Missie en Visie TU Delft

Auto-alignment of the SPARC mirror28-11-2013W.S. Krulnr./30Challenge the futureMovie

nr./30Challenge the futurePresentation goalTo inform you about:

The problemDevelopment of a solution using modeling and experimentsConclusions & recommendationsnr./30Challenge the futureGoal of presentation:Inform you about the project Ive done, show you the results3IntroductionSPARC:Angle-resolved measurementsSpectrometry

Manual alignment:Experienced operatorTakes up to 1 hournr./30Challenge the futureWhy is alignment of the mirror so important?4Off-axis parabolic mirror (OAP)

nr./30Challenge the futureFrom previous:The mirror in the SPARC is an off-axis parabolic mirror

Hole in mirror, combine with next slide5Degrees of Freedom (DoFs)

nr./30Challenge the futureAlignment requirements

nr./30Challenge the future1 um = 1/100th of the thickness of a sheet from your newspaper, or 1/50th of the thickness of an average human hair

cone7Problem formulationDevelop auto-alignment solutionUsing first principles modelingIn 3 DoFsMeeting alignment requirementsnr./30Challenge the futureBullet points8Alignment concept

Advantages:Current manual alignment setupNo extra hardware neededLow costDisadvantages:Unknown whether concept can differentiate between DoFsnr./30Challenge the futureLiterature reviewConcept comparisonMost promising conceptImage sensorExtract misalignments from images:Image analysis, pattern recognition

To next slide:So by using this concept misalignments need to be extracted from images.9ModelingTo relate the images to the misalignments, a model is needed

2 modeling approaches:Build backward modelFind an image metric that is maximized when the system is aligned

Forward image modelMisalignmentImagenr./30Challenge the futurePrevious: to do this, a model is required.

Physical & emperical -> physical chosen. The model that is simulating the real systems behaviour is called the forward image model.

Ideal case would be a closed form analytical backward model. (Just some equations which tell you the misalignments when given an image & source type)

To next:For both approaches, a forward image model is needed. Therefore the first step was to develop such a model.10Modeling assumptionsGeometric opticsPoint source as excitation pointMisalignments modeled as source locationPerfect lens & perfectly shaped mirrorOnly x,y,z, misalignmentsnr./30Challenge the futureFrom previous:To develop a model, first some assumptions have to be made:

To next:So what are the main principles on which the model is built?11Model basics2D-3D2D analogy:Calculate amount of angle Apply radiant intensity

3D:

Analytical approachBackward ray model

nr./30Challenge the futureFrom previous:To explain this easily, lets consider the 2D analogy of the system

First 2D modeling, afterwards 3D

Formula is for 1 pixel, calculation must be done for all pixels which receive light, which are typically hundred thousands of pixelss, therefore this is a computationally expensive operation.

Definition solid angle12Forward ray model (2D)

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Inversion: 1-1 mappingInverting the ray model

nr./30Challenge the future3D model3D:Forward ray model (closed-form)Backward ray model (numerical)Forward image model

To guarantee functionality:Source near focal pointImaged plane near focal plane

Numerical inversion possible (fitting techniques)

nr./30Challenge the futureModel validationFor validation 2 conditions must be met:Experimental conditions should match model parameters and assumptionsThe model must capture all important physical processes

2 steps:Quantitative validation with modelQualitative validation with experimentsnr./30Challenge the futureExplain raytracing?

2 step validation16Model-model validationMisaligned case

Max error:MAE:0,15181,658 x 10-3

Max error:MAE:0,03711,435 x 10-3

nr./30Challenge the future17Experimental validation

nr./30Challenge the futureExperimental validationAligned case:

Max error:MAE:0,2288,610 x 10-3

nr./30Challenge the futureSimulation-experiment comparison

nr./30Challenge the futureModel insensitive20Experimental validationPossible causes mismatches:Exp. conditions dont match model parameters Unmodeled effects

Model & experiments insensitive to misalignments

Find image metric

nr./30Challenge the futureAlignment using image metricTotal intensity (TI) metricDiaphragm

nr./30Challenge the futureDifferent metrics, total intensity best candidate22TI metric, simulations

nr./30Challenge the futureTI metric, Simulations diaphragm offset

nr./30Challenge the futureTI metric, source types

nr./30Challenge the futureTotal intensity metric, experiments

nr./30Challenge the futureAlignment procedure

nr./30Challenge the futureConclusionsBackward model not feasibleQuantitative validation with modelPartial experimental validation Differences images, similar behaviourMaximizing TI metric promising solutionAccuracy achieved of 10,93 mDiaphragm alignment not criticalSource type dependent

nr./30Challenge the futureRecommendationsInclude yaw and pitchSearch algorithmAperture sizesValidation: optical benchnr./30Challenge the futureQuestions?

nr./30Challenge the future3DForward ray model:

Forward image model:

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nr./30Challenge the futureAppendix Results combined misalignmentsnr./30Challenge the future46