Co-phase error detection for segmented mirrors with ptychography

With the development of astronomy, the aperture of space telescopes has gradually expanded to enable fainter and deeper astronomical observations. Large-diameter monolithic mirrors, however, are prohibitively heavy and pose numerous technical difficulties for space-based observatories [1], [2]. In recent years, segmented mirrors have emerged as a popular strategy for reducing the mass, material costs, and launch packing volume of large-aperture telescopes. A segmented primary mirror consists of a collection of smaller sub-mirrors, each of which is a segment of a huge monolithic mirror. Utilizing this approach of segmented mirrors, segmented telescopes are launched in a stowed state. Once in orbit, they can be deployed to their full diameter, allowing the creation of space telescopes with ultra-large apertures. [3]. The James Webb Space Telescope (JWST) [4], which was launched by an Ariane 5 from the Guiana Space Centre on December 25, 2021, is a classic example of such a system.

Unlike monolithic mirrors, there will be relative position errors of sub-mirrors after the primary mirror is deployed. Co-phase errors are comprised of six categories, which correspond to six degrees of freedom for each sub-mirror. The six degrees are characterized as a piston along the optical axis of the primary mirror, tip–tilt around two axes in the sub-mirror plane, rotation around the normal of the sub-mirror, and translation motions perpendicular to the optical axis of the sub-mirror in the surface of the primary mirror [5]. These errors must be correctly detected and corrected to eliminate misalignments of the sub-mirrors and achieve the same image performance as a monolithic mirror. The co-phase errors that have the greatest effect on the image quality of the telescope are piston and tip–tilt errors, which are the focus of the majority of co-phase error detection systems.

Existing co-phase error detection methods can be roughly categorized into two groups: the first uses specific sensors to directly measure co-phase errors, such as modified Shack–Hartmann wavefront sensing (SHWFS) [6], the Mach–Zehnder interferometer sensor [7], curvature sensor [8], pyramid sensor [9], and dispersed fringe sensors [10]. These techniques typically need complex optical detection systems, such as the Shack–Hartmann wavefront sensor, reference light path system, curvature sensor, and pyramid sensor. The second utilizes an image processing method to derive co-phase errors from the recorded images, including the phase retrieval method [11] and the phase diversity method [12]. These image-based wavefront sensing methods record an image in the conventional focal plane and generate additional intensity images by increasing known aberrations. Piston, tip, and tilt errors of segmented mirrors can be recovered by a nonlinear optimization approach based on these intensity images, which applies to both point source and extended targets.

To achieve quantitative measurement of wavefront aberrations of the segmented primary mirror with fewer optical detection elements, we present a new method based on ptychography [13], [14], [15], [16] for detecting co-phase errors. This technology has emerged as an efficacious tool for microscopy and wavefront sensing in the last decade. In addition to a controllable specimen, the measurement technique does not introduce a reference light beam or extra optical elements. The specimen mechanically translates across the illumination beam with adjacent positions sufficiently overlapped. The corresponding diffraction patterns are recorded by the detector. An extended Ptychographic Iterative Engine (ePIE) is an algorithm that can simultaneously reconstruct both the distribution of specimen and illumination light beam without any prior knowledge [17]. Taking advantage of the adequate data redundancy provided by the overlap between adjacent positions, ePIE can increase the robustness against different types of system errors and partial coherence [18]. And it is not influenced by the existence of a singularity in the light beams, regardless of the beam type [19], [20], [21]. Meanwhile, the Wiener filter included in the data reconstruction process makes the reconstructed light beam almost have no speckle noise [22]. Since the recovered illumination beam transforms the wavefront aberration of the segmented mirror surface, the proposed method can simultaneously detect decenter, piston, and tip–tilt errors among multiple sub-mirrors.

The remainder of this paper is organized as follows: Section 2 explains the fundamental theory of the co-phase error detection method based on ptychography for segmented mirrors. In Section 3, a set of simulations to validate the proposed method are described. The experimental verification process and results for piston and decenter error detection are presented in Section 4. The final section concludes this paper.

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