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

2. Experimental Setup

3. Slit 1 Slit 2 Q Z Log I Specular Scan θ 2 = 2θ Q Z Background Scan θ 2 ≠ 2θ Log I White Beam θ I Rocking Curve θ or θ 2 fixed Data Reduction Slit 3 Detector Slit 4 θ2θ2 Sample A= Repeat each curve for: D= −− ++ B= +−+− C= −+ Polarizer and Flipper (+/−) Polarizer and Flipper (+/−) Detector Monochromator Q Z I Slit Scan θ 2 = 0 Fixed slits θ

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

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

6. Fitted Data

7. χ 2 Landscape (ρ 2 vs d 2 )

8. χ 2 Landscape (d 2 vs d 3 )

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

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.