David C. Redding

Experimental verification of dispersed fringe sensing as a segment phasing technique using the Keck Telescope

Dispersed fringe sensing (DFS) is an efficient and robust method for coarse phasing of segmented primary mirrors (from one quarter of a wavelength to as much as the depth of focus of a single segment, typically several tens of microns). Unlike phasing techniques currently used for ground-based segmented telescopes, DFS does not require the use of edge sensors in order to sense changes in the relative heights of adjacent segments; this makes it particularly well suited for phasing of space-borne segmented telescopes, such as the James Webb Space Telescope. We validate DFS by using it to measure the piston errors of the segments of one of the Keck telescopes. The results agree with those of the Shack-Hartmann-based phasing scheme currently in use at Keck to within 2% over a range of initial piston errors of +/-16 microm.

Hubble Space Telescope prescription retrieval.

Prescription retrieval is a technique for directly estimating optical prescription parameters from images. We apply it to estimate the value of the Hubble Space Telescope primary mirror conic constant. Our results agree with other studies that examined primary-mirror test fixtures and results. In addition they show that small aberrations exist on the planetary-camera repeater optics.

Adaptive cross-correlation algorithm for extended scene Shack-Hartmann wavefront sensing

We present an adaptive cross-correlation algorithm for a large dynamic range extended-scene Shack-Hartmann wavefront sensor. We show that it accurately measures very fine image shifts over many pixels under a variety of practical imaging conditions.

Dynamic models of Fabry-Perot interferometers

Long-baseline, high-finesse Fabry-Perot interferometers can be used to make distance measurements that are precise enough to detect gravity waves. This level of sensitivity is achieved in part when the interferometer mirrors are isolated dynamically, with pendulum mounts and high-bandwidth cavity length control servos to reduce the effects of seismic noise. We present dynamical models of the cavity fields and signals of Fabry-Perot interferometers for use in the design and evaluation of length control systems for gravity-wave detectors. Models are described and compared with experimental data.

Calculation of diffraction effects on the average phase of an optical field

We report on algorithms for the computation of the average phase of a beam over a detector in the near field. The basic idea is to reconstruct the optical field numerically and then use a quadrature algorithm to evaluate the quantity of interest. The various algorithms that employ discrete Fourier transform techniques for the computation of the field are described, and numerical tests that assess the accuracy of these algorithms are presented. No particular algorithm delivers the desired accuracy over the entire range of Fresnel numbers of interest, but each can produce satisfactory results within a particular range. Finally, new methods to evaluate the average phase are introduced, and their efficiency is assessed.

Performance of dispersed fringe sensor in the presence of segmented mirror aberrations: modeling and simulation

Dispersed Fringe Sensing (DFS) is an efficient and robust method for coarse phasing of a segmented primary mirror such as the James Webb Space Telescope (JWST). In this paper, modeling and simulations are used to study the effect of segmented mirror aberrations on the DFS fringe image, its signals, and the piston detection accuracy. The simulations show that due to the pixilation spatial filter effect from DFS signal extraction the effect of wavefront error is reduced. In addition, the DFS algorithm is more robust against wavefront aberration when the multi-trace DFS approach is used. We have also studied the JWST Dispersed Hartmann Sensor (DHS) performance in presence of wavefront aberrations caused by the gravity sag and we have used the scaled gravity sag to explore the JWST DHS performance relationship with the level of the wavefront aberration. As a special case of aberration we have also included the effect from line-of-sight jitter in the JWST modeling study.

Analysis of curvature sensing for large-aperture adaptive optics systems

We present an analysis of the curvature sensing method and the associated wave-front reconstruction problem for adaptive optics applications. The analysis includes characterizations of the nonlinear, diffraction, and noise effects for curvature sensing. Reconstruction properties are shown to be characterized in terms of the eigenvalues of a discretized Laplacian operator. A comparison of reconstruction performance for curvature and slope sensing is presented. Simulations based on the Keck telescope optical prescription are used to verify the analysis.

Optical system alignment via optical state estimation using wavefront measurements

Optical State Estimation provides a framework for both separating errors in test optics from the target system and deducing the state of multiple optics in a telescope beam train using wavefront as well as pre-test component measurements including the knowledge of their level of error. Using this framework, we investigate the feasibility of simplifying the interferometric alignment configuration of NASAs James Webb Space Telescope, a large segmented-aperture cryogenic telescope, using a single, static auto-collimating flat instead of six such flats, resulting in a reduced sub-aperture sampling.

Some Aspects of the Mathematical Modeling of Wavefront Controllers for Adaptive Optics Systems

A number of large terrestrial telescope facilities are planning to utilize adaptive optics technology to improve the resolution of their instruments [3], [8], [9], [11], [19]. Telescopes operating in the atmosphere are limited by the seeing conditions at the telescope observational site. At an excellent seeing site such as Mauna Kea the atmosphere affords diffraction limited telescope performance at optical wavelengths to aperture sizes of approximately .3m. The consequence of this limit on astronomical observation is that although a large telescope such as Keck has tremendous light gathering power, the resolution of the 10m instrument is not significantly greater than the resolution of a .3m telescope.