Genetic Invention of Fast and Optimal Broad-band Stokes/Mueller - PowerPoint PPT Presentation

Genetic Invention of Fast and Optimal Broad-band Stokes/Mueller Polarimeter Designs Paul Anton Letnes Ingar Stian Nerbø Lars Martin Sandvik Aas Pål Gunnar Ellingsen Morten Kildemo 14.07.2011

Polarization • Polarization: additional information cf. intensity • Applications: semiconductor industry, astronomy, remote sensing, medicine, and others Photos taken with a linear polarizer.

Polarimeter • Instrument measuring polarization state • Use birefringent materials: ∆ n = n x − n y • Wavelength dependent: ∆ n ( λ ) • Some can be ‘switched’ electronically, e.g. LCD • Problem: design broad-band, low noise polarimeter

Classic design approach • Component parameters chosen from human experience • Component ordering chosen from human experience • Orientation “seeded” by humans, gradient based optimization to improve • Optimization only of orientation angles • Narrower bandwidth is easier

Genetic Algorithm approach • Orientation chosen by GA • Component parameters chosen by GA • Component ordering chosen by GA • Results: • Less noise • Larger bandwidth covered • Custom designs are easily generated

Our result compared to the criteria Fulfills 6 out of 8 ‘arms length’ criteria: (A) Patentable invention: yes! (B) Improvement on published result: yes! (C) Database of results: not relevant (D) Publishable in its own right: yes! (E) Improvement on human-created solution: computer aided design, yes (F) Better than an achievement in its field: arguably yes (G) Solves problem of difficulty: yes! (H) Wins competition with humans: not relevant

(A) Patentable invention 0 . 6 Inv . condition number ( κ − 1 ) 0 . 5 0 . 4 0 . 3 0 . 2 GA design Patent 0 . 1 √ 1 / 3 0 . 0 400 800 1200 1600 2000 Wavelength ( λ ) [nm] • We have filed a patent application for our design • Our solution outperforms the design by D. Cattelan, E. Garcia-Caurel, A. De Martino, and B. Drevillon 1 1 “Device and method for taking spectroscopic polarimetric measurements in the visible and near-infrared ranges”. Patent application 2937732, France.

(B) and (D): scientifically publishable result (B) Our results outperforms published results, by expanding the spectral range from 430–1200 nm 2 to 430–2000 nm. (D) Paper published in Optics Express, a high-profile journal 3 . 2 S. Tomczyk, R. Casini, A. G. de Wijn, and P. G. Nelson. Wavelength-diverse polarization modulators for Stokes polarimetry. Applied Optics , 49(18):3580–3586, 2010. http://dx.doi.org/10.1364/AO.49.003580 3 P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo. Optics Express , 18(22):23095-23103, 2010. http://dx.doi.org/10.1364/OE.18.023095

(G) Problem of difficulty • Complex relationship between optical parameters and polarimeter performance • Combinatorics problem: many-dimensional optimization space (12 dimensions, 2 12 × 8 ≈ 10 29 points in parameter space) • Complex morphology of fitness function 4 . 0 4 . 0 3.5 3 . 5 3 . 0 3 . 0 log( f ) 2 . 5 2 . 5 2 . 0 2 . 0 1 . 5 1 . 5 180 180 180 180 160 160 140 140 140 140 120 120 100 100 100 100 θ θ 80 80 60 60 60 60 40 40 20 20 20 20

Human competitiveness Our results outperform human designs: • Less noise • Larger bandwidth • Design time down to one night (humans use weeks)! • Exploring specialized designs is fast and easy

Summary • A patent application has been submitted for our result • The result is published in a scientific journal • The GA approach makes other design methods obsolete • Our result fulfills 6 of the 8 ‘human competitive’ criteria

Acknowledgments We acknowledge professor Keith Downing at the Department of Computer and Information Science at NTNU for helpful discussions.