Abstract
In recent years, the largest terrestrial and orbital telescopes operating in a wide spectral range of wavelengths use the technology of segmented composite elements to form the main mirror. This approach allows: to expand the spectral operating range from 0.2 to 11.0 μm and to increase the diameter of the entrance pupil of the receiving optical system, while maintaining the optimal value of the exponent m S – mass per unit area. Two variants of adjusting the position of mirror segments are considered when forming an aspherical surface of the second order, with respect to the base surface of the nearest sphere, including geometrical and opto-technical positioning. 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 radius to an aspherical surface, and also to program the output calculation parameters to verify the adequacy of the results obtained. Various methods for forming arrays from regular hexagonal segments with equal air gaps between them are considered. The variant of construction of arrays through concentric rings of an equal step is offered. A sequential three-step method for distributing mosaic segments is presented when performing calculations for aligning the aspherical surface: multipath linear; multipath point; block trapezoidal. In the course of mathematical modeling an algorithm was developed to solve the problem of geometric positioning of flat hexagonal segments of a mirror telescope. In the Python programming language, program loops are designed to form the data array necessary to construct a specular reflective surface of a given aperture. In the software package Zemax , the convergence of optical beams from flat hexagonal elements to the central region of the aspherical surface is verified.
Highlights
The largest terrestrial telescopes operating in a wide spectral range of wavelengths use the technology of segmented composite mirrors [1,2,3,4]
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
The exact mutual position of the mirror segments relative to the base surface is established in two steps [6]
Summary
The largest terrestrial telescopes operating in a wide spectral range of wavelengths use the technology of segmented composite mirrors [1,2,3,4]. The most well-known method of aligning segmented mirrors is described in the works of Mast and Nelson [5] and found practical application in the alignment of Keck telescopes. 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. The second stage of opto-technical positioning is carried out in three angular directions with 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). It should be noted that the complexity of the alignment increases exponentially, so it took 1 year to set up a composite telescope mirror Gran Telescopio CANARIAS with a diameter of 10.4 m (73 m2)
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