### Abstract

An important problem in optics involves the computation of the field amplitude in the Fresnel region of a circular lens. When the observation point lines in the image plane, it is well known that the field can be written in closed form in terms of Bessel functions, i.e. the Airy pattern. In this paper, it is shown that away from the image plane the field can be expressed in terms of incomplete Weber integrals. This closed-form representation is much more accurate than the commonly used technique involving fast Fourier transforms (FFTs). This is demonstrated by comparing the closed-form results with those produced by an FFT. The closed-form solution is used to study the resolution of two point sources under the assumption that the observation plane is misaligned from the image plane.

Original language | English (US) |
---|---|

Pages (from-to) | 49-65 |

Number of pages | 17 |

Journal | Journal of Modern Optics |

Volume | 43 |

Issue number | 1 |

State | Published - Jan 1996 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Modern Optics*,

*43*(1), 49-65.

**A new technique for computing the field amplitude in the Fresnel region of a lens.** / Evans, Glen; Dvorak, Steven L.

Research output: Contribution to journal › Article

*Journal of Modern Optics*, vol. 43, no. 1, pp. 49-65.

}

TY - JOUR

T1 - A new technique for computing the field amplitude in the Fresnel region of a lens

AU - Evans, Glen

AU - Dvorak, Steven L

PY - 1996/1

Y1 - 1996/1

N2 - An important problem in optics involves the computation of the field amplitude in the Fresnel region of a circular lens. When the observation point lines in the image plane, it is well known that the field can be written in closed form in terms of Bessel functions, i.e. the Airy pattern. In this paper, it is shown that away from the image plane the field can be expressed in terms of incomplete Weber integrals. This closed-form representation is much more accurate than the commonly used technique involving fast Fourier transforms (FFTs). This is demonstrated by comparing the closed-form results with those produced by an FFT. The closed-form solution is used to study the resolution of two point sources under the assumption that the observation plane is misaligned from the image plane.

AB - An important problem in optics involves the computation of the field amplitude in the Fresnel region of a circular lens. When the observation point lines in the image plane, it is well known that the field can be written in closed form in terms of Bessel functions, i.e. the Airy pattern. In this paper, it is shown that away from the image plane the field can be expressed in terms of incomplete Weber integrals. This closed-form representation is much more accurate than the commonly used technique involving fast Fourier transforms (FFTs). This is demonstrated by comparing the closed-form results with those produced by an FFT. The closed-form solution is used to study the resolution of two point sources under the assumption that the observation plane is misaligned from the image plane.

UR - http://www.scopus.com/inward/record.url?scp=5244326712&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5244326712&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:5244326712

VL - 43

SP - 49

EP - 65

JO - Journal of Modern Optics

JF - Journal of Modern Optics

SN - 0950-0340

IS - 1

ER -