# Image Ellipticity from Atmospheric Aberrations

## Abstract

We investigate the ellipticity of the point-spread 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 ray-tracing 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 ray-tracing 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):
- UCRL-JRNL-228829

Journal ID: ISSN 0004-637X; ASJOAB; TRN: US200824%%56

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal, vol. 662, N/A, June 10, 2007, pp. 744-749; 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 point-spread 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 ray-tracing 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 ray-tracing 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. 744-749},

number = ,

volume = 662,

place = {United States},

year = {Tue Mar 06 00:00:00 EST 2007},

month = {Tue Mar 06 00:00:00 EST 2007}

}