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Lecture 9: Optimization and Correction (Optimization and Starting Point (3…
Lecture 9: Optimization and Correction
Nonlinear Optimization
Solution by linear algebra system matrix A
cases depending on the number of n/m
m=n: exact
m>n: underdetermined
parameters more than targets-->solution not unique
m<n:overdetermined parameters less than targets-->best approximation solution
Iterative numerical solution
strategy for optimization
direction of improvement step
size of improvement step
Steepest Descent Method
Constraints on Optimization
Boundary conditions and constraints
type of constraints
Numerical realizations
Lagrange multiplier
Penalty function:outside the permitted domain
Barrier function: inside the permitted domain
Regular variable, soft-constraint
Effect of constraints
possible not to obtain the optimizedest solution
Optimization and Starting Point
1.The initial starting point determines the final result
2.First Paraxial layout
3.Pre-calculation
0th properties of the system: focal length, magnification, pupil size and location, size/length of the system, image location
system structure (independent of lens bendings and 3rd order correction)
symmetry, field flattening correction, achromatism, apochromatism, distortion-correction, anastigmatism
Lens bending with 3rd order lens contributions
spherical aberration, coma, astigmatism
Optimization Merit Function
Performance criteria
Ray aberrations
Spot diameter
Wavefront description by Zernike coefficient, rms value
Strehl ratio,PSF
Contrast values for selected spatial frequencies
uniformity of illumination
Global optimization
Escape Function: Adding penalty function
Saddel Point Method
Adding a meniscus lens with thickness zero