# Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

## Abstract

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

- Authors:

- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- Contributing Org.:
- DESI

- OSTI Identifier:
- 1409339

- Report Number(s):
- FERMILAB-PUB-17-508-AE-CD; arXiv:1711.03916

Journal ID: ISSN 0004-6280; 1637059

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Publications of the Astronomical Society of the Pacific

- Additional Journal Information:
- Journal Volume: 130; Journal Issue: 986; Journal ID: ISSN 0004-6280

- Publisher:
- Astronomical Society of the Pacific

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; methods analytical; telescopes

### Citation Formats

```
Kent, Stephen M. Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials. United States: N. p., 2018.
Web. doi:10.1088/1538-3873/aaa6b8.
```

```
Kent, Stephen M. Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials. United States. doi:10.1088/1538-3873/aaa6b8.
```

```
Kent, Stephen M. Thu .
"Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials". United States. doi:10.1088/1538-3873/aaa6b8. https://www.osti.gov/servlets/purl/1409339.
```

```
@article{osti_1409339,
```

title = {Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials},

author = {Kent, Stephen M.},

abstractNote = {If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.},

doi = {10.1088/1538-3873/aaa6b8},

journal = {Publications of the Astronomical Society of the Pacific},

number = 986,

volume = 130,

place = {United States},

year = {2018},

month = {2}

}

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Cited by: 1 work

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#### Figures / Tables:

Figure 1: (a) Schematic diagram showing the orientation and coordinate system definitions of the pupil plane ($ρ, ψ$) and focal plane ($r, \phi$). Each point in the focal plane (e.g., at radius vector $\bar{r}$) sees an image of the exit pupil. A global Cartesian ($x, y$) system is illustrated. (b)more »

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*