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Double-pass optical testing will play a key role in the alignment and verification of the Roman Space Telescope (RST), NASA’s upcoming flagship astrophysics mission, which was formerly known as the Wide Field Infrared Survey Telescope or (WFIRST). In this test configuration, optical fibers adjacent to the focal plane detector array will send light through the entire optical system in reverse, to be reflected off an auto-collimating flat (ACF) mirror and back through the system a second time (at a different angle) before reaching the detector. The ACF will be tilted through a range of angles to provide samples across the entire field of view, which is exceptionally large for a space telescope and will exhibit measurable field-dependent aberration. Phase retrieval analysis of the resulting point-spread functions will provide wavefront estimates; however, these wavefronts will include aberrations that were accumulated on both passes through the system at their respective field angles. In order to evaluate the alignment and verification of the system, we must predict the performance of the observatory when operating in single-pass. Therefore, we present an algorithm that will separate the aberrations from the two passes to provide a prediction of the telescope’s performance in single-pass. This is done by fitting the data to a polynomial representation of the underlying field aberrations and requiring that the aberrations accumulated on the two passes be consistent with that model.

An important question in the development of the Roman Space Telescope (RST) is how to optically test it at the highest levels of assembly, after the instruments have been integrated with the telescope. Our current strategy is double-pass testing using image-based wavefront sensing (phase retrieval). In this paper, we consider alternative strategies based on Hartmann testing, using either a pupil-plane mask or a mirror array. We developed first-order design considerations for the implementation of such Hartmann tests in the context of RST and designed two specific Hartmann tests to evaluate in further simulations. One of the major suggested benefits of Hartmann testing is insensitivity to vibrations that induce either line-of-sight jitter or dynamic changes in wavefront aberration. In order to understand whether this is true (and under what conditions), we developed a physical optics simulation of our two Hartmann tests under both Gaussian line-of-sight jitter and sinusoidal dynamic secondary mirror motion. We then also developed a data reduction process for fitting these Hartmann test images and estimating system wavefronts.

Now in Phase-B, the architecture of the Wide-Field Infra-Red Survey Telescope (WFIRST) payload has matured since 2013 to accommodate various opto-mechanical constraints. Based on a 2.4-meter aperture Forward Optical Assembly (FOA), the Imaging Optics Assembly (IOA) provides corrected optical fields to each on-board instrument. Using a Three Mirror Anastigmat (TMA) optical design, the Wide-Field Channel (WFC) provides ~1/3-square degree of instantaneous field coverage at 0.11 arcsecond pixel scale. The WFC as-built predictive analysis anticipates near diffraction-limited imaging over a focal plane of 300.8 million pixels, operating in seven panchromatic bands between 0.48 – 2.0μm, or a 1-octive multi-spectral imaging mode from ~0.95-1.93μm. The IOA provides the Coronagraph Instrument (CGI) a collimated beam with very specific wavefront constraints. We present configuration changes since 2013 that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift.

NASA’s Wide Field Infrared Survey Telescope (WFIRST) is being designed to deliver unprecedented capability in dark energy and exoplanet science, and to host a technology demonstration coronagraph for exoplanet imaging and spectroscopy. The observatory design has matured since 2013 [“WFIRST 2.4m Mission Study”, D. Content, SPIE Proc Vol 8860, 2013] and we present a comprehensive description of the WFIRST observatory configuration as refined during formulation phase (AKA the phase-A study). The WFIRST observatory is based on an existing, repurposed 2.4m space telescope coupled with a 288 megapixel near-infrared (0.6 to 2 microns) HgCdTe focal plane array with multiple imaging and spectrographic modes. Together they deliver a 0.28 square degree field of view, which is approximately 100 times larger than the Hubble Space Telescope, and a sensitivity that enables rapid science surveys. In addition, the technology demonstration coronagraph will prove the feasibility of new techniques for exoplanet discovery, imaging, and spectral analysis. A composite truss structure meters both instruments to the telescope assembly, and the instruments and the spacecraft are on-orbit serviceable. We present the current design and summarize key Phase-A trade studies and configuration changes that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift. Finally, we summarize the results of technology development and peer reviews, demonstrating our progress towards a low-risk flight development and a launch in the middle of the next decade.

The Wide-Field Infrared Survey Telescope (WFIRST) mission[1] is the top-ranked large space mission in the New Worlds, New Horizon (NWNH) Decadal Survey of Astronomy and Astrophysics. WFIRST will settle essential questions in both exoplanet and dark energy research and will advance topics ranging from galaxy evolution to the study of objects within the galaxy. The WFIRST mission uses a repurposed 2.4-m Forward Optical Telescope assembly (FOA), which, when completed with new aft optics will be an Integrated Optical Assembly (IOA). WFIRST is equipped with a Wide Field Instrument (WFI) and a Coronagraph Instrument (CGI). An Instrument Carrier (IC) meters these payload elements together and to the spacecraft bus (S/C). A distributed ground system receives the data, uploads commands and software updates, and processes the data. After transition from the study phase, Pre-Phase-A (a.k.a., “Cycle 6”) design to NASA Phase A formulation, a significant change to the IOA was initiated; including moving the tertiary mirror from the instrument package to a unified three-mirror anastigmat (TMA) placement, that provides a wide 0.28-sq° instrumented field of view to the Wide Field Instrument (WFI). In addition, separate relays from the primary and secondary mirror feed the Wide Field Instrument (WFI) and Coronagraph Instrument (CGI). During commissioning the telescope is aligned using wavefront sensing with the WFI[2]. A parametric and Monte-Carlo analysis was performed, which determined that alignment compensation with the secondary mirror alone degraded performance in the other instruments. This led to the addition of a second compensator in the WFI optical train to alleviate this concern. This paper discusses the trades and analyses that were performed and resulting changes to the WFIRST telescope architecture.

The James Webb Space Telescope (JWST) project is an international collaboration led by NASA’s Goddard Space Flight Center (GSFC) in Greenbelt, MD. JWST is NASA’s flagship observatory that will operate nearly a million miles away from Earth at the L2 Lagrange point. JWST’s optical design is a three-mirror anastigmat with four main optical components; 1) the eighteen Primary Mirror Segment Assemblies (PMSA), 2) a single Secondary Mirror Assembly (SMA), 3) an Aft-Optics Subsystem (AOS) consisting of a Tertiary Mirror and Fine Steering Mirror, and 4) an Integrated Science Instrument Module consisting of the various instruments for JWST. JWST’s optical system has been designed to accommodate a significant amount of alignment capability and risk with the PMSAs and SMA having rigid body motion available on-orbit just for alignment purposes. However, the Aft-Optics Subsystem (AOS) and Integrated Science Instrument Module (ISIM) are essentially fixed optical subsystems within JWST, and therefore the cryogenic alignment of the AOS to the ISIM is critical to the optical performance and mission success of JWST. In support of this cryogenic alignment of the AOS to ISIM, an array of fiber optic sources, known as the AOS Source Plate Assembly (ASPA), are placed near the intermediate image location of JWST (between the secondary and tertiary mirrors) during thermal vacuum ground-test operations. The AOS produces images of the ASPA fiber optic sources at the JWST focal surface location, where they are captured by the various science instruments. In this manner, the AOS provides an optical yardstick by which the instruments within ISIM can evaluate their relative positions to and the alignment of the AOS to ISIM can be quantified. However, since the ASPA is located at the intermediate image location of the JWST three-mirror anastigmat design, the images of these fiber optic sources produced by the AOS are highly aberrated with approximately 2-3μm RMS wavefront error consisting mostly of 3rd-order astigmatism and coma. This is because the elliptical tertiary mirror of the AOS is used off of its ideal foci locations without the compensating wavefront effects of the JWST primary and secondary mirrors. Therefore, the PSFs created are highly asymmetric with relatively complex structure and the centroid and encircled energy analyses traditionally used to locate images are not sufficient for ensuring the AOS to ISIM alignment. A novel approach combining phase retrieval and spatial metrology was developed to both locate the images with respect to the AOS and provide calibration information for eventual AOS to ISIM alignment verification. During final JWST OTE and ISIM (OTIS) testing, only a single thru-focus image will be collected by the instruments. Therefore, tools and processes were developed to perform single-image phase retrieval on these highly aberrated images such that any single image of the ASPA source can provide calibrated knowledge of the instruments’ position relative to the AOS. This paper discusses the results of the methodology, hardware, and calibration performed to ensure that the AOS and ISIM are aligned within their respective tolerances at JWST OTIS testing.

The James Webb Space Telescopes segmented primary and deployable secondary mirrors will be actively con- trolled to achieve optical alignment through a complex series of steps that will extend across several months during the observatory's commissioning. This process will require an intricate interplay between individual wavefront sensing and control tasks, instrument-level checkout and commissioning, and observatory-level calibrations, which involves many subsystems across both the observatory and the ground system. Furthermore, commissioning will often exercise observatory capabilities under atypical circumstances, such as fine guiding with unstacked or defocused images, or planning targeted observations in the presence of substantial time-variable offsets to the telescope line of sight. Coordination for this process across the JWST partnership has been conducted through the Wavefront Sensing and Control Operations Working Group. We describe at a high level the activities of this group and the resulting detailed commissioning operations plans, supporting software tools development, and ongoing preparations activities at the Science and Operations Center. For each major step in JWST's wavefront sensing and control, we also explain the changes and additions that were needed to turn an initial operations concept into a flight-ready plan with proven tools. These efforts are leading to a robust and well-tested process and preparing the team for an efficient and successful commissioning of JWSTs active telescope.

In this paper, we discuss two effective methods for computing optical propagations using two-dimensional (2D) discrete Fourier transforms: the matrix triple product (MTP) and the chirp z-transform (CZT) and analyze their performance both in theory and via benchmarks compared to the performance of a traditional padded fast Fourier transform (FFT). We show that, in many regimes of interest for phase-retrieval algorithms, the MTP or CZT is comparable to or better than the FFT in terms of run time while offering more flexible control over the sampling. We propose that for many applications, the CZT makes a robust general purpose alternative to the padded 2D FFT.

The search spaces in nonlinear optimization phase retrieval problems are of high dimensionality, making them difficult to visualize. Using a simplified low-order model, we explore the shape of the phase retrieval error surfaces using two-dimensional (2D) slices to visualize the relationship between different aberrations. We show how different pairs of aberrations exhibit very different coupling with one another and different distributions and frequencies of local minima, and discuss how this relates to the phase retrieval capture-range problem.

The GRavitational lEnsing Accuracy Testing 3 (GREAT3) challenge is the third in a series of image analysis challenges, with a goal of testing and facilitating the development of methods for analyzing astronomical images that will be used to measure weak gravitational lensing. This measurement requires extremely precise estimation of very small galaxy shape distortions, in the presence of far larger intrinsic galaxy shapes and distortions due to the blurring kernel caused by the atmosphere, telescope optics, and instrumental effects. The GREAT3 challenge is posed to the astronomy, machine learning, and statistics communities, and includes tests of three specific effects that are of immediate relevance to upcoming weak lensing surveys, two of which have never been tested in a community challenge before. These effects include realistically complex galaxy models based on high-resolution imaging from space; spatially varying, physically-motivated blurring kernel; and combination of multiple different exposures. To facilitate entry by people new to the field, and for use as a diagnostic tool, the simulation software for the challenge is publicly available, though the exact parameters used for the challenge are blinded. Sample scripts to analyze the challenge data using existing methods will also be provided. See http://great3challenge.info and http://great3.projects.phys.ucl.ac.uk/leaderboard/ for more information., 30 pages, 13 figures, published in MNRAS. URLs in abstract no longer work, but all data are available for download as described in https://github.com/barnabytprowe/great3-public (v4 only has updates to comments)

Extending previous work by Thurman on wavefront sensing for segmented-aperture systems, we developed an algorithm for estimating segment tips and tilts from multiple point spread functions in different defocused planes. We also developed methods for overcoming two common modes for stagnation in nonlinear optimization-based phase retrieval algorithms for segmented systems. We showed that when used together, these methods largely solve the capture range problem in focus-diverse phase retrieval for segmented systems with large tips and tilts. Monte Carlo simulations produced a rate of success better than 98% for the combined approach.

We present an overview of computationally efficient alternatives to the Fast Fourier Transform (FFT) that allow arbitrary sample spacing, and their application to research in the field of wavefront sensing by phase retrieval.

In this paper we demonstrate a formulation for determining the F/# or sampling factor from a measured point-spread function in a nonlinear optimization algorithm with analytic gradients and FFT-like asymptotic complexity for phase retrieval.

In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.

We introduce a new approximation method for broadband phase retrieval. We show that it yields results of comparable quality to the traditional broadband phase retrieval algorithm with a large improvement in speed.

We applied an approximate technique for broadband phase retrieval to a modeled segmented-aperture system in the ultra-broadband (133% bandwidth) regime, where it yielded an over-200X improvement in runtime, but at the cost of reduced accuracy.

A new method of image-based wavefront sensing is introduced. It solves the capture range problem for segment tip-tilt in segmented or multi-aperture systems with focus-diverse phase retrieval.

Image-based wavefront sensing using ray and wave optics are compared. Marriage of a new ray-based technique with phase retrieval combines speed, robustness, and accuracy.

In this paper, we generalize the techniques of reverse-mode algorithmic differentiation to include elementary operations on multidimensional arrays of complex numbers. We explore the application of the algorithmic differentiation to phase retrieval error metrics and show that reverse-mode algorithmic differentiation provides a framework for straightforward calculation of gradients of complicated error metrics without resorting to finite differences or laborious symbolic differentiation.