Deconvolution From Wavefront Sensing Research Articles

Constrained deconvolution from wavefront sensing using the frozen flow hypothesis and complex wavelet regularization.

Deconvolution from wavefront sensing (DWFS) is a high-performance image restoration technique designed to compensate for atmospheric turbulence-induced wavefront distortions. It uses simultaneously recorded short-exposure images of the object and high cadence wavefront sensor (WFS) data to estimate both the wavefronts and the object. Conventional DWFS takes no account of the temporal correlations in WFS data, which limits the reconstruction of high-spatial frequency components of wavefront distortion and then the recovery of the object. This paper takes the frozen flow hypothesis (FFH) to model the temporal evolution of atmospheric turbulence. Under this assumption, a joint estimation is performed in a Bayesian framework to simultaneously estimate the object and the turbulence phases with strict constraints imposed by WFS data and the FFH. It takes into account the temporal correlations in WFS data as well as the available a priori knowledge about the object and turbulence phases. Taking advantage of the sparse analysis prior of the object in the wavelet domain, a sparse regularization of the object based on the 2D dual-tree complex wavelet transform is proposed. Numerical experiments show that the proposed method is robust and effective for high-resolution image restoration in different seeing conditions.

Sequential deconvolution from wave-front sensing using bivariate simplex splines

Deconvolution from wave-front sensing (DWFS) is an imaging compensation technique for turbulence degraded images based on simultaneous recording of short exposure images and wave-front sensor data. This paper employs the multivariate splines method for the sequential DWFS: a bivariate simplex splines based average slopes measurement model is built firstly for Shack–Hartmann wave-front sensor; next, a well-conditioned least squares estimator for the spline coefficients is constructed using multiple Shack–Hartmann measurements; then, the distorted wave-front is uniquely determined by the estimated spline coefficients; the object image is finally obtained by non-blind deconvolution processing. Simulated experiments in different turbulence strength show that our method performs superior image restoration results and noise rejection capability especially when extracting the multidirectional phase derivatives.

Deconvolution from wave front sensing using the frozen flow hypothesis

Deconvolution from wave front sensing (DWFS) is an image-reconstruction technique for compensating the image degradation due to atmospheric turbulence. DWFS requires the simultaneous recording of high cadence short-exposure images and wave-front sensor (WFS) data. A deconvolution algorithm is then used to estimate both the target object and the wave front phases from the images, subject to constraints imposed by the WFS data and a model of the optical system. Here we show that by capturing the inherent temporal correlations present in the consecutive wave fronts, using the frozen flow hypothesis (FFH) during the modeling, high-quality object estimates may be recovered in much worse conditions than when the correlations are ignored.

Experimental measurements of estimator bias and the signal-to-noise ratio for deconvolution from wave-front sensing

Deconvolution from wave-front sensing (DWFS) has been proposed as a method for achieving high-resolution images of astronomical objects from ground-based telescopes. The technique consists of the simultaneous measurement of a short-exposure focal-plane speckled image, as well as the wave front, by use of a Shack-Hartmann sensor placed at the pupil plane. In early studies it was suspected that some problems would occur in poor seeing conditions; however, it was usually assumed that the technique would work well as long as the wave-front sensor subaperture spacing was less than r(0) (L/r(0) < 1). Atmosphere-induced phase errors in the pupil of a telescope imaging system produce both phase errors and magnitude errors in the effective short-exposure optical transfer function (OTF) of the system. Recently it has been shown that the commonly used estimator for this technique produces biased estimates of the magnitude errors. The significance of this bias problem is that one cannot properly estimate or correct for the frame-to-frame fluctuations in the magnitude of the OTF but can do so only for fluctuations in the phase. An auxiliary estimate must also be used to correct for the mean value of the magnitude error. The inability to compensate for the magnitude fluctuations results in a signal-to-noise ratio (SNR) that is less favorable for the technique than was previously thought. In some situations simpler techniques, such as the Knox-Thompson and bispectrum methods, which require only speckle gram data from the focal plane of the imaging system, can produce better results. We present experimental measurements based on observations of bright stars and the Jovian moon Ganymede that confirm previous theoretical predictions.

Comparison of Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction

Atmospheric turbulence limits the resolution of astronomical optical imaging systems. Speckle imaging and deconvolution from wavefront sensing (DWFS) are two post-detection image processing methods for overcoming some turbulence effects which do not require adaptive optics. Both speckle imaging and DWFS create estimates of the object irradiance distribution by first estimating the Fourier transform, or spectrum of the object. Previous work has established the signal-to-noise ratio performance for some of the estimators used in both speckle imaging and DWFS. However, the comparative quality of the object spectrum phase estimation provided by these two techniques has not been studied in detail. In this paper we present the results of a simulation study of the comparative Fourier phase estimation errors for speckle imaging using the bispectrum technique, and DWFS. It is shown that even for good wavefront sampling and bright objects DWFS provides Fourier phase spectrum estimation of lower quality than the phase spectrum estimate provided by the bispectrum technique. When the beacon is not bright enough to provide a good signal-to-noise ratio in the wavefront sensor the bispectrum technique provides much better Fourier phase spectrum estimation than DWFS.

Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction

It is well known that atmospheric turbulence severely degrades the performance of ground-based imaging systems. Techniques to overcome the effects of the atmosphere have been developing at a rapid pace over the past 10 years. These techniques can be grouped into two broad categories: predetection and postdetection techniques. A recent newcomer to the postdetection scene is deconvolution from wave-front sensing (DWFS). DWFS is a postdetection image-reconstruction technique that makes use of one feature of predetection techniques. A wave-front sensor (WFS) is used to record the wave-front phase distortion in the pupil of the telescope for each short-exposure image. The additional information provided by the WFS is used to estimate the system's point-spread function (PSF). The PSF is then used in conjunction with the ensemble of short-exposure images to obtain an estimate of the object intensity distribution through deconvolution. With the addition of DWFS to the suite of possible postdetection image-reconstruction techniques, it is natural to ask "How does DWFS compare with both traditional linear and speckle image-reconstruction techniques?" In the results we make a direct comparison based on a frequency-domain signal-to-noise-ratio performance metric. This metric is applied to each technique's image-reconstruction estimator. We find that DWFS nearly always results in improved performance over the estimators of traditional linear image reconstruction such as Wiener filtering. On the other hand, DWFS does not always outperform speckle-imaging techniques, and in cases that it does the improvement is small.

Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing

The method of deconvolution from wave-front sensing (DWFS), which is a method for improving the quality of astronomical images measured through atmospheric turbulence, uses simultaneous shortexposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function (OTF). This estimate of the OTF is then used in a deconvolution procedure. We point out the existence and origin of an unnoticed bias in the estimator for the DWFS method. This bias leads to nonrandom errors in the estimated object spectrum beyond those expected to arise by virtue of low-pass filtering and noise, including the possibility of an overall system transfer function greater than unity at some spatial frequencies. An alternative measurement and postprocessing scheme to overco e this source of error is suggested.