Wavefront Sensing for WFIRST with a Linear Optical Model

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

The Third Gravitational Lensing Accuracy Testing (GREAT3) Challenge Handbook

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.Comment: 30 pages, 13 figures, submitted for publication, with minor edits (v2) to address comments from the anonymous referee. Simulated data are available for download and participants can find more information at http://great3.projects.phys.ucl.ac.uk/leaderboard

The James Webb Space Telescope Mission: Optical Telescope Element Design, Development, and Performance

The James Webb Space Telescope (JWST) is a large, infrared space telescope that has recently started its science program which will enable breakthroughs in astrophysics and planetary science. Notably, JWST will provide the very first observations of the earliest luminous objects in the Universe and start a new era of exoplanet atmospheric characterization. This transformative science is enabled by a 6.6 m telescope that is passively cooled with a 5-layer sunshield. The primary mirror is comprised of 18 controllable, low areal density hexagonal segments, that were aligned and phased relative to each other in orbit using innovative image-based wavefront sensing and control algorithms. This revolutionary telescope took more than two decades to develop with a widely distributed team across engineering disciplines. We present an overview of the telescope requirements, architecture, development, superb on-orbit performance, and lessons learned. JWST successfully demonstrates a segmented aperture space telescope and establishes a path to building even larger space telescopes.Comment: accepted by PASP for JWST Overview Special Issue; 34 pages, 25 figure

Phase retrieval for chromatic aberrations and wide-field detectors

Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2017. "Chapter 3 was co-authored with Alden Jurling, who wrote the introduction as well as Sections 3.2 and 3.3, except for subsections 3.2.5 and 3.3.3"--Page xiii.We present a series of advancements to the state of the art in computational optics, in particular by enabling new areas of application for image-based wavefront sensing via phase retrieval. This includes demonstration of a parameterized model for chromatic aberrations which can improve diagnostics in dispersive optical systems. Potential sign ambiguities are identified and strategies to avoid or remove them are prescribed. The algorithm is also tested in a real-world laboratory environment, with results in good agreement with expected values. As a prerequisite to this advance, we also evaluate a collection of less frequently utilized discrete Fourier transform (DFT) algorithms that have an advantage over the fast Fourier transform in that they allow for an arbitrary scaling factor between the input and output domains. The trade-off in terms of computation speed is demonstrated using timing benchmarks for a variety of physical optics modeling scenarios, and multiple cases are found where the arbitrarily-scaled DFTs are preferable. In addition, we address issues with image-based wavefront sensing that arise from the unusually-large detector plane of a wide-field space telescope, where large chief ray angles at the edges of the field violate the small angle assumption of the usual Fresnel propagationintegral. By starting from an exact expression and adapting an approximation approach previously derived for digital holography with non-parallel planes, we find an algorithm that is both computationally efficient and sufficiently accurate. Finally, we present a computational optical system with an extended depth of field that was achieved by inducing field-independent coma intrinsic to the geometrical optics design via optimized decentration of the lens elements. This is a departure from the more common approach that requires a phase mask to control the wavefront

Advances in algorithms for image based wavefront sensing

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2015. "Chapter 5 was co-authored with Matthew Bergkoetter, who wrote Sections 5.2.5, 5.3.3, and 5.4"--Page xi.Image-based wavefront sensing via phase retrieval is used to align and characterize optical systems. It was famously used to deduce the prescription error in the Hubble Space Telescope, allowing fabrication of corrective optics. It is being used in ground-based testing of the James Webb Space Telescope (JWST) and is planned for use during JWST’s on-orbit commissioning and maintenance. This thesis presents advances in image-based wavefront sensing techniques. Phase retrieval algorithms estimate aberrations of optical systems by using measured point-spread functions (images of unresolved stars), typically at one or more planes through focus, though other measurement schemes are possible. Our nonlinear optimization (NLO) approach to phase retrieval uses a numerical model of the optical system (in terms of the aberration function) and a data consistency error metric. We use a nonlinear optimizer to find the aberration function that best matches the measured data. We describe several advancements within this paradigm. Phase retrieval algorithms rely on a starting estimate; if that estimate is too far from the true solution, the algorithm may never reach a good solution. This problem is particularly serious for segment tips and tilts in segmented aperture telescopes. Extending previous work by S. T. Thurman, we developed a geometrical-optics-based method for estimating segment tips and tilts to produce good starting estimates for phase retrieval. NLO phase retrieval relies on analytic gradients to achieve efficiency. We developed a new approach for calculating these gradients, based on the technique of “reverse-mode algorithmic differentiation” which allows gradients to be derived quickly and reduces the work of developing new phase retrieval models. We developed an algorithm for reconstructing pupil amplitude and phase from a single defocused image (previously three or more were needed) for hard-edged binary apertures. We developed Fourier transform models, based on the chirp z-transform (CZT), that allow flexible control of sampling in the pupil and image domains for phase retrieval algorithms. In some common cases, these models can be at least as fast as FFT-based algorithms. We used the CZT model to derive an algorithm for retrieving unknown sampling ratios (Q) jointly with wavefronts using an analytic gradient