Abstract
Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.
| Language | English |
|---|---|
| Title of host publication | Numerical Mathematics and Advanced Applications ENUMATH 2017 |
| Editors | Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop |
| Place of Publication | Cham |
| Publisher | Springer |
| Pages | 301-309 |
| Number of pages | 9 |
| ISBN (Electronic) | 978-3-319-96415-7 |
| ISBN (Print) | 978-3-319-96414-0 |
| DOIs | |
| State | Published - 1 Jan 2019 |
| Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Volume | 126 |
| ISSN (Print) | 1439-7358 |
Conference
| Conference | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 |
|---|---|
| Country | Norway |
| City | Voss |
| Period | 25/09/17 → 29/09/17 |
Fingerprint
Cite this
}
A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. / Yadav, N.K.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.
Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Cham : Springer, 2019. p. 301-309 (Lecture Notes in Computational Science and Engineering; Vol. 126).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
TY - GEN
T1 - A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design
AU - Yadav,N.K.
AU - ten Thije Boonkkamp,J.H.M.
AU - IJzerman,W.L.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.
AB - Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.
UR - http://www.scopus.com/inward/record.url?scp=85060038051&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-96415-7_26
DO - 10.1007/978-3-319-96415-7_26
M3 - Conference contribution
SN - 978-3-319-96414-0
T3 - Lecture Notes in Computational Science and Engineering
SP - 301
EP - 309
BT - Numerical Mathematics and Advanced Applications ENUMATH 2017
PB - Springer
CY - Cham
ER -