John H. Seldin

Hubble Space Telescope characterized by using phase-retrieval algorithms.

We describe several results characterizing the Hubble Space Telescope from measured point spread functions by using phase-retrieval algorithms. The Cramer-Rao lower bounds show that point spread functions taken well out of focus result in smaller errors when aberrations are estimated and that, for those images, photon noise is not a limiting factor. Reconstruction experiments with both simulated and real data show that the calculation of wave-front propagation by the retrieval algorithms must be performed with a multiple-plane propagation rather than a simple fast Fourier transform to ensure the high accuracy required. Pupil reconstruction was performed and indicates a misalignment of the optical axis of a camera relay telescope relative to the main telescope. After we accounted for measured spherical aberration in the relay telescope, our estimate of the conic constant of the primary mirror of the HST was - 1.0144.

Evaluation of phase-diversity techniques for solar-image restoration

Phase-diversity techniques provide a novel observational method for overcomming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method.

Numerical investigation of the uniqueness of phase retrieval

Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms. Analytic expressions for the subspace of ambiguous solutions to the phase-retrieval problem are derived for 2 × 2 and 3 × 2 objects. Monte Carlo digital experiments using a reduced-gradient search of these subspaces are used to estimate the probability that the worst-case nearest ambiguous image to a given object has a Fourier modulus error of less than a prescribed amount. Probability distributions for nearest ambiguities are estimated for different object-domain constraints.

Iterative blind deconvolution algorithm applied to phase retrieval

The iterative blind deconvolution algorithm proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and improved on by Davey et al. [ Opt. Commun.69, 353 ( 1989)] is applied to the problem of phase retrieval, which is a special case of the blind deconvolution problem. A close relationship between this algorithm and the error-reduction version of the iterative Fourier-transform phase-retrieval algorithm is shown analytically. The performance of the blind deconvolution algorithm is compared with the error-reduction and hybrid input–output versions of the iterative Fourier-transform algorithm by reconstruction experiments on real-valued, nonnegative images with and without noise.

Phase-diverse speckle reconstruction of solar data

Phase-diverse speckle imaging is a novel imaging modality that makes use of both speckle-imaging and phase-diversity concepts. A phase- diverse speckle data set consists of one conventional image and at least one additional image with known phase diversity for each of multiple atmospheric phase realizations. We demonstrate the use of a phase-diverse speckle data set collected at the Swedish Vacuum Solar Telescope on La Palma to overcome the effects of atmospheric turbulence and to restore a fine-resolution image of solar granulation. We present preliminary results of simultaneously reconstructing an object and a sequence of atmospheric phase aberrations from these data using a maximum-likelihood parameter- estimation framework. The consistency of the reconstructions is demonstrated using subsets of the sequence of images pairs. The use of different phase-aberration parameterization schemes and their affect on parameter estimates are discussed. Insight into the desired number of atmospheric realizations is provided.

Adaptive multispectral CFAR detection of land mines

An automatic target detection algorithm which exploits spectral and spatial signatures of mines is described. Key features of this approach include the ability to adapt to unknown or changing background statistics and the capability to operate with unknown spectral signatures. Preliminary results of applying this algorithm for surface mine detection in video-based multispectral imagery covering the 400-900 nm region are presented. Tests on actual airborne data collected during 1992, 1993, and 1994 show that at 8-inch ground resolution (with 4x over-sampling), 12-inch diameter circular mines can be discriminated from natural backgrounds with a probability of detection around 85% with 3-4 false alarms per image in a relatively harsh clutter environment. This capability has been shown to be sufficient to meet COBRA minefield requirements during preliminary system testing.

Phase-diversity correction of turbulence-induced space-variant blur

Space-variant blur is encountered when objects extend beyond the isoplanatic patch associated with the intervening atmospheric turbulence. The method of phase diversity, used to estimate jointly the object and the aberrations, is generalized to accommodate turbulence-induced space-variant blur. This generalization utilizes a parametric model for the blur function that is constructed with multiple phase screens. Simulation results are presented that demonstrate the recovery of near-diffraction-limited imagery from phase-diversity imagery that has been degraded with rather severe anisoplanatism.

Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data

In phase-diverse speckle imaging one collects a time series of phase-diversity image sets that are used to jointly estimate the object and each of the phase-aberration functions. Current approaches model the total phase aberration in some deterministic parametric fashion. For many imaging schemes, however, additional information can be exploited. Specifically, the total aberration function consists of the fixed aberrations combined with dynamic (time-varying), turbulence-induced aberrations, about whose stochastic behavior we often have some knowledge. One important example is that in which the wave-front phase error corresponds to Kolmogorov turbulence. In this context using the extra statistical information available may be a powerful aid in the joint aberration/object estimation. In addition, such a framework provides an attractive method for calibrating fixed aberrations in an imaging system. The discipline of Bayesian statistical inference provides a natural framework for using the stochastic information regarding the wave fronts. Here one imposes an a priori probability distribution on the turbulence-induced wave fronts. We present the general Bayesian approach for the joint-estimation problem of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data that leads to a maximum a posteriori estimator. We also present results based on simulated data, which show that the Bayesian approach provides an increase in accuracy and robustness for this joint estimation.

Closed-loop wavefront sensing for a sparse-aperture multitelescope array using broadband phase diversity

The Lockheed Martin phased-array telescope developed at the Palo Alto Research Laboratory is a 0.75-m imaging system consisting of 9 separate 90-mm telescopes. One of the technology drivers behind this design is the ability to maintain the phasing of the individual telescopes to sub- wavelength tolerances. We demonstrate here the use of the focal-plane method of phase diversity for maintaining the phased-array alignment. The telescope is designed to operate with white light, so the phase diversity concept is extended to accommodate a broad optical bandwidth. A simulation of white-light phase-diverse wavefront sensing is presented as a demonstration of the robustness of the method with respect to sparse pupil and wavelength sampling. The simulation is validated with laboratory experiments using a point source. Finally, a closed-loop experiment is conducted that demonstrates the ability of phase diversity to sense piston error and maintain the alignment of the phased-array system.

Fine-resolution astronomical imaging with phase-diverse speckle

Phase-diverse speckle imaging is a novel post-detection correction technique for use in imaging through atmospheric turbulence. When the wavelength dependence is introduced, the data-collection model and problem statement are seen to accommodate a variety of existing and proposed data-collection schemes, including speckle imaging, multi-frame blind deconvolution, deconvolution with wavefront sensing, and hybrid adaptive optics.