### Abstract

Although scattering from spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygen's principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mie's solution of plane wave scattering was recovered. Potential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Köhler illumination show agreement with numerical tests.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | C.J. Cogswell, J.A. Conchello, J.M. Lerner, T. Lu, T. Wilson |

Pages | 7-16 |

Number of pages | 10 |

Volume | 3261 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | Proceedings of Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V - San Jose, CA, United States Duration: Jan 27 1998 → Jan 29 1998 |

### Other

Other | Proceedings of Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V |
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Country | United States |

City | San Jose, CA |

Period | 1/27/98 → 1/29/98 |

### Fingerprint

### Keywords

- Generalized Mie theory
- Scattering
- Spherical wave functions

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 3261, pp. 7-16) https://doi.org/10.1117/12.310545

**Imaging spheres with general incident wavefronts using a dipole decomposition.** / Izen, S. H.; Ovryn, B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 3261, pp. 7-16, Proceedings of Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, San Jose, CA, United States, 1/27/98. https://doi.org/10.1117/12.310545

}

TY - GEN

T1 - Imaging spheres with general incident wavefronts using a dipole decomposition

AU - Izen, S. H.

AU - Ovryn, B.

PY - 1998

Y1 - 1998

N2 - Although scattering from spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygen's principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mie's solution of plane wave scattering was recovered. Potential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Köhler illumination show agreement with numerical tests.

AB - Although scattering from spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygen's principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mie's solution of plane wave scattering was recovered. Potential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Köhler illumination show agreement with numerical tests.

KW - Generalized Mie theory

KW - Scattering

KW - Spherical wave functions

UR - http://www.scopus.com/inward/record.url?scp=0032224293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032224293&partnerID=8YFLogxK

U2 - 10.1117/12.310545

DO - 10.1117/12.310545

M3 - Conference contribution

AN - SCOPUS:0032224293

VL - 3261

SP - 7

EP - 16

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Cogswell, C.J.

A2 - Conchello, J.A.

A2 - Lerner, J.M.

A2 - Lu, T.

A2 - Wilson, T.

ER -