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NCNR Summer School '06

NCNR Summer School '06. Reflectometry Reduction and Analysis. Paul Kienzle paul.kienzle@nist.gov. Experimental Setup. Polarizer and Flipper (+/ − ). Detector. Polarizer and Flipper (+/ − ). Slit 4. θ 2. Slit 3. Sample. Detector. I. Specular Scan θ 2 = 2 θ. Log I. Slit Scan

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NCNR Summer School '06

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  1. NCNR Summer School '06 Reflectometry Reduction and Analysis Paul Kienzle paul.kienzle@nist.gov

  2. Experimental Setup

  3. Polarizer and Flipper (+/−) Detector Polarizer and Flipper (+/−) Slit 4 θ2 Slit 3 Sample Detector I Specular Scan θ2 = 2θ Log I Slit Scan θ2 = 0 Rocking Curve θ or θ2 fixed I θ Fixed slits Q Z Log I Background Scan θ2 ≠ 2θ Q Z Repeat each curve for: +− −− B= A= −+ D= ++ C= Q Z Data Reduction White Beam Monochromator Slit 1 Slit 2 θ

  4. What is it good for? • Subsurface structure up to 1μm • Polymers, biofilms, magnetic surfaces, ... • Determines average density at depth z

  5. z where translates reflectivity into lab frame Oscillations in reflectivity R(Q) of period Optical Matrix Formalism

  6. Fitted Data

  7. χ2 Landscape (ρ2 vs d2)

  8. χ2 Landscape (d2 vs d3)

  9. 170 0.0085 ≈2π/740 710 0.035 ≈2π/180 Heuristics

  10. Prior Knowledge

  11. Simultaneous Fitting

  12. Our Problem • Many local minima • 'Garden Path' fit space • Expensive objective function • Continuous but no analytic derivative • Significant number of parameters • ... but many priors • E.g., known material, known sputtering time, information from other measurements, theoretical models, bounds constraints • There is hope for ye who enter.

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