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Method for Optimizing As-Built Optical Designs

Current commercial lens design software does not have a method for practically implementing tolerances and compensators into the optimization process. Some codes can use sensitivity calculations to reduce the sensitivity of user-specified tolerances, but these do not consider the action of compensators, and do not provide a direct, quantitative link to performance. Other codes can theoretically include tolerancing and compensators, but this is computationally impractical because the algorithm is highly-nested with computationally-intensive ray-tracing in the innermost nested loop. Some authors have tried simultaneous optimization of an ensemble of misaligned systems but it requires many (10s-1000s) misaligned systems in the ensemble and also includes heavy ray-tracing in the innermost nested loop, and so is inefficient. Other authors have generated several candidates from a global optimization search and then selected the candidate that performs best when toleranced; this approach does not find solutions with lesser nominal performance, but which outperform others when toleranced. Finally, some authors have generated long vectors of Zernike coefficients at many field points to characterize misaligned systems and then used singular value decomposition (SVD) to find appropriate corrections. This approach, however, is slow and does not use the insight available through nodal aberration theory, which describes the behavior of perturbed optical systems. What users have wanted is an approach that accurately predicts the behavior of toleranced/compensated systems, without adding significant computational load.
Patent Abstract: 
The LLNL method for optimizing as built optical designs uses insights from perturbed optical system theory and reformulates perturbation of optical performance in terms of double Zernikes, which can be calculated analytically rather than by tracing thousands of rays. A new theory of compensation is enabled by the use of double Zernikes which allows the performance degradation of a perturbed and compensated optical system to be calculated with a matrix multiplication using paraxial quantities rather than by iteration involving tracing large sets of rays.
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