MID-SPATIAL FREQUENCY CHARACTERIZATION AND SPECIFICATION FOR FREEFORM SURFACES USING ZERNIKE POLYNOMIALS

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Hosseinimakarem, Z. (2017). MID-SPATIAL FREQUENCY CHARACTERIZATION AND SPECIFICATION FOR FREEFORM SURFACES USING ZERNIKE POLYNOMIALS. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

Mid-spatial frequency on freeform optical elements induces small-angle scatter and affects the optical performance. Fabrication techniques involved in making freeform surfaces leave tooling marks on the surface due to the sub-aperture nature of the fabrication process. In recent years, there has been a growing need for specification and characterization of the mid-spatial frequencies for freeform surfaces. There is a range of methods to consider for representing the mid-spatial frequency content: the power spectral density (PSD), the structure function (SF), and a polynomial basis representation such as Zernike and Forbes polynomials. Using research discussed here and published discussions from the literature, we compare a Zernike representation to a PSD representation, and structure-function representation in terms of ability to connect to optical performance, ability to connect to the fabrication process, and other practical considerations. Our focus is on investigating a Zernike polynomial representation for quantifying the mid-spatial frequency content in the height maps. We will illustrate how this polynomial representation captures certain characteristics of the mid-spatial frequency texture. A filtering aspect of these polynomials is also explored and optical performance is predicted based on very large orders of Zernike polynomials.

Details
Author

Hosseinimakarem, Zahra

Title

MID-SPATIAL FREQUENCY CHARACTERIZATION AND SPECIFICATION FOR FREEFORM SURFACES USING ZERNIKE POLYNOMIALS

Physical Description

1 online resource (175 pages) : PDF

Date

2017

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

Mid-spatial frequency on freeform optical elements induces small-angle scatter and affects the optical performance. Fabrication techniques involved in making freeform surfaces leave tooling marks on the surface due to the sub-aperture nature of the fabrication process. In recent years, there has been a growing need for specification and characterization of the mid-spatial frequencies for freeform surfaces. There is a range of methods to consider for representing the mid-spatial frequency content: the power spectral density (PSD), the structure function (SF), and a polynomial basis representation such as Zernike and Forbes polynomials. Using research discussed here and published discussions from the literature, we compare a Zernike representation to a PSD representation, and structure-function representation in terms of ability to connect to optical performance, ability to connect to the fabrication process, and other practical considerations. Our focus is on investigating a Zernike polynomial representation for quantifying the mid-spatial frequency content in the height maps. We will illustrate how this polynomial representation captures certain characteristics of the mid-spatial frequency texture. A filtering aspect of these polynomials is also explored and optical performance is predicted based on very large orders of Zernike polynomials.

Genre

doctoral dissertations

Subjects--Topics

Optics
Engineering

Degree

Ph.D.

Keywords

Freeform Optics
Mid Spatial Frequency
Optical Metrology
Optical Performance
Surface Characterization
Zernike Polynomials

Subject Area

Optical Science & Engineering

Advisor(s)

Davies, Angela

Committee Members

Evans, Christopher
Suleski, Thomas
Gbur, Gregory

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2017.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Hosseinimakarem_uncc_0694D_11313

Permalink

http://hdl.handle.net/20.500.13093/etd:1431