Phase-Retrieval Wave-Front Sensing for the Hubble and Future Space Telescopes

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Nonnegative Matrix Factorization for Efficient Hyperspectral Image Projection

Hyperspectral imaging for remote sensing has prompted development of hyperspectral image projectors that can be used to characterize hyperspectral imaging cameras and techniques in the lab. One such emerging astronomical hyperspectral imaging technique is wide-field double-Fourier interferometry. NASA's current, state-of-the-art, Wide-field Imaging Interferometry Testbed (WIIT) uses a Calibrated Hyperspectral Image Projector (CHIP) to generate test scenes and provide a more complete understanding of wide-field double-Fourier interferometry. Given enough time, the CHIP is capable of projecting scenes with astronomically realistic spatial and spectral complexity. However, this would require a very lengthy data collection process. For accurate but time-efficient projection of complicated hyperspectral images with the CHIP, the field must be decomposed both spectrally and spatially in a way that provides a favorable trade-off between accurately projecting the hyperspectral image and the time required for data collection. We apply nonnegative matrix factorization (NMF) to decompose hyperspectral astronomical datacubes into eigenspectra and eigenimages that allow time-efficient projection with the CHIP. Included is a brief analysis of NMF parameters that affect accuracy, including the number of eigenspectra and eigenimages used to approximate the hyperspectral image to be projected. For the chosen field, the normalized mean squared synthesis error is under 0.01 with just 8 eigenspectra. NMF of hyperspectral astronomical fields better utilizes the CHIP's capabilities, providing time-efficient and accurate representations of astronomical scenes to be imaged with the WIIT

Wavefront-Error Performance Characterization for the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) Science Instruments

The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES) test chamber. In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing, and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) F-number and pupil-distortion measurements made using a pseudo-nonredundant mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated and/or rotated across the exit pupil of the system. Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront-error maps

Wavefront-Error Performance Characterization for the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) Science Instruments

The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES). In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing (also known as phase retrieval), and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) plate scale measurements made using a Pseudo-Nonredundant Mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated andor rotated across the exit pupil of the system.Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront error maps

Theory and Applications of X-ray Standing Waves in Real Crystals

Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this theory is applied to different concreat cases. Various models of deformed crystals like: bicrystal model, multilayer model, crystals with extended deformation field are considered in detailes. Peculiarities of x-ray standing wave behavior in different scattering geometries (Bragg, Laue) are analysed in detailes. New possibilities to solve the phase problem with x-ray standing wave method are discussed in the review. General theoretical approaches are illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table

Image Reconstruction for Interferometric Imaging of Geosynchronous Satellites

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2017.Imaging distant objects at a high resolution has always presented a challenge due to the diffraction limit. Larger apertures improve the resolution, but at some point the cost of engineering, building, and correcting phase aberrations of large apertures become prohibitive. Interferometric imaging uses the Van Cittert-Zernike theorem to form an image from measurements of spatial coherence. This effectively allows the synthesis of a large aperture from two or more smaller telescopes to improve the resolution. We apply this method to imaging geosynchronous satellites with a ground-based system. Imaging a dim object from the ground presents unique challenges. The atmosphere creates errors in the phase measurements. The measurements are taken simultaneously across a large bandwidth of light. The atmospheric piston error, therefore, manifests as a linear phase error across the spectral measurements. Because the objects are faint, many of the measurements are expected to have a poor signal-to-noise ratio (SNR). This eliminates possibility of use of commonly used techniques like closure phase, which is a standard technique in astronomical interferometric imaging for making partial phase measurements in the presence of atmospheric error. The bulk of our work has been focused on forming an image, using sub-Nyquist sampled data, in the presence of these linear phase errors without relying on closure phase techniques. We present an image reconstruction algorithm that successfully forms an image in the presence of these linear phase errors. We demonstrate our algorithm’s success in both simulation and in laboratory experiments

Phase retrieval with transverse translation diversity: a nonlinear optimization approach,

Abstract: We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored. References and links 1. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). 2. J. R. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987). 3. P. S. Idell, J. R. Fienup and R. S. Goodman, "Image synthesis from nonimaged laser-speckle patterns," Opt. Lett. 12, 858-860 (1987). 4. J. N. Cederquist, J. R. Fienup, J. C. Marron and R. G. Paxman, "Phase retrieval from experimental far-field speckle data," Opt. Lett. 13, 619-621 (1988). 5. J. Miao, P. Charalambous, J. Kirz and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999

Expanding the capture range of image-based wavefront sensing problems

Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2019.Image-based wavefront sensing using phase retrieval is a method to determine wavefront error in a system using images taken with that system. It has been used to determine the error in the Hubble Space Telescope and develop the necessary prescription to correct the aberrations in this telescope. This method is being used by the James Webb Space Telescope (JWST) in order to characterize wavefront error and perform correction both in ground-based testing and on orbit. This thesis considers methods by which to improve the efficacy of phase retrieval and expand its usage for image-based wavefront sensing. Phase retrieval algorithms operate by using point-spread functions (PSFs), which are images of unresolved stars. A numerical model to simulate the aberrated system is developed, and then nonlinear optimization (NLO) adjusts the parameters of this system to minimize an error metric which quantifies the difference between measured PSFs and the simulated PSFs from the numerical model. In our case, the parameters we adjust are related to the wavefront of the system, and we use NLO to recover this wavefront aberration based on the imaged PSFs. This method is reliable when the starting guess for the aberrations is close to the true solution. If this is not the case, then the NLO can fall into a local minimum of the error metric function and fail to recover the true wavefront aberration. When the starting guess does not converge to a good solution, it is considered to be outside of the capture range of the phase retrieval algorithm. This capture range problem is present with piston errors in segmented telescopes, where the error metric value has multiple minima. By examining the error metric function, we show that by imaging with broadband light, we developed a grid search to move out of these local minima and recover the real wavefront error in a system with piston errors on the order of several waves. In order to fall within the capture range for a certain phase retrieval problem, a good starting guess is necessary. Classically, one can use many random starting guesses for parameters in an attempt to land within the capture range of the true solution. Alternatively, we show that one can train a convolutional neural network (CNN) on simulated PSFs to predict Zernike coefficients, which can then be used as starting guesses for phase retrieval. We show that this trained neural network outperforms random starting guesses in simulation for large amounts of wavefront error on a single PSF image. Another telescope, on which phase retrieval will be used, is the Wide-Field Infrared Survey Telescope (WFIRST). Scientists intend to use this telescope to measure the ellipticity of galaxies as a way to measure dark energy. To perform this tasks, the ellipticity of PSFs must be known extremely well. It therefore becomes important to consider the eect of polarization on the simulated PSFs, and determine if it is necessary to simulate polarization aberrations to accurately measure PSF ellipticity. We show that it is possible to add polarization terms separately from the scalar wavefront terms, and examine the effect of these additional polarization terms on the error in the recovered ellipticity of the system PSFs. The detector for WFIRST is not located on the optical axis, and therefore is not located in a plane normal to the exit pupil of the system. This will warp the underlying grid of the wavefront aberration, requiring resampling. If the grid is expressed using Zernike polynomials, then no interpolation becomes necessary, since these polynomials are continuously defined. We developed a method by which the coefficients of the Zernike polynomials can be changed, and compare it to applying the Zernike polynomials to a warped grid