Image Ellipticity from Atmospheric Aberrations
Abstract
We investigate the ellipticity of the pointspread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a raytracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1/{radical}N). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the raytracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not anmore »
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 940493
 Report Number(s):
 UCRLJRNL228829
Journal ID: ISSN 0004637X; ASJOAB; TRN: US200824%%56
 DOE Contract Number:
 W7405ENG48
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal, vol. 662, N/A, June 10, 2007, pp. 744749; Journal Volume: 662
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 GENERAL AND MISCELLANEOUS; APPROXIMATIONS; BREAKDOWN; GALAXIES; SAMPLING; SHAPE; SIMULATION; STATISTICS; TURBULENCE
Citation Formats
de Vries, W H, Olivier, S S, Asztalos, S J, Rosenberg, L J, and Baker, K L. Image Ellipticity from Atmospheric Aberrations. United States: N. p., 2007.
Web. doi:10.1086/517873.
de Vries, W H, Olivier, S S, Asztalos, S J, Rosenberg, L J, & Baker, K L. Image Ellipticity from Atmospheric Aberrations. United States. doi:10.1086/517873.
de Vries, W H, Olivier, S S, Asztalos, S J, Rosenberg, L J, and Baker, K L. Tue .
"Image Ellipticity from Atmospheric Aberrations". United States.
doi:10.1086/517873. https://www.osti.gov/servlets/purl/940493.
@article{osti_940493,
title = {Image Ellipticity from Atmospheric Aberrations},
author = {de Vries, W H and Olivier, S S and Asztalos, S J and Rosenberg, L J and Baker, K L},
abstractNote = {We investigate the ellipticity of the pointspread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a raytracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1/{radical}N). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the raytracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.},
doi = {10.1086/517873},
journal = {Astrophysical Journal, vol. 662, N/A, June 10, 2007, pp. 744749},
number = ,
volume = 662,
place = {United States},
year = {Tue Mar 06 00:00:00 EST 2007},
month = {Tue Mar 06 00:00:00 EST 2007}
}

Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition andmore »

Properties of Ellipticity Correlation with Atmospheric Structure from Gemini South
Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition andmore » 
Origin and implication of ellipticity in highorder harmonic generation from aligned molecules
We address theoretically and numerically the possibility of observing ellipticity in highorder harmonic generation (HHG) from aligned molecules driven by linearly polarized fieldsa subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from aligned molecules. Our numerical results are in good agreement with recent experimental data. The theory explains analytically several observations of polarization experiments. We note the conditions under which ellipticity can be observed and the information content of elliptically polarized harmonics regarding the molecular system. 
Polarization and ellipticity of highorder harmonics from aligned molecules generated by linearly polarized intense laser pulses
We present theoretical calculations for polarization and ellipticity of highorder harmonics from aligned N{sub 2}, CO{sub 2}, and O{sub 2} molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photorecombination amplitudes for photons emitted with polarization parallel or perpendicular to the direction of the same returning electron wave packet. Our results show clear speciesdependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a 'complete' experiment in molecules. 
Twocenter interference and ellipticity in highorder harmonic generation from H{sub 2}{sup +}
We present a theoretical investigation into the twocenter interference in aligned H{sub 2}{sup +}. The influence of the laser field on the recombination step is investigated by comparing laserinduced harmonic generation with harmonic generation from fieldfree collisions of Gaussian wave packets with the core. We find that for different Gaussian wave packets colliding with the molecule, the interference minimum occurs at the same alignment angle. The same result is obtained for the laserinduced spectrum when only a single electronic trajectory per harmonic contributes. When multiple electronic trajectories contribute, we find an effect on the minimum position because the interference betweenmore »