David W. Tyler

Model-based image reconstruction by means of a constrained least-squares solution

The problem of the optimal use of object model information in image reconstruction is addressed. A closed-form solution for the estimated object spectrum is derived with the Lagrange multiplier technique, which assumes a measured image, knowledge of the optical transfer function, statistical information about the measurement noise, and a model of the object. This reconstruction algorithm is iterative in nature because the optimal Lagrange multiplier is not generally known at the start of the problem. We derive the estimator, describe one technique for determining the optimal Lagrange multiplier, demonstrate a stopping criterion based on the mean-square error between a noise-free image and the photon-limited version of the image, and show representative results for both filled- and sparse-aperture imaging applications.

Comparison of image reconstruction algorithms using adaptive optics instrumentation

We present preliminary results from a comparison of image estimation and recovery algorithms developed for use with advanced telescope instrumentation and adaptive optics systems. Our study will quantitatively compare the potential of these techniques to boost the resolution of imagery obtained with undersampled or low-bandwidth adaptive optics; example applications are optical observations with IR- optimized AO, AO observations in server turbulence, and AO observations with dim guidestars. We will compare the algorithms in terms of morphological and relative radiometric accuracy as well as computational efficiency. Here, we present qualitative comments on image results for two levels each of seeing, object brightness, and AO compensation/wavefront sensing.

Reduction of nonstationary noise in telescope imagery using a support constraint

We demonstrate the use of image support constraints in a noise-reduction algorithm. Previous work has revealed serious limits to the use of support if image noise is wide-sense stationary in the frequency domain; we use simulation and numerical calculations to show these limits are removed for nonstationary noise generated by inverse-filtering adaptive optics image spectra. To quantify the noise reduction, we plot fractional noise removed by the proposed algorithm over a range of support sizes. We repeat this calculation for other noise sources with varying degrees of stationarity.

Effects of predetection atmospheric compensation and post-detection image processing on imagery collected at a ground-based telescope

Short exposure imagery of single and binary stars was collected at the 1.6-m Air Force Maui Optical Station (AMOS) telescope, using a low-noise CCD camera. Atmospheric turbulence effects were partially mitigated using the Compensated Imaging System (CIS), a predetection wavefront sensor and deformable mirror adaptive optical system. We present images and power spectra from both partially compensated and uncompensated short exposure simulations and field data. Our results illustrate that the use of lower-cost partially compensating adaptive optical systems combined with post-detection processing provides a viable alternative to expensive, fully compensated adaptive imaging systems for achieving high-resolution imagery through the atmosphere.

Optimal SNR exposure time for speckle imaging: experimental results with frequency-dependent detector noise

We review recent arguments for using increased spectral bandwidth and exposure times to optimize the signal-to-noise ratio of speckle imaging estimators and discuss the tradeoff between camera exposure time and the number of data frames collected when observing time is fixed. We compare experimental results with a previously-derived expression for optimal exposure time and find reasonable agreement after accounting for frequency-dependent camera noise.

Optimal wavelength selection for adaptive optics telescopes

We derive an expression for the wavelength (lambda) o giving maximum resolution for an adaptive-optics compensated telescope. An approximate expression for average on-axis intensity is written to account for the competing effects of diffraction and residual (post-compression) phase error; this expression is then differentiated with respect to the imaging wavelength (lambda) to yield (lambda) o. The analytically predicted (lambda) o is compared to simulation results and correspondence is shown to be good at widely separated seeing conditions and adaptive optics geometries.

Sky coverage calculations for spectrometer slit power coupling with adaptive optics compensation

We present an extension of adaptive optics sky coverage calculations to include spectrometer slit power coupling. As an example, we show several slit coupling sky coverage calculations for the Gemini-North telescope. Our calculations quantify the effect on sky coverage of previous work, where we showed Strehl is not in general a good predictor of slit coupling, and provide an example of the utility of instrument-specific calculations.

Near-real-time speckle imaging for optimization of observing parameters

Images of astronomical objects acquired by ground-based telescopes are blurred by atmospheric turbulence. These blurring effects can be partially overcome by post-detection processing such as speckle imaging (SI). We have developed a parallel implementation of SI to dramatically reduce the time required to reduce imaging data, allowing us to implement a near realtime (NRT) SI image feedback capability. With NRT SI feedback, telescope operators can select observing parameters to optimize data quality while the data is being taken. NRT processing also allows easy selection of the best data from a long observation for later post-detection processing using more sophisticated algorithms. Similar NRT schemes could also be implemented for non-imaging measurements, such as spectroscopy. NRT feedback will yield higher quality data products and better utilization of observatory resources.

Positivity and support: a comparison

Positivity and support have long been used to improve image quality beyond that achievable from the measured data alone. In this paper we analyze how positivity functions to reduce noise levels in measured Fourier data and the corresponding images. We show that positivity can be viewed as a signal- dependent support constraint, and thus it functions by enforcing Fourier-domain correlations. Using computer simulated data, we show the effects that positivity has upon measured Fourier data and upon images. We compare these results to equivalent result obtained using support as constraint. We show that support is a more powerful constraint than positivity in several ways: (1) more super- resolution is possible, (2) more Fourier domain noise reduction can occur, and (3) more image-domain noise reduction can occur.

Iterative model-based image reconstruction using a constrained least squares technique

In this paper the problem of optimally using object model information in image reconstruction is addressed. A closed form solution for the estimated object spectrum is derived using the Lagrange multiplier technique which assumes a measured image, knowledge of the optical transfer function, statistical information about the measurement noise, and a model of the object. This reconstruction algorithm is iterative in nature for two reasons: (1) because the optimal Lagrange multiplier is not generally known at the start of the problem; and (2) we can use the object estimate obtained from one step of the algorithm as the model input for the next step. In this paper we derive the estimator, describe one technique for determining the optimal Lagrange multiplier, demonstrate a stopping criterion based on the mean squared error between a noise free image and the photon-limited version of the image, and show representative results for a sparse aperture imaging application.