The application of wavefront coding technology to a large segmented synthetic aperture telescope

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-off between planet light throughput and diffracted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) diffracted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the ”Auxiliary Field Optimization” (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, specifically fictitious ”auxiliary” electric fields which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a ”dark hole” region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured off-axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

The cophase calibration system is applied for adaptive optical phasing with a large segmented telescope mirror, which commonly uses 3-DOF micro-position device with three micro-displacement actuators to drive segments in parallel, making the entire segmented mirror in phase at one time and obtaining the desired sensor readings accordingly. In order to run the active control system to make the segments cophase, it is necessary to calculate the coordinates of the three driving points correctly for segmented mirrors specially limited in geometric parameters, especially for the stability and sensitivity of the micro-positioning device. The mirrors will be supported on a massively parallel system of electrostatically controlled, interconnected microactuators that can be coordinated to achieve precise actuation Adjusting posture of each segment independently so as to obtain the co-phasing errors and to control them at a nanometer level. Several generations of individual actuators as well as parallel arrays of actuators with segmented mirrors have been designed. A mechanical model of the system has been constructed and simulated numerically to obtain the actual position of three actuators using the RPY angle describing means. A three-channel parallel control scheme has been developed and implemented on a segmented mirror array. A universal evaluating method for optimization is prompted and will be a good guide to the design optimization of micro-positioning device for each segmented mirror when the mirrors are groundbased horizontally.

As part of leading research for future space missions, we have been conducting a feasibility study on an optical imager system assumed to be mounted on a geostationary satellite for instantaneous Earth observation as needed. The target for ground sampling resolution was less than 10 m from geostationary orbit, and the primary mirror was set to a diameter of 3.5 m based on our previous conceptual study. Moreover, the primary mirror was conceptually designed with cuttingedge technologies such as segmented mirror technology for scalability to larger sizes in the future. The main technical challenges in achieving such a large optical system entailed reducing the primary mirror weight and minimizing dimensional changes in the space environment. Optical material selection was a particularly key consideration in defining the optical system performance. Therefore, a trade-off study was conducted on the selection of materials for the segmented primary mirror. The thermal deformation behaviors of certain low thermal expansion materials as mirror substrates were analytically compared under the assumed unsteady and inhomogeneous thermal conditions in geostationary orbit, in consideration of the deterioration induced by radiation.

Application of an interferometric method in phasing the segmented primary mirrors of the high-aperture telescope

Segmented deployable space imaging systems represent a promising solution for future ultra-large aperture space optical systems. With the proposal of larger aperture segmented telescope designs, ultra-lightweight primary mirror (PM) segments with lower areal density have become a research hotspot. However, the lightweight structure poses more stringent challenges in maintaining a high-precision surface figure of PM segments. Active deformable PM segments with surface shape adjustment capability serve as an effective approach to address these challenges. To achieve surface figure control at the PM segments scale, accurate determination of the PM segments' surface figure error magnitude is fundamentally required. After in-orbit deployment of segmented mirror systems, deviations between the actual position and ideal position of PM segments will induce optical pupil localization errors in the system's overall pupil plane. The optical pupil localization error (OPLE) of PM segments leads to an inaccurate decoupling of wavefront errors into individual PM segments, thereby compromising the accuracy of surface figure correction. This paper proposes an active segmented mirror optical pupil localization method based on local wavefront sensitivity analysis. By utilizing the deformation capability of active optics, we establish sensitivity equations through wavefront variations within the PM segments' pupil region before and after surface shape adjustments, enabling the inverse solution for the OPLE of PM segments. The proposed method achieves micrometer-level positioning accuracy of PM segments' positional errors solely relying on focal plane information, while avoiding the introduction of additional mechanisms. Experimental validations were designed to verify the feasibility of the method.

The primary mirror's aperture limits the telescope's resolution. A segmented primary mirror is adopted to improve the resolution. Since the primary mirror with large diameter is segmented, the segmented mirrors must be co-phased to ensure the imaging quality. Optical method and electrics method can be used to test the co-phasing error between the two adjacent segment mirrors. However the optical system of telescope will be complicated by attaching an optical cophasing test system, and some unstable factors will be introduced. In this paper, an electrics co-phasing testing method was discussed. Capacitance micrometer technology was used in this method, and relevant experiments have been carried out. And the result of these experiments indicated that the method described in this paper is feasible.

Numerical simulation of closest vane thermal performance in large aperture Space Solar Telescope

Off-axis refractive system with the noticeable advantages such as high resolution, large view field and central obscuration removed, has been one of the powerful systems for space astronomical telescopes in recent years. However, misalignment errors and surface error of mirrors are significant especially in the alignment progress of off-axis reflective telescope with large aperture. Computer aided assembling (CAA) jointly provide a robust misalignment correction method to ensure the accurate alignment of telescope. In this paper, system aberration of misalignment coaxial system with two mirrors is analyzed in detail, moreover, the off-axis system is studied further, especially in the off-axis Gregorian system. And the feasibility of correction values solution about off-axis refractive system is discussed. Both the simulation and experiment results demonstrate the feasibility of the proposed alignment method and high accuracy has been achieved. In the testing off-axis Gregorian system, the primary mirror is paraboloid with 1200 mm diameter, 210 mm off-axis distance, and the second mirror is ellipsoid with off-axis distance 129.0 mm, focal length 425 mm and 2125 mm, respectively. For the testing off-axis Gregorian system, the RMS value of primary mirror and second mirror are 0.021 λ and 0.027 λ (λ = 0.6328 nm), and the testing optimization result of system wavefront aberration with RMS value is better than 0.058 λ is achieved. The reverse optimization method testing can achieve high-accuracy measurement ability, which provides efficient and flexible way for the off axis refractive system from various types of elements with complex surfaces.

TMA (Three Mirror Anastigmatic) is popular to the design of space-based optical system. This paper describes the characteristics of the on-axis TMA optical system. An on-axis TMA system with 13m focal length is designed and analyzed. To solve the initial configuration parameters, Cassagrain structure is confirmed firstly, and then the tertiary mirror. Based on initial configuration parameters, automatic optimization is executed in ZEMAX program, and design result with excellent image quality is acquired, which shows the procedure we choosed with good advantage of computer processing. As the distortion of the design reaches 1%, its influences on TDICCD brushing camera are discussed. The source of distortion is analyzed and correcting methods are considered. Zero focal power corrector is chosen to correct the distortion, and the corrected distortion is less than 0.02%. The research on on-axis TMA system in this paper makes a foundation for farther high-resolution remote sensing applications.

Some proposed architectures for large telescopes in space such as the Next Generation Space Telescope (NGST) utilize a segmented primary mirror with active control. The image quality for those systems can be characterized by the quality of the point spread function (PSF). We will present results from our simulations that demonstrate the quality of the PSF at various wavelengths, as characterized by the metrics of Strehl Ratio and encircled energy fraction. These metrics capture the critical features of the PSF that ensure good spatial resolution of the core at the nominal diffraction limited wavelength without having excessive scattering into the nearby diffraction pattern for observations at shorter wavelengths. The relationship of the image quality to the spatial frequency content of the system wave front error and to the image motion that occurs during the exposure (line-of-sight jitter) are explored.

NASA's Marshall Space Flight Center, in collaboration with Blue Line Engineering of Colorado Springs, Colorado, is developing a Segment Alignment Maintenance System (SAMS) for McDonald Observatory's Hobby-Eberly Telescope (HET). The SAMS shall sense motions of the 91 primary mirror segments and send corrections to HET's primary mirror controller as the mirror segments misalign due to thermo-elastic deformations of the mirror support structure. The SAMS consists of inductive edge sensors. All measurements are sent to the SAMS computer where mirror motion corrections are calculated. In October 2000, a prototype SAMS was installed on a seven-segment cluster of the HET. Subsequent testing has shown that the SAMS concept and architecture are a viable practical approach to maintaining HET's primary mirror figure, or the figure of any large segmented telescope. This paper gives a functional description of the SAMS sub-array components and presents test data to characterize the performance of the sub-array SAMS.

A 3.8 m segmented telescope is planned to be built at the Okayama Astrophysical Observatory by the joint program among Kyoto university, Nagoya university, NAOJ, and Nano-Optonics Energy Inc. This is the world’s first optical-infrared telescope whose primary mirror is composed of “petal-shaped” segment mirrors. To investigate the best layout of the displacement sensors as well as to study the control algorithm, we have developed a simulation software for the segmented petaloid mirrors. This simulator calculates the vertical position differences between the segments at the 60 displacement sensors based on the three-dimensional movements of the 54 actuators, and enables us to test the control algorithms under various conditions including random noise on the displacement sensors, random movement errors of the actuators, and unexpected lateral shifts of the segments. The outputs of the simulator are not only the phase error of the primary mirror but also the PSF image, taking the structure function of the optical surfaces into account. Using a singular value decomposition method, we found that the 18 petal-shaped segments are controllable within the required displacement errors of 15 nm under the following three conditions: 1) the displacement measurement sensors are placed in staggered fashion between segments, 2) the displacement measurement sensors are axisymmetrically placed with respect to the optical axis, and 3) the relative lateral shift and rotation of each segment are less than 500 μm and 0.05 degree, respectively. In this report, the control algorithm, requirements for the layout of the displacement measurement sensors, and the simulated performance will be presented.

Sensitivity analysis of test methods for aspheric off-axis mirrors

The phase diversity (PD) algorithm is an image-based co-phasing error detection method for segmented mirror synthetic aperture optical systems. Particle swarm optimization (PSO) is suitable for PD for its fast convergence speed and simple structure. However, with the increase of the numbers of subapertures, optimization of cost function formed by the PD algorithm becomes a high-dimension non-linear optimization problem, which would lead PSO to result in a premature solution. Regarding the problem above, this paper presented a modified PSO in the PD algorithm to co-phase the segmented primary mirror, which overcame drawbacks of the traditional PSO, such as premature convergence and deactivation of particles, and enhanced the dig ability of the algorithm. Vast simulation results show that the modified PSO in the PD algorithm can effectively restore the segmented primary mirror, reducing the peak-to-valley (PV) value to 0.0012λ and the root mean square error to 0.0007λ, and raising the Strehl ratio to over 0.999. A comparison was also conducted to show that the modified PSO has advantages over two existing algorithms in higher accuracy and faster convergence speed.

CTA (Cherenkov Telescope Array) is a project for the next generation of the ground-based gamma-ray observatory. CTA will cover a wide energy range, 20 GeV and 300 TeV, by 3 types of the telescopes whose diameters are different. The Large-Sized Telescopes (LSTs) of the CTA are designed to cover the lowest energy range. We are working on mirrors for 4 LSTs which will be built at La Palma, Spain. The parabolic primary mirror of CTA-LST is 23 m diameter and its focal length is 28 m. The primary mirror consists of 198 segmented mirrors. Total effective reflective area is about 370 m2. Each mirror has a hexagonal shape of 1.51 m side-by-side size. It has a sandwich structure which consists of aluminum honeycomb (60 mm thickness) and two glass surfaces (2.7 mm) and the total weight is about 47 kg. We used a sputtering deposition technique to coat in the surface with 5 layer. The coated layers protect the surface for long operation such as 10 years at outside with a reflectance degradation of less than 1 % a year. The reflectance of the mirror reaches about 92 % at 400 nm and its resolution is 0.5 mrad in diameter that contains the 80 % light reflected by the mirror. The production technique based on cold slumping gave us the stable its production. We report on the design of the segment mirror and the production of about 950 hexagonal 2 m2 mirrors to achieve the parabolic shape of the optical system for 4 LSTs.