1/30 Challenge the future Auto-alignment of the SPARC mirror W.S. Krul

2/30 Challenge the future Movie

3/30 Challenge the future Presentation goal To inform you about: The problem Development of a solution using modeling and experiments Conclusions & recommendations ProblemModelingValidationAlignmentConclusions

4/30 Challenge the future Introduction SPARC: Angle-resolved measurements Spectrometry Manual alignment: Experienced operator Takes up to 1 hour ProblemModelingValidationAlignmentConclusions

5/30 Challenge the future Off-axis parabolic mirror (OAP) ProblemModelingValidationAlignmentConclusions

6/30 Challenge the future Degrees of Freedom (DoFs) ProblemModelingValidationAlignmentConclusions

7/30 Challenge the future Alignment requirements ProblemModelingValidationAlignmentConclusions

8/30 Challenge the future Problem formulation Develop auto-alignment solution Using first principles modeling In 3 DoFs Meeting alignment requirements ProblemModelingValidationAlignmentConclusions

9/30 Challenge the future Alignment concept Advantages: Current manual alignment setup No extra hardware needed Low cost Disadvantages: Unknown whether concept can differentiate between DoFs ProblemModelingValidationAlignmentConclusions

10/30 Challenge the future Modeling To relate the images to the misalignments, a model is needed 2 modeling approaches: Build backward model Find an image metric that is maximized when the system is aligned Forward image model Misalignment Image ProblemModelingValidationAlignmentConclusions

11/30 Challenge the future Modeling assumptions Geometric optics Point source as excitation point Misalignments modeled as source location Perfect lens & perfectly shaped mirror Only x,y,z, misalignments ProblemModelingValidationAlignmentConclusions

12/30 Challenge the future Model basics 2D-3D 2D analogy: Calculate “amount of angle” Apply radiant intensity 3D: Analytical approach Backward ray model ProblemModelingValidationAlignmentConclusions

13/30 Challenge the future Forward ray model (2D) ProblemModelingValidationAlignmentConclusions

14/30 Challenge the future Inversion: 1-1 mapping Inverting the ray model ProblemModelingValidationAlignmentConclusions

15/30 Challenge the future 3D model 3D: Forward ray model (closed-form) Backward ray model (numerical) Forward image model To guarantee functionality: Source near focal point Imaged plane near focal plane Numerical inversion possible (fitting techniques) ProblemModelingValidationAlignmentConclusions

16/30 Challenge the future Model validation For validation 2 conditions must be met: 1.Experimental conditions should match model parameters and assumptions 2.The model must capture all important physical processes 2 steps: Quantitative validation with model Qualitative validation with experiments ProblemModelingValidationAlignmentConclusions

17/30 Challenge the future Model-model validation Misaligned case Max error: MAE: 0,1518 1,658 x Max error: MAE: 0,0371 1,435 x ProblemModelingValidationAlignmentConclusions

18/30 Challenge the future Experimental validation ProblemModelingValidationAlignmentConclusions

19/30 Challenge the future Experimental validation Aligned case: Max error: MAE: 0,228 8,610 x ProblemModelingValidationAlignmentConclusions

20/30 Challenge the future Simulation-experiment comparison ProblemModelingValidationAlignmentConclusions

21/30 Challenge the future Experimental validation Possible causes mismatches: Exp. conditions don’t match model parameters Unmodeled effects Model & experiments insensitive to misalignments Find image metric ProblemModelingValidationAlignmentConclusions

22/30 Challenge the future Alignment using image metric Total intensity (TI) metric Diaphragm ProblemModelingValidationAlignmentConclusions

23/30 Challenge the future TI metric, simulations ProblemModelingValidationAlignmentConclusions

24/30 Challenge the future TI metric, Simulations diaphragm offset ProblemModelingValidationAlignmentConclusions

25/30 Challenge the future TI metric, source types ProblemModelingValidationAlignmentConclusions

26/30 Challenge the future Total intensity metric, experiments ProblemModelingValidationAlignmentConclusions

27/30 Challenge the future Alignment procedure ProblemModelingValidationAlignmentConclusions

28/30 Challenge the future Conclusions Backward model not feasible Quantitative validation with model Partial experimental validation Differences images, similar behaviour Maximizing TI metric promising solution Accuracy achieved of 10,93 µm Diaphragm alignment not critical Source type dependent ProblemModelingValidationAlignmentConclusions

29/30 Challenge the future Recommendations Include yaw and pitch Search algorithm Aperture sizes Validation: optical bench ProblemModelingValidationAlignmentConclusions

30/30 Challenge the future Questions?

31/30 Challenge the future 3D Forward ray model: Forward image model: (emission angles) (landing point)

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46/30 Challenge the future Appendix Results combined misalignments