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Related Experiment Video

Updated: Mar 28, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin

Z Zubac, J Fostier, D De Zutter

|December 25, 2015

Summary

This study introduces a parallelized Multilevel Fast Multipole Method (MLFMM) based Stochastic Galerkin Method (SGM) for uncertainty quantification (UQ) in large optical systems. The novel approach efficiently handles complex lens systems, significantly reducing simulation times.

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Last Updated: Mar 28, 2026

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Published on: August 12, 2013

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Area of Science:

Optical engineering
Computational physics
Uncertainty quantification

Background:

Manufacturing tolerances in optical devices cause geometrical variations, degrading performance.
Traditional Polynomial Chaos Expansion (PCE) methods are computationally intensive and memory-demanding for large systems.
Efficient uncertainty quantification (UQ) is crucial for reliable optical system design.

Purpose of the Study:

To present a novel, efficient, and parallelized method for UQ in large-scale optical systems.
To overcome the limitations of traditional PCE solvers in terms of computational time and memory usage.
To demonstrate the applicability and scalability of the proposed method on complex lens systems.

Main Methods:

Development and implementation of a parallelized Multilevel Fast Multipole Method (MLFMM) based Stochastic Galerkin Method (SGM).
Leveraging SGM as an intrusive PCE method for accurate uncertainty quantification.
Utilizing MLFMM, preconditioning, and parallel algorithms for high computational efficiency.

Main Results:

The proposed method successfully handles large optical structures with millions of unknowns in reasonable time (e.g., <1 hour for >10 million unknowns on 3 nodes).
Demonstrated high parallel scalability of the SGM-MLFMM approach.
Achieved a speed-up of over 12× compared to traditional collocation methods for a Cassegrain system.

Conclusions:

The parallelized SGM-MLFMM is a highly efficient and accurate technique for UQ in large optical systems.
This method significantly reduces simulation time, making UQ tractable for complex designs.
The approach offers a viable solution for improving the reliability and performance of manufactured optical devices.