We present a block-matching and Wiener filtering approach to atmospheric turbulence mitigation for long-range imaging of extended scenes. We evaluate the proposed method, along with some benchmark methods, using simulated and real-image sequences. The simulated data are generated with a simulation tool developed by one of the authors. These data provide objective truth and allow for quantitative error analysis. The proposed turbulence mitigation method takes a sequence of short-exposure frames of a static scene and outputs a single restored image. A block-matching registration algorithm is used to provide geometric correction for each of the individual input frames. The registered frames are then averaged, and the average image is processed with a Wiener filter to provide deconvolution. An important aspect of the proposed method lies in how we model the degradation point spread function (PSF) for the purposes of Wiener filtering. We use a parametric model that takes into account the level of geometric correction achieved during image registration. This is unlike any method we are aware of in the literature. By matching the PSF to the level of registration in this way, the Wiener filter is able to fully exploit the reduced blurring achieved by registration. We also describe a method for estimating the atmospheric coherence diameter (or Fried parameter) from the estimated motion vectors. We provide a detailed performance analysis that illustrates how the key tuning parameters impact system performance. The proposed method is relatively simple computationally, yet it has excellent performance in comparison with state-of-the-art benchmark methods in our study.

Abstract. Atmospheric turbulence is a fundamental problem in imaging through long slant ranges, horizontalrange paths, or uplooking astronomical cases through the atmosphere. An essential characterization of atmospheric turbulence is the point spread function (PSF). Turbulence images can be simulated to study basic questions, such as image quality and image restoration, by synthesizing PSFs of desired properties. In this paper, we report on a method to synthesize PSFs of atmospheric turbulence. The method uses recent developments in sparse and redundant representations. From a training set of measured atmospheric PSFs, we construct a dictionary of "basis functions" that characterize the atmospheric turbulence PSFs. A PSF can be synthesized from this dictionary by a properly weighted combination of dictionary elements. We disclose an algorithm to synthesize PSFs from the dictionary. The algorithm can synthesize PSFs in three orders of magnitude less computing time than conventional wave optics propagation methods. The resulting PSFs are also shown to be statistically representative of the turbulence conditions that were used to construct the dictionary.

An extension of the fusion of interpolated frames superresolution (FIF SR) method to perform SR in the presence of atmospheric optical turbulence is presented. The goal of such processing is to improve the performance of imaging systems impacted by turbulence. We provide an optical transfer function analysis that illustrates regimes where significant degradation from both aliasing and turbulence may be present in imaging systems. This analysis demonstrates the potential need for simultaneous SR and turbulence mitigation (TM). While the FIF SR method was not originally proposed to address this joint restoration problem, we believe it is well suited for this task. We propose a variation of the FIF SR method that has a fusion parameter that allows it to transition from traditional diffraction-limited SR to pure TM with no SR as well as a continuum in between. This fusion parameter balances subpixel resolution, needed for SR, with the amount of temporal averaging, needed for TM and noise reduction. In addition, we develop a model of the interpolation blurring that results from the fusion process, as a function of this tuning parameter. The blurring model is then incorporated into the overall degradation model that is addressed in the restoration step of the FIF SR method. This innovation benefits the FIF SR method in all applications. We present a number of experimental results to demonstrate the efficacy of the FIF SR method in different levels of turbulence. Simulated imagery with known ground truth is used for a detailed quantitative analysis. Three real infrared image sequences are also used. Two of these include bar targets that allow for a quantitative resolution enhancement assessment.

This paper investigates anisoplanatic numerical wave simulation in the context of lucky look imaging. We demonstrate that numerical wave propagation can produce root mean square (RMS) wavefront distributions and probability of lucky look (PLL) statistics that are consistent with Kolmogorov theory. However, the simulated RMS statistics are sensitive to the sampling parameters used in the propagation window. To address this, we propose and validate a new sample spacing rule based on the point source bandwidth used in the propagation and the level of atmospheric turbulence. We use the tuned simulator to parameterize the wavefront RMS probability density function as a function of turbulence strength. The fully parameterized RMS distribution model is used to provide a way to accurately predict the PLL for a range of turbulence strengths. We also propose and validate a new parametric average lucky look optical transfer function (OTF) model that could be used to aid in image restoration. Our OTF model blends the theoretical diffraction-limited OTF and the average turbulence short exposure OTF. Finally, we show simulated images for several anisoplanatic imaging scenarios that reveal the spatially varying nature of the RMS values impacting local image quality.

Field tests have been conducted of a broadband illuminator for active hyperspectral imaging (HSI) using a short-wave infrared supercontinuum laser (SWIR-SCL). We demonstrated irradiance comparable to the sun for two-way measurements at a 1.4 km distance between laser and target, and performed change detection and ranging. The experimental results suggest that the range resolution of our method is ∼1.5  cm even at the 1.4 km distance. Hence, we demonstrated the possibility to perform HSI with active broadband illumination using the SWIR-SCL. To our knowledge, this experiment is the first-ever to test two-way propagation of the active HSI illumination over a long distance. The 64 W SWIR-SCL provides near sunlight-equivalent illumination over multiple square meters, and the laser could enable HSI 24 h a day, even under a cloud cover, as well as enhanced capabilities such as change detection and ranging.