Stellar scintillation technique for the measurement of tilt anisoplanatism

Winick, Kim A.; Marquis, D.

doi:10.1364/josaa.5.001929

Cited by 19 publications

(11 citation statements)

References 29 publications

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“…For a spherical wave characterized by the Kolmogorov power spectrum, an analytical expression for the Z-tilt correlation has been derived by Basu (now Bose-Pillai) et al, 16 following techniques outlined by Fried 20 and Winick. 21 The tilt correlation can be expressed as a weighted integral of C 2 n ðzÞ as follows:…”

Section: Anisoplanatic Tilt Statisticsmentioning

confidence: 99%

Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis

et al. 2017

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, "Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis," Opt. Eng. 56(7), 071502 (2017), doi: 10.1117/1.OE.56.7.071502. Abstract. We present a numerical wave propagation method for simulating imaging of an extended scene under anisoplanatic conditions. While isoplanatic simulation is relatively common, few tools are specifically designed for simulating the imaging of extended scenes under anisoplanatic conditions. We provide a complete description of the proposed simulation tool, including the wave propagation method used. Our approach computes an array of point spread functions (PSFs) for a two-dimensional grid on the object plane. The PSFs are then used in a spatially varying weighted sum operation, with an ideal image, to produce a simulated image with realistic optical turbulence degradation. The degradation includes spatially varying warping and blurring. To produce the PSF array, we generate a series of extended phase screens. Simulated point sources are numerically propagated from an array of positions on the object plane, through the phase screens, and ultimately to the focal plane of the simulated camera. Note that the optical path for each PSF will be different, and thus, pass through a different portion of the extended phase screens. These different paths give rise to a spatially varying PSF to produce anisoplanatic effects. We use a method for defining the individual phase screen statistics that we have not seen used in previous anisoplanatic simulations. We also present a validation analysis. In particular, we compare simulated outputs with the theoretical anisoplanatic tilt correlation and a derived differential tilt variance statistic. This is in addition to comparing the long-and short-exposure PSFs and isoplanatic angle. We believe this analysis represents the most thorough validation of an anisoplanatic simulation to date. The current work is also unique that we simulate and validate both constant and varying C 2 n ðzÞ profiles. Furthermore, we simulate sequences with both temporally independent and temporally correlated turbulence effects. Temporal correlation is introduced by generating even larger extended phase screens and translating this block of screens in front of the propagation area. Our validation analysis shows an excellent match between the simulation statistics and the theoretical predictions. Thus, we think this tool can be used effectively to study optical anisoplanatic turbulence and to aid in the development of image restoration methods. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Section: Anisoplanatic Tilt Statisticsmentioning

confidence: 99%

Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis

et al. 2017

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“…The integrations over r and r 0 can be done using techniques outlined by Fried 15 and Winick and Marquis. 16 Applying those techniques, Eq. 7reduces to E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 3 2 6 ; 5 0 4…”

Section: Path Weighting Functions For Differential Patch-averaged Tilmentioning

confidence: 99%

Estimation of atmospheric turbulence using differential motion of extended features in time-lapse imagery

Bose‐Pillai¹,

McCrae²,

Rice³

et al. 2018

Opt. Eng.

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Accurate characterization of atmospheric turbulence is useful for performance assessment of optical systems operating in real environments and for designing systems to mitigate turbulence effects. Irradiancebased techniques such as scintillometry, suffer from saturation, and hence commercial scintillometers have limited operational ranges. A method to estimate turbulence parameters, such as path weighted C 2 n and Fried's coherence diameter r 0 from turbulence-induced random, differential motion of extended features in the timelapse imagery of a distant target is presented. Since the method is phase-based, it can be applied to longer paths. It has an added advantage of remotely sensing turbulence without the need for deployment of sensors at the target location. The approach uses a derived set of path weighting functions that drop to zero at both ends of the imaging path, the peak location depending on the size of the imaging aperture, and the relative sizes and separations of the features whose motions are being tracked. Using different sized features separated by different amounts, a rich set of weighting functions can be obtained. These weighting functions can be linearly combined to approximate a desired weighting function such as that of a scintillometer or that of r 0 in inhomogeneous turbulence. The time-lapse measurements can thus mimic the measurements of a scintillometer or any other instrument. The method is applied to images captured along two different paths, and the estimates are compared to co-located scintillometer measurements. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…The image is about 60 meters on a side at the hospital, and the pixels are about 0.24 meters across. The expected variance of the wavefront tilt was evaluated using an approach outlined by Fried [9] and Winick and Marquis [10]. More precisely, the referenced technique to evaluate the expected tilt-difference variance between two sources averaged across a receiver aperture was modified for spherical rather than plane waves, then turned around and applied at the source plane too to generate the expected tilt variance as averaged over both the aperture and a Gaussian source patch.…”

Section: Time Lapse Imaging Experiments and Path Weighting Functionsmentioning

confidence: 99%

Estimation of atmospheric parameters from time-lapse imagery

McCrae¹,

Basu²,

Fiorino³

2016

SPIE Proceedings

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A time-lapse imaging experiment was conducted to estimate various atmospheric parameters for the imaging path. Atmospheric turbulence caused frame-to-frame shifts of the entire image as well as parts of the image. The statistics of these shifts encode information about the turbulence strength (as characterized by C n 2 , the refractive index structure function constant) along the optical path. The shift variance observed is simply proportional to the variance of the tilt of the optical field averaged over the area being tracked. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions can be derived which relate the turbulence strength along the path to the shifts measured. These weighting functions peak at the camera and fall to zero at the object. The larger the area observed, the more quickly the weighting function decays. One parameter we would like to estimate is r 0 (the Fried parameter, or atmospheric coherence diameter.) The weighting functions derived for pixel sized or larger parts of the image all fall faster than the weighting function appropriate for estimating the spherical wave r 0 . If we presume C n 2 is constant along the path, then an estimate for r 0 can be obtained for each area tracked, but since the weighting function for r 0 differs substantially from that for every realizable tracked area, it can be expected this approach would yield a poor estimator. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore-Penrose pseudo-inverse to create a new weighting function which yields the least-squares optimal linear combination of measurements for estimation of r 0 . This approach is carried out, and it is observed that this approach is somewhat noisy because the pseudo-inverse assigns weights much greater than one to many of the observations.

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Stellar scintillation technique for the measurement of tilt anisoplanatism

Cited by 19 publications

References 29 publications

Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis

Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis

Estimation of atmospheric turbulence using differential motion of extended features in time-lapse imagery

Estimation of atmospheric parameters from time-lapse imagery

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