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Register a new userGeneralized image deconvolution by exploiting spatially variant point spread functions
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An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted defects. Image deconvolution, also known as inverse filtering, has been widely exploited as a recovery technique because of its practical feasibility, and operates by assuming the linear shift-invariant property of the imaging system. However, shift invariance is not rigorously hold in all imaging situations and it is not a necessary condition for solving the inverse problem of light propagation. Here, we present a method to solve the linear inverse problem of coherent light propagation without assuming shift invariance. Full characterization of imaging capability of the system is achieved by successively recording optical responses, using various laser illumination angles which are systematically controlled by a digital micro-mirror device. Experimental results show that image distortions caused by optical defocus can be restored by conventional deconvolution, but severe aberrations produced by a tilted lens or an inserted disordered layer can be corrected only by the proposed generalized image deconvolution. This work generalizes the theory of optical imaging and deconvolution, and enables distortion-free imaging under any general imaging condition.
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An explanation for the origin of asymmetry along the preferential axis of the PSF of an AO system is developed. When phase errors from high altitude turbulence scintillate due to Fresnel propagation, wavefront amplitude errors may be spatially offset from residual phase errors. These correlated errors appear as asymmetry in the image plane under the Fraunhofer condition. In an analytic model with an open-loop AO system, the strength of the asymmetry is calculated for a single mode of phase aberration, which generalizes to two dimensions under a Fourier decomposition of the complex illumination. Other parameters included are the spatial offset of the AO correction, which is the wind velocity in the frozen flow regime multiplied by the effective AO time delay, and propagation distance or altitude of the turbulent layer. In this model, the asymmetry is strongest when the wind is slow and nearest to the coronagraphic mask when the turbulent layer is far away, such as when the telescope is pointing low towards the horizon. A great emphasis is made about the fact that the brighter asymmetric lobe of the PSF points in the opposite direction as the wind, which is consistent analytically with the clarification that the image plane electric field distribution is actually the inverse Fourier transform of the aperture plane. Validation of this understanding is made with observations taken from the Gemini Planet Imager, as well as being reproducible in end-to-end AO simulations.
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of points. The ensuing deconvolution problem has been solved in many ways, mainly by algorithms based on CLEAN. However, such algorithms that use image pixels as basis functions have inherent limitations and by using an orthonormal basis that span the whole image, we can overcome them. The construction of such an orthonormal basis involves fine tuning of many free parameters that define the basis functions. The optimal basis for a given problem (or a given extended source) is not guaranteed. In this paper, we discuss the use of generalized prolate spheroidal wave functions as a basis. Given the geometry (or the region of interest) of an extended source and the sampling points on the visibility plane, we can construct the optimal basis to model the source. Not only does this gives us the minimum number of basis functions required but also the artifacts outside the region of interest are minimized.
A new method is presented for determining the Point Spread Function (PSF) of images that lack bright and isolated stars. It is based on the same principles as the MCS (Magain, Courbin, Sohy, 1998) image deconvolution algorithm. It uses the information contained in all stellar images to achieve the double task of reconstructing the PSFs for single or multiple exposures of the same field and to extract the photometry of all point sources in the field of view. The use of the full information available allows to construct an accurate PSF. The possibility to simultaneously consider several exposures makes it very well suited to the measurement of the light curves of blended point sources from data that would be very difficult or even impossible to analyse with traditional PSF fitting techniques. The potential of the method for the analysis of ground-based and space-based data is tested on artificial images and illustrated by several examples, including HST/NICMOS images of a lensed quasar and VLT/ISAAC images of a faint blended Mira star in the halo of the giant elliptical galaxy NGC5128 (Cen A).
With Aperture synthesis (AS) technique, a number of small antennas can assemble to form a large telescope which spatial resolution is determined by the distance of two farthest antennas instead of the diameter of a single-dish antenna. Different from direct imaging system, an AS telescope captures the Fourier coefficients of a spatial object, and then implement inverse Fourier transform to reconstruct the spatial image. Due to the limited number of antennas, the Fourier coefficients are extremely sparse in practice, resulting in a very blurry image. To remove/reduce blur, CLEAN deconvolution was widely used in the literature. However, it was initially designed for point source. For extended source, like the sun, its efficiency is unsatisfied. In this study, a deep neural network, referring to Generative Adversarial Network (GAN), is proposed for solar image deconvolution. The experimental results demonstrate that the proposed model is markedly better than traditional CLEAN on solar images.
A new concept of using focus-diverse point spread functions (PSFs) for modal wavefront sensing (WFS) is explored. This is based on relatively straightforward image moment analysis of measured PSFs, which differentiates it from other focal-plane wavefront sensing techniques (FPWFS). The presented geometric analysis shows that the image moments are non-linear functions of wave aberration coefficients, but notes that focus-diversity (FD) essentially decouples the coefficients of interest from others, resulting in a set of linear equations whose solution corresponds to modal coefficient estimates. The presented proof-of-concept simulations suggest the potential of the concept in WFS with strongly aberrated high SNR objects in particular.
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