### Abstract

Biaxial ellipsometry is a technique that measures the dielectric tensor and thickness of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (n_{x}+ ik_{x}, n_{y}+ iky and n_{z} + ik_{z}) and three Euler angles (⊖, Φ Δ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging Polarimeter equipped with a pair of microscope objectives with low polarization aberrations. The dielectric tensors for multilayer samples are determined from multi-spectral angle-of-incidence Mueller matrix images in either a transmission or reflection mode using an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones matrix image is first calculated by solving Maxwell's equations at each surface which is then transformed into a Mueller matrix image. An optimization algorithm then finds the best fit dielectric tensor based on matching the measured and calculated angle-of-incidence Mueller matrix images. One use for this application is to more accurately determine the dielectric tensors of biaxial films used in liquid crystal displays.

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

Volume | 6682 |

DOIs | |

State | Published - 2007 |

Event | Polarization Science and Remote Sensing III - San Diego, CA, United States Duration: Aug 29 2007 → Aug 30 2007 |

### Other

Other | Polarization Science and Remote Sensing III |
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Country | United States |

City | San Diego, CA |

Period | 8/29/07 → 8/30/07 |

### Fingerprint

### Keywords

- Biaxial
- Birefringent
- Dielectric tensor
- Ellipsometry
- Polarimetry

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 6682). [66820N] https://doi.org/10.1117/12.735335

**Characterizing dielectric tensors from angle-of-incidence mueller matrix images.** / Smith, Paula K.; Chipman, Russell A.

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

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 6682, 66820N, Polarization Science and Remote Sensing III, San Diego, CA, United States, 8/29/07. https://doi.org/10.1117/12.735335

}

TY - GEN

T1 - Characterizing dielectric tensors from angle-of-incidence mueller matrix images

AU - Smith, Paula K.

AU - Chipman, Russell A

PY - 2007

Y1 - 2007

N2 - Biaxial ellipsometry is a technique that measures the dielectric tensor and thickness of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (nx+ ikx, ny+ iky and nz + ikz) and three Euler angles (⊖, Φ Δ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging Polarimeter equipped with a pair of microscope objectives with low polarization aberrations. The dielectric tensors for multilayer samples are determined from multi-spectral angle-of-incidence Mueller matrix images in either a transmission or reflection mode using an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones matrix image is first calculated by solving Maxwell's equations at each surface which is then transformed into a Mueller matrix image. An optimization algorithm then finds the best fit dielectric tensor based on matching the measured and calculated angle-of-incidence Mueller matrix images. One use for this application is to more accurately determine the dielectric tensors of biaxial films used in liquid crystal displays.

AB - Biaxial ellipsometry is a technique that measures the dielectric tensor and thickness of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (nx+ ikx, ny+ iky and nz + ikz) and three Euler angles (⊖, Φ Δ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging Polarimeter equipped with a pair of microscope objectives with low polarization aberrations. The dielectric tensors for multilayer samples are determined from multi-spectral angle-of-incidence Mueller matrix images in either a transmission or reflection mode using an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones matrix image is first calculated by solving Maxwell's equations at each surface which is then transformed into a Mueller matrix image. An optimization algorithm then finds the best fit dielectric tensor based on matching the measured and calculated angle-of-incidence Mueller matrix images. One use for this application is to more accurately determine the dielectric tensors of biaxial films used in liquid crystal displays.

KW - Biaxial

KW - Birefringent

KW - Dielectric tensor

KW - Ellipsometry

KW - Polarimetry

UR - http://www.scopus.com/inward/record.url?scp=42149096698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149096698&partnerID=8YFLogxK

U2 - 10.1117/12.735335

DO - 10.1117/12.735335

M3 - Conference contribution

AN - SCOPUS:42149096698

SN - 9780819468307

VL - 6682

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

ER -