JWST Wavefront Control Toolbox

A Matlab-based toolbox has been developed for the wavefront control and optimization of segmented optical surfaces to correct for possible misalignments of James Webb Space Telescope (JWST) using influence functions. The toolbox employs both iterative and non-iterative methods to converge to an optimal solution by minimizing the cost function. The toolbox could be used in either of constrained and unconstrained optimizations. The control process involves 1 to 7 degrees-of-freedom perturbations per segment of primary mirror in addition to the 5 degrees of freedom of secondary mirror. The toolbox consists of a series of Matlab/Simulink functions and modules, developed based on a "wrapper" approach, that handles the interface and data flow between existing commercial optical modeling software packages such as Zemax and Code V. The limitations of the algorithm are dictated by the constraints of the moving parts in the mirrors

Optical Testing of the James Webb Space Telescope

The James Webb Space Telescope (JWST) will be a large infrared telescope with a 6.5-meter primary mirror, working to a 2018 launch date. Ground testing for the JWST will occur in two test campaigns, at NASAs Goddard Space Flight Center and Johnson Space Center. The talk describes the JWST and its optical ground testing, highlighting the roles of many of the University of Rochester Institute of Optics' alumni as well as current faculty and students

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms

System and Method for Null-Lens Wavefront Sensing

A method of measuring aberrations in a null-lens including assembly and alignment aberrations. The null-lens may be used for measuring aberrations in an aspheric optic with the null-lens. Light propagates from the aspheric optic location through the null-lens, while sweeping a detector through the null-lens focal plane. Image data being is collected at locations about said focal plane. Light is simulated propagating to the collection locations for each collected image. Null-lens aberrations may extracted, e.g., applying image-based wavefront-sensing to collected images and simulation results. The null-lens aberrations improve accuracy in measuring aspheric optic aberrations

Qualification of a Null Lens Using Image-Based Phase Retrieval

In measuring the figure error of an aspheric optic using a null lens, the wavefront contribution from the null lens must be independently and accurately characterized in order to isolate the optical performance of the aspheric optic alone. Various techniques can be used to characterize such a null lens, including interferometry, profilometry and image-based methods. Only image-based methods, such as phase retrieval, can measure the null-lens wavefront in situ - in single-pass, and at the same conjugates and in the same alignment state in which the null lens will ultimately be used - with no additional optical components. Due to the intended purpose of a Dull lens (e.g., to null a large aspheric wavefront with a near-equal-but-opposite spherical wavefront), characterizing a null-lens wavefront presents several challenges to image-based phase retrieval: Large wavefront slopes and high-dynamic-range data decrease the capture range of phase-retrieval algorithms, increase the requirements on the fidelity of the forward model of the optical system, and make it difficult to extract diagnostic information (e.g., the system F/#) from the image data. In this paper, we present a study of these effects on phase-retrieval algorithms in the context of a null lens used in component development for the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission. Approaches for mitigation are also discussed

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

Revivals and classical-motion bases of quantum wave packets

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2002.This thesis explores the boundary between classical and quantum mechanics by studying wave packets, coherent superpositions of the stationary states of a quantum system. Such wave packets travel as localized entities along the trajectories predicted by classical mechanics for small windows of time before they spread out and decay away. Our investigations focus on two central issues - the revivals of the shape and classical motion of these wave packets that occur long after their initial decay, and the classical-motion bases that describe the quantum wavefunction in terms of constitutive objects that move classically. We study the infinite square-well potential, a simple model of complete confinement in a one-dimensional interval. The quantum motion seen in this potential is compared with classical models of a particle bouncing between two walls and of a wave traveling along a stretched string with both ends secured. We uncover a remarkable wave-motion basis, with which the wavefunction at any moment in time can be decomposed into a sum of distinct wave propagations of the initial quantum wavefunction in the classical wave equation. These results are extended to the finite square-well potential and we show how the wave-motion basis can be reconciled with the seemingly disparate theory of revivals for highly excited quantum wave packets. We explore the commonalities of the quantum revivals seen in a wide variety of systems by developing a mathematical formalism called phase-difference equations. These equations connect physical models for revivals with the subsequent prediction of revival times in a general way and offer a comprehensive "calculus" for understanding revival phenomena. We apply this calculus to several examples to demonstrate its power and versatility. Using a recently developed semiclassical basis for quantum states, we explore the radial wave packets of the hydrogen atom. Viewed in the semiclassical basis, the revivals of these wave packets are shown to arise from constructive interference among groups of classical particles on neighboring tracks of a Lagrange manifold in phase space, in a way that parallels the interference among discrete stationary states found in the standard view of revivals

Phase-Retrieval Uncertainty Estimation and Algorithm Comparison for the JWST-ISIM Test Campaign

Phase retrieval, the process of determining the exitpupil wavefront of an optical instrument from image-plane intensity measurements, is the baseline methodology for characterizing the wavefront for the suite of science instruments (SIs) in the Integrated Science Instrument Module (ISIM) for the James Webb Space Telescope (JWST). JWST is a large, infrared space telescope with a 6.5-meter diameter primary mirror. JWST is currently NASA's flagship mission and will be the premier space observatory of the next decade. ISIM contains four optical benches with nine unique instruments, including redundancies. ISIM was characterized at the Goddard Space Flight Center (GSFC) in Greenbelt, MD in a series of cryogenic vacuum tests using a telescope simulator. During these tests, phase-retrieval algorithms were used to characterize the instruments. The objective of this paper is to describe the Monte-Carlo simulations that were used to establish uncertainties (i.e., error bars) for the wavefronts of the various instruments in ISIM. Multiple retrieval algorithms were used in the analysis of ISIM phase-retrieval focus-sweep data, including an iterativetransform algorithm and a nonlinear optimization algorithm. These algorithms emphasize the recovery of numerous optical parameters, including low-order wavefront composition described by Zernike polynomial terms and high-order wavefront described by a point-by-point map, location of instrument best focus, focal ratio, exit-pupil amplitude, the morphology of any extended object, and optical jitter. The secondary objective of this paper is to report on the relative accuracies of these algorithms for the ISIM instrument tests, and a comparison of their computational complexity and their performance on central and graphical processing unit clusters. From a phase-retrieval perspective, the ISIM test campaign includes a variety of source illumination bandwidths, various image-plane sampling criteria above and below the Nyquist- Shannon critical sampling value, various extended object sizes, and several other impactful effects