Using spherical harmonics to describe large-angle freeform lenses

Caleb Gannon, Rongguang Liang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We propose the use of spherical harmonics for large-angle freeform lenses as a dramatic improvement over polynomials set on the disk and plane, such as Zernike and X -Y polynomials. This new representation enables fitting of surfaces designed in spherical coordinates, such as freeform illumination lenses that would be impossible to describe with respect to a plane. The proposed representation is validated through an extremely compact, high-performance design.

Original languageEnglish (US)
Pages (from-to)8143-8147
Number of pages5
JournalApplied Optics
Volume57
Issue number28
DOIs
StatePublished - Oct 1 2018

Fingerprint

spherical harmonics
Lenses
polynomials
lenses
Polynomials
spherical coordinates
Lighting
illumination

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Electrical and Electronic Engineering

Cite this

Using spherical harmonics to describe large-angle freeform lenses. / Gannon, Caleb; Liang, Rongguang.

In: Applied Optics, Vol. 57, No. 28, 01.10.2018, p. 8143-8147.

Research output: Contribution to journalArticle

@article{14f748490d954704bfe2034b32f078cb,
title = "Using spherical harmonics to describe large-angle freeform lenses",
abstract = "We propose the use of spherical harmonics for large-angle freeform lenses as a dramatic improvement over polynomials set on the disk and plane, such as Zernike and X -Y polynomials. This new representation enables fitting of surfaces designed in spherical coordinates, such as freeform illumination lenses that would be impossible to describe with respect to a plane. The proposed representation is validated through an extremely compact, high-performance design.",
author = "Caleb Gannon and Rongguang Liang",
year = "2018",
month = "10",
day = "1",
doi = "10.1364/AO.57.008143",
language = "English (US)",
volume = "57",
pages = "8143--8147",
journal = "Applied Optics",
issn = "1559-128X",
publisher = "The Optical Society",
number = "28",

}

TY - JOUR

T1 - Using spherical harmonics to describe large-angle freeform lenses

AU - Gannon, Caleb

AU - Liang, Rongguang

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We propose the use of spherical harmonics for large-angle freeform lenses as a dramatic improvement over polynomials set on the disk and plane, such as Zernike and X -Y polynomials. This new representation enables fitting of surfaces designed in spherical coordinates, such as freeform illumination lenses that would be impossible to describe with respect to a plane. The proposed representation is validated through an extremely compact, high-performance design.

AB - We propose the use of spherical harmonics for large-angle freeform lenses as a dramatic improvement over polynomials set on the disk and plane, such as Zernike and X -Y polynomials. This new representation enables fitting of surfaces designed in spherical coordinates, such as freeform illumination lenses that would be impossible to describe with respect to a plane. The proposed representation is validated through an extremely compact, high-performance design.

UR - http://www.scopus.com/inward/record.url?scp=85054193381&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054193381&partnerID=8YFLogxK

U2 - 10.1364/AO.57.008143

DO - 10.1364/AO.57.008143

M3 - Article

C2 - 30461762

AN - SCOPUS:85054193381

VL - 57

SP - 8143

EP - 8147

JO - Applied Optics

JF - Applied Optics

SN - 1559-128X

IS - 28

ER -