David A. Carrara

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.

Comparison of phase diversity and curvature wavefront sensing

We compare phase diversity and curvature wavefront sensing. Besides having completely different reconstruction algorithms, the two methods measure data in different domains: phase diversity very near to the focal plane, and curvature wavefront sensing far from the focal plane in quasi-pupil planes, which enable real-time computation of the wavefront using analog techniques. By using information- theoretic lower bounds, we show that the price of measuring far from the focal lane is an increased error in estimating the phase. Curvature wavefront sensing is currently operating in the field, but phase diversity should produce superior estimates as real-time computing develops.

Comparison of Shack-Hartmann wavefront sensing and phase-diverse phase retrieval

The effect of focus anisoplanatism upon the performance of an astronomical laser guide star (LGS) adaptive optics (AO) system can in principle be reduced if the lowest order wavefront aberrations are sensed and corrected using a natural guide star (NGS). For this approach to be useful, the noise performance of the wavefront sensor (WFS) used for the NGS measurements must be optimized to enable operation with the dimmest possible source. Two candidate sensors for this application are the Shack-Hartmann sensor and “phase-diverse phase retrieval,” a comparatively novel approach in which the phase distortion is estimated from two or more well-sampled, full-aperture images of the NGS measured with known adjustments applied to the phase profile. We present analysis and simulation results on the noise-limited performance of these two methods for a sample LGS AO observing scenario. The common parameters for this comparison are the NGS signal level, the sensing wavelength, the second-order statistics of the phase distortion, and the RMS detector read noise. Free parameters for the two approaches are the Shack-Hartmann subaperture geometry, the focus biases used for the phase-diversity measurements, and the algorithms used to estimate the wavefront. We find that phase-diverse phase retrieval provides consistently superior wavefront estimation accuracy when the NGS signal level is high. For lower NGS signal levels on the order of 103 photodetection events, the Shack-Hartmann (phase diversity) approach is preferred at a RMS detector read noise level of 5 (0) electrons/pixel.

Cyclostationary signal models for the detection and characterization of vibrating objects in SAR data

We present a novel method of detecting and characterizing vibrating objects in synthetic aperture radar (SAR) data. We model the SAR phase history as having cyclostationary characteristics when a vibrating object is present in the scene. Within this framework, we develop a generalized likelihood ratio test to detect the presence of the vibrating object and provide estimates of the vibration frequency, amplitude, and the spread of the vibration spectrum. We provide analytical and empirical results outlining the performance of this detection scheme.

Aberration correction of segmented-aperture telescopes by using phase diversity

There is currently much interest in deploying large space- based telescopes for various applications including fine- resolution astronomical imaging and earth observing. Often a large primary mirror is synthesized by the precise alignment of several smaller mirror segments. Misalignment or misfigure of these segments results in phase error which degrade the resolution of collected imagery. Phase diversity (PD) is a technique used to infer unknown phase aberrations form image data. It requires the collection of two or more images of the same object, each incorporating a known phase perturbation in addition to the unknown aberrations. Statistical estimation techniques are employed to identify a combination of object and aberrations that is consistent with all of the collected images. The wavefront- sensing performance of PD is evaluated through simulation for a variety of signal and aberration strengths. The aberrations are parameterizes by piston and tilt misalignment of each segment. An unknown extended scene is imaged, complicating the estimation procedure. Since wavefront correction is often an iterative process, moderate estimation errors can be corrected by subsequent estimates. The interpretation of iterative wavefront adjustments as creating new phase-diversity channels suggests a more sophisticated processing approach, called Actuated Phase Diversity. This technique is shown to significantly improve PD wavefront-sensing performance.

Fine-resolution imagery of extended objects observed through volume turbulence using phase-diverse speckle

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. This condition arises in a variety of imaging geometries, including astronomical imaging, horizontal-path imaging, and slant-path (e.g. air-to-ground) imaging. Space-variant effects are particularly severe when much of the optical path is immersed in turbulent media. We present a novel post-processing algorithm based on the technique of phase- diverse speckle (PDS) and a physical model for the space- variant blur. PDS imaging is a combination of phase diversity and speckle imaging which has proven to be an effective post-processing technique for cases with space- invariant blur. We present the details of the algorithm modified to accommodate space-variance and demonstrate its performance with results from both simulation experiments and real-data experiments. The results show that the space- variant PDS algorithm is very effective in cases involving severe space-variant blur, which cause correction techniques based on space-invariant models to fail.

Myopic deblurring of space-variant blur by using phase-diverse speckle

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. This condition arises in a variety of imaging geometries, including astronomical imaging, horizontal-path imaging, and slant-path (e.g., air-to-ground) imaging. Space-variant effects are particularly severe when much of the optical path is immersed in turbulent media. Phase-diverse speckle (PDS), an imaging modality that blends the strengths of phase diversity and speckle imaging, can be used to sense the space-variant blur from image data and recover fine-resolution images. Technically, PDS does not perform blind deblurring because it utilizes auxiliary data provided by the diversity channel. The function performed by PDS is more appropriately referred to as myopic deblurring. We present results demonstrating the recovery of fine-resolution features from both simulated and real data exhibiting space-variant blur.

Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery

Phase-Diverse Speckle (PDS) is a short-exposure data- collection and processing technique that blends phase- diversity and speckle-imaging concepts. PDS has been successfully used for solar astronomy to achieve near diffraction-limited resolution in ground-based imaging of solar granulation. Variants of PDS that involve narrow-band, spectroscopic, and polarimetric data provide more information observations. We present results from processing data collected with the 76-cm Richard B. Dunn Solar Telescope (DST) on Sacramento Peak, NM. Three-channel data sets consisting of a pair of phase-diverse images of the solar continuum and a narrow-band image were collected over spans of 15 - 20 minutes. Point-spread functions that are estimated from the PDS data are used in a multi-frame deconvolution algorithm to correct the narrow-band imagery. The data were processed into a number of time series. A rare, short-lived continuum bright point with a peak intensity at a factor of 2.1 above the mean intensity in the continuum was observed in one such sequence. The field of view spans multiple isoplanatic patches, and strategies for processing these large fields were developed. We will discuss these methods along with other techniques that were explored for accelerating the processing. Finally, we show the first PDS reconstruction of adaptive-optics (AO) compensated solar granulation taken at the DST. As expected, we find that these data are less aberrated and, thus, the use of AO in future experiments is planned.

Pre- and post-detection correction of turbulence-induced space-variant blur

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. Space- variant effects are particularly severe in horizontal-path imaging, slant-path (air-to-ground or ground-to-air) geometries, and ground-based imaging of low-elevation satellites or astronomical objects. In these geometries, the isoplanatic angle can be comparable to or even smaller than the diffraction-limited resolution angle. Clearly, space-invariant methods used in conjunction with mosaicing will fail in this regime. Our approach to this problem has been to generalize the method of Phase-diverse Speckle (PDS) by using a physically motivated distributed phase-screen model to accomplish both pre- and post-detection correction. Previously reported simulation results have demonstrated the reconstruction of near diffraction-limited imagery using imagery which was severely degraded by space-variant blur. In this paper, we present a novel adaptation of the space- variant PDS scheme for use as a beacon-less wavefront sensor in a multi-conjugate AO system when imaging extended scenes. We then present results of simulation experiments demonstrating that this multi-conjugate AO-compensation scheme is very effective in improving the quality and resolution of collected imagery.

CHAMP: a locally adaptive unmixing-based hyperspectral anomaly detection algorithm

Anomaly detection offers a means by which to identify potentially important objects in a scene without prior knowledge of their spectral signatures. As such, this approach is less sensitive to variations in target class composition, atmospheric and illumination conditions, and sensor gain settings than would be a spectral matched filter or similar algorithm. The best existing anomaly detectors generally fall into one of two categories: those based on local Gaussian statistics, and those based on linear mixing moles. Unmixing-based approaches better represent the real distribution of data in a scene, but are typically derived and applied on a global or scene-wide basis. Locally adaptive approaches allow detection of more subtle anomalies by accommodating the spatial non-homogeneity of background classes in a typical scene, but provide a poorer representation of the true underlying background distribution. The CHAMP algorithm combines the best attributes of both approaches, applying a linear-mixing model approach in a spatially adaptive manner. The algorithm itself, and teste results on simulated and actual hyperspectral image data, are presented in this paper.