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 = nx − ny
• 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

400 800 1200 1600 2000 Wavelength (λ) [nm] 0.0 0.1 0.2 0.3 0.4 0.5 0.6

• Inv. condition number (κ−1)

GA design Patent 1/ √ 3

• 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. Drevillon1

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 nm2 to 430–2000 nm. (D) Paper published in Optics Express, a high-profile journal3.

• 2S. 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

• 3P. 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, 212×8 ≈ 1029 points in parameter space)

• Complex morphology of fitness function

θ 20 40 60 80 100 120 140 160 180 θ 20 40 60 80 100 120 140 160 180 log(f)

1.5 2.0 2.5 3.0 3.5 4.0 20 60 100 140 180 20 60 100 140 180 1.5 2.0 2.5 3.0 3.5 4.0

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.