Secondary Mirror Research Articles

Field of view-independent detection of secondary mirror position errors in coaxial reflecting space telescopes using deep learning

The operation of coaxial reflecting space telescopes in orbit is affected by adjustments and space disturbance, causing position errors in the secondary mirror (SM), which reduce resolution and seriously affect imaging quality. Most existing methods for detecting SM position errors rely on wavefronts or images obtained from one or more fixed field of views (FOVs), yet the inherent uncertainty of the FOV can lead to significant errors in detecting SM position errors. To address this problem, this paper, believed to be the first, proposes an FOV-independent SM position error detection method for coaxial reflecting space telescopes based on a pair of symmetric positive and negative defocus point spread functions (PSFs) and the dual-branch convolutional neural network (DB-CNN). First, a nonlinear relationship between the SM position errors and the PSFs at arbitrary FOV is established, using the DB-CNN. Then, the method using a pair of symmetric positive and negative defocus PSFs at arbitrary FOV to obtain the position errors of the SM is proposed, and the simulation results show that, despite the uncertainty of the FOV, the SM position errors can be detected with high precision. This approach enables SM position error correction independent of the FOV, significantly enhancing the imaging quality. Finally, a modified method is proposed to address the problem caused by the primary mirror (PM) figure errors. Simulations prove that the SM position errors can be accurately obtained even in the presence of PM figure errors.

Off-axis freeform optical design for large curved field of view imaging

Recording neuron activities is pivotal for elucidating the functionality of the nervous system. However, the curved cortex surface of experimental mice presents a significant challenge for optical systems, particularly when a larger field of view (FOV) is required. To address this challenge, we have designed an off-axis three-mirror system that incorporates freeform surfaces on both the primary and secondary mirrors. This system achieves a large imaging FOV of 18°×9°, delivering near-diffraction-limit imaging quality across a curvature spectrum of −14.7 to −15.3mm. A manufacturability analysis indicates that the freeform surfaces are straightforward to produce, and the overall system demonstrates low sensitivity to tolerance and measurement errors. This study introduces a novel, to the best of our knowledge, solution to the field curvature constraints in optical imaging of cortical activity, providing substantial technical support for in vivo neuronal imaging endeavors.

Telescope Alignment Method Using a Modified Stochastic Parallel Gradient Descent Algorithm

To satisfy the demands of high image quality and resolutions, telescope alignment is indispensable. In this paper, a wavefront sensorless method based on a modified stochastic parallel gradient descent algorithm (SPGD) called the adaptive moment estimation SPGD (Adam SPGD) algorithm is proposed. Simulations are carried out using a four-mirror telescope, whose aperture is 6 m and fields of view are Φ2°. Three misalignments are shown as examples. Positions of the secondary mirror and third mirror are employed to compensate aberrations. The results show that merit functions and energy distributions of corrected images match with the designed ones. The mean RMS of residual wavefront errors is smaller than λ/14 (λ = 0.5 μm), indicating that the misalignments are well compensated. The results verify the effectiveness of our method.

Design of off-axis reflective dual-channel zoom freeform optical systems

In this work, two off-axis reflective dual-channel zoom optical systems are conceived and designed. These two systems achieve good imaging quality and compact system volume by introducing freeform surfaces. Firstly, the system models of the off-axis reflective dual-channel zoom optical systems are introduced, and the first-order analysis is carried out. Then, a design method of an off-axis reflective dual-channel zoom freeform optical system is introduced, and two examples are designed using this method. In one example, the two channels have a separate primary mirror and share a secondary mirror and a third mirror. The system achieves a zoom ratio of 2 times. The two different channels of the other system have separate third mirror and share the primary mirror and the secondary mirror. The system achieves a zoom ratio of 4 times. The two systems have good imaging performance close to the diffraction limit in the visible light band. Finally, the proposed off-axis reflective dual-channel zoom freeform optical system is analyzed and discussed.

Research on the Image-Motion Compensation Technology of the Aerial Camera Based on the Multi-Dimensional Motion of the Secondary Mirror

Research on the Image-Motion Compensation Technology of the Aerial Camera Based on the Multi-Dimensional Motion of the Secondary Mirror

Multi-field Split Curvature Wavefront Sensing and its Application in the Large Field Survey Telescope

The image quality of a large field survey telescope with a fast focal ratio of the primary mirror is high sensitivity to the optical elements’ misalignments and the primary mirror’s deformations. To maintain good optical performance, the perturbations need to be aligned, and the tomographic reconstruction of these perturbations can be derived from wavefront sensing with multi-field points for alignment. This work undertakes a comprehensive examination related to the implementation and optimization of a multi-field split curvature wavefront sensing system, including defocus distance, signal pre-processing, deblending of overlapped doughnuts, field-dependent correction, and distorted coordinate correction. We also conduct experiments to demonstrate the application and performance of a multi-field split curvature wavefront sensing system in Mephisto. In the context of the decentering of the secondary mirror, the coefficient of determination (R) attains a high value of 0.993, indicating a robust linearity between the coma coefficients and the decentering of the secondary mirror. A comparative analysis of the simulated and experimental results shows that the difference between them is less than 0.1 λ.

Delayed-focus micro-angle measurement optical system based on structural segregation

In this paper, we propose a delayed-focusing type micro-angle measurement optical system based on the Cassegrain structure (cassette structure), analyze the basic cassette structure and the Galilean laser beam expanding system, and determine the primary and secondary mirror structure as a reflective focusless system as a determining module. This focusless system emits and receives parallel light, and the light source and detector separated by the beam splitter are designed as replaceable modules. Additionally, the imaging quality of the system can be optimized, or the effect of meeting different imaging requirements can be achieved, by changing the number and type of corrective mirrors and the parameters of the specific glass elements in the replaceable modules. After the final optimization, the radius of the imaging spot of the combined mirror group can be limited to 6.1 µm; the modulation transfer function is better than 0.6 at 100 lp/mm; the difference between the meridian and the arc-vector curves is less than 0.1; and the theoretical angular accuracy reaches 0.2″. The delayed-focusing system structure is analyzed under different temperature fields to provide guidance for the design of the subsequent structure temperature control. Comparison and analysis with commonly used angle measurement optical systems are also made. It is concluded that the structure meets the requirements for use in the on-orbit environment, completes the reuse of the established structural modules, and further saves the manufacturing cost, which provides a feasible solution to the problem of monitoring the small angular changes in the field of space.

Analysis and reduction of back-reflection straylight in laser ranging system

In the coaxial satellite laser ranging system or the other telescope-based measurement systems, the emitted beam produces backward reflection at the center of the secondary mirror, which affects the detector in the system. To reduce the impact of straylight, a new device for reduce the backward reflection of the secondary mirror has been proposed. The specific parameters of the device have been determined through numerical calculation and computer simulation. The device has been implemented in a 1.2 m laser ranging system and has been experimentally proven to reduce the laser straylight by 32.4 % with the single photon detector and there is an increase in the camera's contrast for target imaging, making it more effective to measuring the space target.

PASAT: pathfinder in solar adaptive telescope

In the forefront of quantitative solar physics research using large-aperture ground-based solar optical telescopes, high-contrast observation along with high-accuracy polarimetric measurement in the solar active region are required. In this paper, we propose a novel high-contrast imaging telescope construction with a 60 cm medium aperture, namely, the PAthfinder in Solar Adaptive Telescope (PASAT), in which a deformable secondary mirror is used as the adaptive optical correction device and a symmetrical optical path design is employed, leading to the least Muller matrix polarization instruments. The telescope can provide a high-resolution magnetic field with high accuracy for the solar active regions, as well as high-contrast images with a superior signal-to-noise ratio and photometric accuracy of the solar photosphere and chromosphere. These data will be directly used for a better understanding of the evolution and release of magnetic energy, which will help in improving space weather forecasting. Meanwhile, PASAT will accumulate the relevant techniques for constructing similar, larger solar telescopes in the future.

Field-balancing alignment of the secondary mirror of space telescope using a self-calibrated model

In-orbit alignment of the secondary mirror (SM) of deployable space telescopes is crucial for high-resolution imaging. Traditional alignment methods, which typically involve dedicated wavefront sensors or numerous iterations to optimize a metric function, are not well-suited for space applications. In this paper, an improved model-based SM alignment method is proposed. The term model refers to the relationship between misalignments and a metric function. The improved method offers two advantages over the previous model-based method in [12]. Firstly, our method allows for self-calibration of the model without the need for an additional wavefront sensor, which greatly simplifies the calibration process. Secondly, our method enables field-balancing alignment of the SM with several correction cycles. The exposure number is only six in one correction cycle and is regardless of the number of FOV sampling points, making it highly efficient for telescopes with a large FOV. The feasibility and performance of our method are verified by simulation. A comparison with existing methods is also given to show the advantages of our method in convergence speed and accuracy.

Design of a focusing system for micro-nano satellite remote sensing camera based on thermal control technology

Remote sensing cameras mounted on micro-nano satellite mare susceptible to optical system defocusing during launch and operation due to environmental influences. Traditional focusing system encounter issues such as large volume and mass, making them unsuitable for the design requirements of micro-nano satellite. Proposes a thermal control-based focusing system for compact systems with maintained imaging quality. The design is developed according to the characteristics of a compact coaxial four-mirror remote sensing camera optical system and the overall structure of the system. The focusing system utilizes structural thermal expansion to alter the distance between the primary and secondary mirrors, achieving the purpose of adjusting the system’s focal length. Finite element simulations were conducted to analyze the modal and thermal deformations of the overall structure, validating the rationality of the system design. Experimental verification of the thermal control focusing system demonstrated its adjustment accuracy and range, with clear imaging obtained after system focusing. The results indicate that when the temperature control accuracy reaches ±0.5 °C, the focal length adjustment accuracy can reach 0.0052 mm. This article proposed thermal control focusing system can adjust the camera’s focal length in orbit, exhibiting advantages such as a small volume, high stiffness, and high precision.

Optical design of a visible/short-wave infrared common-aperture optical system with a long focal length and a wide field-of-view.

Addressing the urgent need for long-distance dim target detection with a wide field-of-view and high sensitivity, this paper proposes a visible and short-infrared dual-band common-aperture optical system characterized by a broad field and extended focal length. To achieve system miniaturization and high-sensitivity target detection, the visible and infrared optical systems share a Ritchey-Chretien primary and secondary mirror. The primary optical path is segmented into visible light (0.45-0.75µm) and short-wave infrared (SWIR) (2-3µm) bands by a dichroic spectral splitter prism. The SWIR optical system utilizes four short-wave cooled infrared detectors, and wide-field stitching is achieved using a field-of-view divider. While ensuring the high cold-shield efficiency of cooled infrared detectors, this common-aperture optical system delivers visible and SWIR dual-band images with expansive fields, elongated focal lengths, and sizable apertures. The visible-light optical system has a focal length of 277mm, a field-of-view of 2.3∘×2.3∘, and an entrance pupil diameter of 130mm. Meanwhile, the SWIR optical system features a focal length of 480mm, a field-of-view of 2.26∘×1.8∘ and an entrance pupil diameter of 160mm. The design outcomes suggest that the imaging quality of the optical system approaches the diffraction limit. This visible/SWIR common-aperture optical system exhibits high sensitivity, a large field-of-view, compact structure, and excellent imaging quality, thereby meeting the requirements for long-distance dim target detection and imaging.

A Secondary Mirror Alignment Method for Segmented Telescopes Using a Wavefront Sensor-Less Method

A Secondary Mirror Alignment Method for Segmented Telescopes Using a Wavefront Sensor-Less Method

Principle and application of holographic modal wavefront sensor for extended objects and general aberration modes

By employing a computer-generated hologram (CGH) to modulate the incident wavefront, the holographic modal wavefront sensor (HMWFS) can efficiently measure multiple aberration modes in a single shot, providing significant advantages such as computational simplicity, rapid measurement speed, and customizable assessment of aberration modes. However, the current HMWFS is confined to point-like objects and aberrations with specific orthogonality, thereby limiting its application scope. In this paper, we introduce a novel HMWFS that, to the best of our knowledge, is compatible with extended objects and general aberration modes. We establish the theoretical relationship between the second moment of the image intensity and the coefficients of general aberration modes for extended objects. Simulation and experimental results confirm the feasibility and performance of the proposed HMWFS. Additionally, we demonstrated its practical use in measuring misalignments of the secondary mirror of a space telescope. Simulations show that the misalignments can be effectively corrected within 2∼3 iterations.

Simulation alignment of optical system for space gravitational wave telescope

The performance of telescopes, important components of space interferometry systems, directly affects the accuracy of gravitational wave signals. Space gravitational wave telescopes typically employ an off-axis four-mirror system. When aligned, this system not only has multiple misalignments, but also exhibits interrelated aberrations from various misalignments. These characteristics may lead to difficult alignment of the telescope system as well as significant deviation between the position of the telescope after alignment and the ideal position. To address these issues, first, a sensitivity matrix equation was established between the misalignment of optical components and the Fringe Zernike coefficients. Based on the sensitivity matrix equation, a damping least-squares evaluation function was constructed to reduce the significant deviation between the aligned and ideal positions. Second, a typical optical system of a space gravitational wave telescope was designed, and the sensitivity matrix was calculated. The relationship between the wavefront distortions caused by misalignments in each optical component was examined. To simplify telescope installation, a strategy using secondary mirrors as compensatory elements was proposed. Finally, to verify the effectiveness of the scheme, 200 sets of tolerance files were randomly generated. Based on the evaluation function of the damping least-squares method, a reasonable damping factor was set to limit the solution range of the misalignment, which enabled calculating the secondary mirror compensation amount. Experimental results indicate that after aligning the 200 random telescope files, the root-mean-square wavefront error was reduced to less than 0.0030λ, and the maximum error between the magnification after alignment and the ideal position magnification was only 0.57%, which confirms the feasibility of this alignment scheme.

Optimal design of a gravitational wave telescope system for the suppression of stray light.

For gravitational wave detection, the telescope is required to have an ultra-low wavefront error and ultra-high signal-to-noise ratio, where the power of the stray light should be controlled on the order of less than 10-10. In this work, we propose an alternative stray light suppression method for the optical design of an off-axis telescope with four mirrors by carefully considering the optimal optical paths. The method includes three steps. First, in the period of the optical design, the stray light caused by the tertiary mirror and the quaternary mirror is suppressed by increasing the angle formed by the optical axes of the tertiary mirror and the quaternary mirror and reducing the radius of curvature of the quaternary mirror as much as possible to make sure the optical system provides a beam quality with a wavefront error less than λ/80. Next, the stray light could satisfy the requirement of the order of 10-10 when the level of roughness reaches 0.2nm, and the pollution of mirrors is controlled at the level of CL100. Finally, traditional stray light suppression methods should also be applied to mechanics, including the use of the optical barrier, baffle tube, and black paint. It can be seen that the field stop can efficiently reduce stray light caused by the secondary mirror by more than 55% in the full field of view. The baffle tube mounted on the position of the exit pupil can reduce the overall stray light energy by 5%, and the difference between the ideal absorber (absorption coefficient is 100%) and the actual black paint (absorption coefficient is 90%) is 3.2%. These simulation results are confirmed by the Monte Carlo method for a stray light analysis. Based on the above results, one can conclude that the geometry structure of the optical design, the quality of mirrors, and the light barrier can greatly improve the stray light suppression ability of the optical system, which is vital when developing a gravitational wave telescope with ultra-low stray light energy.

Optimization of Thermal Control Design for Aerial Reflective Opto-Mechanical Structure.

To improve the adaptability of aerial reflective opto-mechanical structures (mainly including the primary mirror and secondary mirror) to low-temperature environments, typically below -40 °C, an optimized thermal control design, which includes passive insulation and temperature-negative feedback-variable power zone active heating, is proposed. Firstly, the relationship between conventional heating methods and the axial/radial temperature differences of mirrors with different shapes is analyzed. Based on the heat transfer analyses, it is pointed out that optimized thermal control design is necessary to ensure the temperature uniformity of the fused silica mirror, taking into account the temperature level when the aerial electro-optics system is working in low-temperature environments. By adjusting the input voltage based on the measured temperature, the heating power of the subregion is changed accordingly, so as to locally increase or decrease the temperature of the mirrors. The thermal control scheme ensures that the average temperature of the mirror fluctuates slowly and slightly around 20 °C. At the same time, the temperature differences within a mirror and between the primary mirror and the secondary mirror can be controlled within 5 °C. Thereby, the resolution of EO decreases by no more than 11.4%.

Analysis of alignment requirements for off-axis resonant cavity based on coupling efficiency

The optical path length stability of the off-axis four-reflection telescope is one of the key technical indicators for the TianQin gravitational wave detection system. In the mHz observation band, the telescope must exhibit an optical path length stability of 0.4pm/Hz1/2. As a feasible solution, the optical path length stability measurement of the off-axis four-reflection telescope based on the Pound–Drever–Hall (PDH) technique imposes stringent requirements on the alignment of the off-axis resonant cavity (ORC). Taking the off-axis two-reflection prototype as the research object, we propose a Monte Carlo analysis-based method for ORC alignment precision analysis. By considering misalignment as an intermediate function, we establish a relationship between the coupling efficiency of the ORC and the wavefront aberration of the telescope. The research results show that by considering the combined effects of multiple misalignment couplings of the primary and secondary mirrors, when the detected telescope wavefront aberration is better than 0.068λ (λ=1064nm) with a probability of 98%, the ORC coupling efficiency can achieve greater than 40% with a probability of 97.13%, which can be used as the main reference indicator for system misalignment analysis. This method simplifies the alignment difficulty of the target under test and can provide alignment reference for subsequent resonant cavities with internal off-axis telescopes.

Comparison of the Optical Efficiency of Two Designs of the Maksutov–Cassegrain Telescope

The research aims to develop the best possible design for the widely used Cassegrain telescope. The system consists of two models of different designs: (a) the telescope consists of a Maksutov lens, a spherical primary mirror, and a secondary mirror attached to the lens; (b) it consists of a Maksutov lens and a spherical primary mirror, plus a non-lens attached secondary mirror located between the lens and the primary mirror. The image was evaluated and analyzed using the analysis tools in Zemax software. The results of the two designs showed that the telescope whose secondary mirrors are not adjacent to the Maksutov lens produces high quality image that is almost free from aberration, and then comes the telescope whose secondary mirrors are adjacent to the Maksutov lens in terms of image quality. In the first design, the tangential and sagittal axes in the MTF function of the remaining angles (0.1, 0.2, 0.3, 0.4, and 0.5) contain two curves, which show how the loss of symmetry has changed the value of the function for the two axes. In the second design, the sagittal and tangential axes are identical in the angles of incidence (0, 0.1, and 0.2), and the transverse and sagittal axes of the remaining angles (0.3, 0.4, and 0.5) contain two curves. In PSF for the first design, there are several pretty high peaks on the surface of the image at the angle of incidence (0, 0.1). Since the shape is regular, the point spread function indicates that there isn't an aberration, but in terms of the angles (0.2, 0.3, 0.4, 0.5), we observe a gradual loss in intensity and the appearance of elevations on both sides of the picture. In the second design, at the angles (0, 0.1, 0.2, 0.3), we observe in Figure 5 that there are several high peaks free from aberration.

Lightweight and High-Stiffness Metal Optical Systems Based on Additive Manufacturing.

To build a long-wave infrared catadioptric optical system for deep space low-temperature target detection with a lightweight and wide field of view, this work conducted a study that encompasses a local cooling optical system, topology optimization-based metal mirror design, and additive manufacturing. First, a compact catadioptric optical system with local cooling was designed. This system features a 55 mm aperture, a 110 mm focal length, and a 4-degree by 4-degree field of view. Secondly, we applied the principles of topology optimization to design the primary mirror assembly, the secondary mirror assembly, and the connecting baffle. The third and fourth modes achieved a resonance frequency of 1213.7 Hz. Then, we manufactured the mirror assemblies using additive manufacturing and single-point diamond turning, followed by the centering assembly method to complete the optical assembly. Lastly, we conducted performance testing on the system, with the test results revealing that the modulation transfer function (MTF) curves of the optical system reached the diffraction limit across the entire field of view. Remarkably, the system's weight was reduced to a mere 96.04 g. The use of additive manufacturing proves to be an effective means of enhancing optical system performance.