Imaging through turbulence using compressive coherence sensing

Abstract

Previous studies have shown that the isoplanatic distortion due to turbulence and the image of a remote object may be jointly estimated from the 4D mutual intensity across an aperture. This Letter shows that decompressive inference on a 2D slice of the 4D mutual intensity, as measured by a rotational shear interferometer, is sufficient for estimation of sparse objects imaged through turbulence. The 2D slice is processed using an iterative algorithm that alternates between estimating the sparse objects and estimating the turbulence-induced phase screen. This approach may enable new systems that infer object properties through turbulence without exhaustive sampling of coherence functions. © 2010 Optical Society of America OCIS codes: 110.1650, 110.3175, 280.7060. Atmospheric turbulence distorts the wavefronts from incoherent sources radiating in the far field so that imaging the sources without compensating for the distortion results in a degraded image. Distorted wavefronts may be characterized by wavefront sensors [1] to control the actuators of a deformable mirror in an adaptive optics system so that the wavefront aberrations may be removed. After characterization, the distorted wavefront may also be used to digitally compensate the degraded images [2]. Alternatively, phase diversity [3] may be used to digitally estimate both the scene and the turbulenceinduced aberrations. Another strategy relies on measurement of the mutual intensity, a 4D function that captures the correlations between every pair of points in a 2D aperture. For example, the astigmatic coherence sensor [4], which may be viewed as a generalized phase diversity sensor, samples the 4D mutual intensity of the distorted optical field from remote sources, and uses the coherent-mode decomposition technique to correct an isoplanatic refractive distortion in the pupil. This approach is slow and impractical for image formation, as it requires complete sampling of the mutual intensity.We propose an approach inspired by compressive sampling (CS) [5] to digitally process a limited subset of samples of the mutual intensity and jointly recover (i) an unaberrated distribution of incoherent sources radiating in the far field and (ii) the phase screen introduced by turbulence that distorts the propagating wavefronts.The mutual intensity is a 4D function describing the coherence of the optical field and is given bywhere E͑r͒ is a quasi-monochromatic, statistically wide sense stationary electromagnetic field of wavenumber k = / c and r is the mean position of a pair of coordinates separated by ⌬r. The van CittertZernike (VCZ) theorem [6] states that J in a 2D aperture in the far field of spatially incoherent sources with irradiance S͑r͒ depends only on ⌬r asThus, J is the 2D Fourier transform of the scene. To image the scene, J may be sampled as a function of ⌬r about a central point using an interferometer and then inverse Fourier transformed. If isoplanatic turbulence with an optical path delay, d͑r͒, is present between the scene and the aperture,Note that...

Compressive Sampling for Non-Imaging Remote Classification

“…Another application of compressive sensing is the measurement of objects through turbulence using compressive coherence sensing 9 . The coherence of an incoherently radiating object that is corrupted by turbulence contains both the object structure and a random turbulence phase.…”