he standard method for modeling the atmospheric short-exposure modulation transfer function (MTF) is due to Fried. This method involves evaluating the impact of amplitude and phase modulations of the propagating wavefront after the removal of the mean wavefront tilt. This tilt is determined by a least-squares analysis. We retain a term involving the correlation between tilt-corrected phase and computed tilt vector that was formerly assumed to be zero. Inclusion of this term yields a new turbulence-strength-dependent effect that degrades performance at high integrated turbulence levels and also predicts super-resolution effects at lower integrated turbulence levels. An analytical approximation is derived from this analysis that describes the new MTF model as a function of three dimensionless parameters related to the angular frequency, system aperture diameter, and integrated turbulence strength.

/pdf/errata-reanalysis-of-turbulence-effects-on-short-exposure-20wgdm38fw.pdf

Errata: Reanalysis of turbulence effects on short-exposure passive imaging

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. This work explores the mean square error (MSE) performance of a multiframe blind deconvolution (MFBD) technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate, and severe turbulence conditions. Each set consisted of 1000 simulated turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. A Gaussian noise model-based MFBD algorithm reconstructs objects that showed as much as 40% improvement in MSE with as few as 14 frames and 30 Zernike coefficients used in the reconstruction, despite the presence of anisoplanatism in the data. An MFBD algorithm based on the Poisson noise model required a minimum of 50 frames to achieve significant improvement over the average MSE for the data set. Reconstructed objects show as much as 38% improvement in MSE using 175 frames and 30 Zernike coefficients in the reconstruction.

https://www.spiedigitallibrary.org/journals/Optical-Engineering/volume-52/issue-8/083108/Reconstruction-of-long-horizontal-path-images-under-anisoplanatic-conditions-using/10.1117/1.OE.52.8.083108.pdf

Reconstruction of long horizontal-path images under anisoplanatic conditions using multiframe blind deconvolution

We explore the feasibility of post-detection restoration when imaging through deep turbulence characterized by extreme anisoplanatism. A wave-optics code was used to simulate relevant short-exposure point spread functions (PSFs) and their decorrelation as a function of point-source separation was computed. In addition, short-exposure images of minimally extended objects were simulated and shown to retain a central lobe that is clearly narrower than the long-exposure counterpart. This suggests that short-exposure image data are more informative than long-exposure data, even in the presence of extreme anisoplanatism. The implications of these findings for image restoration from a sequence of short-exposure images are discussed.

Spatial stabilization of deep-turbulence-induced anisoplanatic blur.

We propose the use of an aperture diverse imaging system for high-resolution imaging through strong atmospheric
turbulence The system has two channels One channel partitions the aperture into a set of annular apertures that provide
a set of images of the target at different spatial resolutions The other channel feeds an imaging Shack-Hartmann wavefront
sensor with a small number of sub-apertures The combined imagery from this setup is processed using a blind
restoration algorithm that captures the inherent temporal correlations in the observed atmospheric wave fronts This
approach shows significant promise for providing high-fidelity imagery for observations acquired through strong
atmospheric turbulence The approach also allows for the separation of the phase perturbations from different layers of
the atmosphere This characteristic offers potential for the accurate restoration of images with fields of view substantially
larger than the isoplanatic angle

High-resolution imaging through strong atmospheric turbulence

Systems and methods which combine standard image reconstruction and beam-control techniques with tomographic estimation of three-dimensional atmospheric turbulence to enable high-quality anisoplanatic imaging of distant objects at long range through the atmosphere over an extended field-of-view using a large aperture. More specifically, the systems and methods combine the concepts of atmospheric tomography, forward-model image reconstruction and tip, tilt, beam-walk, and focus control techniques to produce image reconstructions of high quality for large objects that move rapidly as viewed by large apertures in weak or strong extended atmospheric turbulence. The systems and methods use wavefront sensors and diversity concepts for modelling the atmospheric turbulences and to deconvolut the recorded images. Dievverity is introduced by in/out of focus images and translation of a lenslet array (22) of the wavefront sensor (24).

Lenslet, beamwalk and tilt diversity for anisoplanatic imaging by large-aperture telescopes

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view Space-variant effects are particularly severe in horizontal-path imaging, slant-path (air-to-ground or ground-to-air) geometries, and ground-based imaging of low-elevation satellites or astronomical objects In these geometries, the isoplanatic angle can be comparable to or even smaller than the diffraction-limited resolution angle We report on a postdetection correction method that seeks to correct for the effects of space-variant aberrations, with the goal of reconstructing near-diffraction-limited imagery Our approach has been to generalize the method of phase-diverse speckle (PDS) by using a physically motivated distributed-phase-screen model Simulation results are presented that demonstrate the reconstruction of near-diffraction-limited imagery under both matched and mismatched model assumptions In addition, we present evidence that PDS could be used as a beaconless wavefront sensor in a multiconjugate adaptive optics system when imaging extended scenes

Overcoming turbulence-induced space-variant blur by using phase-diverse speckle

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view, and it is particularly severe in horizontal-path imaging and slant-path (air- to-ground or ground-to-air) geometries. We report on pre and post-detection correction methods based on the method of Phase-Diverse-Speckle (PDS), and demonstrate its potential for dramatic improvement via simulation results.

Imaging through volume turbulence by using phase-diverse speckle

Nearly all imaging systems exhibit aberrations with some degree of field dependence. We examine sensing and managing space-variant wavefront error when imaging (1) with multiple-telescope arrays, (2) through extended-path turbulence, and (3) through turbid media.

Sensing and Managing Field-Dependent Wavefront Error

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Overcoming turbulence-induced space-variant blur by using phase-diverse speckle

Imaging through volume turbulence by using phase-diverse speckle

Sensing and Managing Field-Dependent Wavefront Error