Alden S. Jurling

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 many novel aspects including realistically complex galaxy models based on high-resolution imaging from space; a spatially varying, physically motivated blurring kernel; and a 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.

Applications of algorithmic differentiation to phase retrieval algorithms.

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.

Extended capture range for focus-diverse phase retrieval in segmented aperture systems using geometrical optics

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.

Phase retrieval with unknown sampling factors via the two-dimensional chirp z-transform

We derive the analytic gradient of a phase retrieval error metric with respect to the sampling factor or the f-number that produced the measured point-spread function. This allows us to efficiently optimize over the sampling factor, thereby improving the accuracy of the phase estimate. Computer simulation results show its effectiveness.

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.

A numerical exploration of phase-retrieval error-metric surfaces

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.

F/# Estimation Using a Chirp z-Transform and Analytic Gradients for Wavefront Sensing

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.

A Fast Approximation Method for Broadband Phase Retrieval

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.

Rays and Waves in Wavefront Sensing

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.

Improved Method for Solving the Capture Range Problem in Focus-Diverse Phase Retrieval for Segmented Systems

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.