Active Alignment of Large-Aperture Space Telescopes for Optimal Ellipticity Performance.

Ellipticity performance of space telescopes is important for exploration of dark matter. However, traditional on-orbit active optical alignment of space telescopes often takes "minimum wavefront error across the field of view" as the correction goal, and the ellipticity performance after correcting the wave aberration is not optimal. This paper proposes an active optical alignment strategy to achieve optimal ellipticity performance. Based on the framework of nodal aberration theory (NAT), the aberration field distribution corresponding to the optimal full field-of-view ellipticity is determined using global optimization. The degrees of freedom (DOFs) of the secondary mirror and the folded flat mirror are taken as the compensation DOFs to achieve the optimal ellipticity performance. Some valuable insights into aberration field characteristics corresponding to optimal ellipticity performance are presented. This work lays a basis for the correction of ellipticity for complicated optical systems.

Fast High-Resolution Phase Diversity Wavefront Sensing with L-BFGS Algorithm.

The presence of manufacture error in large mirrors introduces high-order aberrations, which can severely influence the intensity distribution of point spread function. Therefore, high-resolution phase diversity wavefront sensing is usually needed. However, high-resolution phase diversity wavefront sensing is restricted with the problem of low efficiency and stagnation. This paper proposes a fast high-resolution phase diversity method with limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, which can accurately detect aberrations in the presence of high-order aberrations. An analytical gradient of the objective function for phase-diversity is integrated into the framework of the L-BFGS nonlinear optimization algorithm. L-BFGS algorithm is specifically suitable for high-resolution wavefront sensing where a large phase matrix is optimized. The performance of phase diversity with L-BFGS is compared to other iterative method through simulations and a real experiment. This work contributes to fast high-resolution image-based wavefront sensing with a high robustness.

Detecting radius of curvature (ROC) mismatch among primary mirror (PM) segments.

A segmented primary mirror (PM) is an efficient solution to the problems of a monolithic PM manufacture, testing, transportation, and launch. However, the problem of the radius of curvature (ROC) matching among PM segments will arise, which if not solved will seriously degrade the final imaging quality of the system. Accurately detecting ROC mismatch among PM segments from the wavefront map is of crucial importance for efficiently correcting this kind of manufacturing error, while currently there are few related studies. Based on the inherent relation between the PM segment's ROC error and corresponding sub-aperture defocus aberration, this paper proposes that the ROC mismatch can be accurately estimated from the sub-aperture defocus aberration. Secondary mirror (SM) lateral misalignments will influence the accuracy of estimating ROC mismatch. A strategy is also proposed to reduce the influence of SM lateral misalignments. Detailed simulations are performed to demonstrate the effectiveness of the proposed method for detecting ROC mismatch among PM segments. This paper paves a road for detecting ROC mismatch using image-based wavefront sensing methods.

Jitter-Robust Phase Retrieval Wavefront Sensing Algorithms.

Phase retrieval wavefront sensing methods are now of importance for imaging quality maintenance of space telescopes. However, their accuracy is susceptible to line-of-sight jitter due to the micro-vibration of the platform, which changes the intensity distribution of the image. The effect of the jitter shows some stochastic properties and it is hard to present an analytic solution to this problem. This paper establishes a framework for jitter-robust image-based wavefront sensing algorithm, which utilizes two-dimensional Gaussian convolution to describe the effect of jitter on an image. On this basis, two classes of jitter-robust phase retrieval algorithms are proposed, which can be categorized into iterative-transform algorithms and parametric algorithms, respectively. Further discussions are presented for the cases where the magnitude of jitter is unknown to us. Detailed simulations and a real experiment are performed to demonstrate the effectiveness and practicality of the proposed approaches. This work improves the accuracy and practicality of the phase retrieval wavefront sensing methods in the space condition with non-ignorable micro-vibration.

Active alignment of space astronomical telescopes by matching arbitrary multi-field stellar image features.

Space-based optical astronomical telescopes are susceptible to mirror misalignments due to space disturbance in mechanics and temperature. Therefore, it is of great importance to actively align the telescope in orbit to continuously maintain imaging quality. Traditional active alignment methods usually need additional delicate wavefront sensors and complicated operations (such as instrument calibration and pointing adjustment). This paper proposes a novel active alignment approach by matching the geometrical features of several stellar images at arbitrary multiple field positions. Based on nodal aberration theory and Fourier optics, the relationship between stellar image intensity distribution and misalignments of the system can be modeled for an arbitrary field position. On this basis, an objective function is established by matching the geometrical features of the collected multi-field stellar images and modeled multi-field stellar images, and misalignments can then be solved through nonlinear optimization. Detailed simulations and a real experiment are performed to demonstrate the effectiveness and practicality of the proposed approach. This approach eliminates the need for delicate wavefront sensors and pointing adjustment, which greatly facilitates the maintainance of imaging quality.

Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes.

This paper discusses compensation strategies for the aberration fields caused by the error in the radius of curvature (ROC) of the primary mirror (PM) in pupil-offset off-axis three-mirror anastigmatic (TMA) astronomical telescopes. Based on the nodal aberration theory framework, the specific astigmatic and coma aberrations of the off-axis three-mirror system in the presence of the ROC error of the PM are derived. It is demonstrated that some field-dependent aberration components can be induced by ROC error in the off-axis TMA telescopes, apart from the dominating field-constant aberration terms. To reduce the influence of the ROC error on the aberration fields, we propose two aberration compensation strategies: adjusting the position of the PM and introducing axial misalignment of the secondary mirror (SM). Through theoretical analysis and simulations, we conclude that the compensation strategy of changing the axial position of the PM can make the aberration distribution close to the nominal state; the compensation strategy of axially adjusting the SM can make the aberration distribution meet the observation requirements, which is more suitable for space applications. We also discuss compensating the effect of the ROC error using lateral misalignments.

Aberration fields of pupil-offset off-axis two-mirror astronomical telescopes induced by ROC error.

This paper presents a systematic and deep discussion on the aberration field characteristics of pupil-offset off-axis two-mirror astronomical telescopes induced by the radius of curvature (ROC) error based on the framework of the nodal aberration theory (NAT). The expressions of the third-order aberrations in off-axis two-mirror astronomical telescopes with ROC error are derived first. Then the astigmatic and coma aberration fields are discussed, and it is shown in a field constant astigmatism and coma will be induced by ROC error. The aberration compensation between axial misalignments and ROC error are further discussed, and it is shown that the net astigmatic and coma aberration field induced by ROC error can well be compensated by axial misalignments. Importantly, it is also demonstrated that the focal plane shift induced by ROC error can also be compensated at the same time. Also, this paper briefly analyzes the aberration field characteristics when there is the error of conic constant in optical system. Some other discussions are also presented concerning the ROC inconsistency in astronomical telescopes with a segmented primary mirror. This work will lead to a deep understanding of the influence of ROC error in pupil-offset off-axis astronomical telescopes.

Aberrational interactions between axial and lateral misalignments in pupil-offset off-axis two-mirror astronomical telescopes.

Due to the absence of rotational symmetry, the effects of axial and lateral misalignments couple tightly together, which leads to special aberration field characteristics. This paper will present an in-depth and systematic discussion on the interactions between the effects of axial and lateral misalignments in pupil-offset off-axis two-mirror astronomical telescopes. The aberration function of this class of telescopes in the presence of axial and lateral misalignments is derived. The specific expressions of two dominant non-rotationally symmetric aberrations, i.e., astigmatism and coma, are obtained and the aberration field characteristics are discussed. Importantly, it is shown that under certain conditions, a node will arise in the field of view for these two kinds of aberrations. Then the aberrational compensation mechanisms between axial and lateral misalignments are quantitatively explicated, and it is shown that the non-rotationally symmetric aberrations induced by axial misalignments can well be compensated by lateral misalignments. However, we also find that in this process, the defocus aberration induced by these two kinds of misalignments will accumulate (rather than cancel out). Therefore, in practice, it is better to separate these two kinds of misalignment. Finally, we propose a simple method to decouple axial misalignments from lateral misalignments with wavefront measurement at one field position. Most of this work can be extended to other kind of pupil-offset off-axis astronomical telescopes, such as off-axis three-mirror anastigmatic telescopes.