first approximation on a flat surface we create an
array of identical regular hexagons separated by
homogeneous gaps.
b) An alternative technique was proposed by
Mast and Nelson fo
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In the
first approximation on a flat surface we create an
array of identical regular hexagons separated by
homogeneous gaps.
b) An alternative technique was proposed by
Mast and Nelson for the TMT (Thirteenmeter
telescope)
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, according to which hexagonal
segments are not separated by spaces. An array
аb
a diameter of 10.4 m (73 m2).
The purpose of the research was to develop
an algorithm for solving the problem of geometric
positioning of hexagonal segments of a mirror
telescope, constructing an optimal circuit for traversing elements when aligning to the nearest
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