Deconvolution of Atomic Force Measurements in Special Modes Methodology and Application

Transcription

1 1 Deconvolution of Atomic Force Measurements in Special Modes Methodolog and Application Dipl.-Ing. T. Machleidt PD Dr.-Ing. habil. K.-H. Franke Dipl.-Ing. E. Sparrer Computer Graphics Group / TU-Ilmenau Nanopositionier- und Nanomessmaschinen Teilprojekt C2 Sensornahe Messdatenerfassung und Verarbeitung Dipl.-Ing. R. Nestler Zentrum für Bild und Signalverarbeitung e.v. Dipl. Wirtsch. Ing. M. Niebelschütz FG Nanotechnologie / TU Ilmenau Nanopositionier- und Nanomessmaschinen Teilprojekt A8 Multifunktionale Nanoanaltik

2 2 Contents Measurement Sstem / Atomic Force Microscope Imaging Model of Kelvin Force Microscop (KFM Noise in KFM Data Analtical PSF Estimation Model Limitations Deconvolution Algorithm Deconvolution Results Conclusion & Outlook

3 Goal: Nanopositioning and Nanomeasuring Machine Positioning volume: 350 mm 350 mm 5-50 mm Mesurement sstem: echangable 2.5D 3D Resolution: 0.05 nm Reproducibilit: < 1 nm Role of supproject C2 Metrological Frame Probes / Primar Tools 3D Features Measurement X Mirror Interaction Probe / Object from the View of IP User-PC Server Measurement Z Data Compression Digital Signal Processor DSP Measured Data Processing 52. Internationales Wissenschaftliches Kolloquium TU Ilmenau 3

4 4 Measurement Sstem / Atomic Force Microscope Lateral Resolution: Cantilever AFM topograph mode: appro. 2 nm AFM special mode: appro nm potential measurement (EFM KFM magnetic force measurement (MFM... Stage Sample Deconvolution? Topograph measured b AFM Potential (KFM measured b AFM

5 5 Measurement Sstem / Atomic Force Microscope Deconvolution of AFM Measurement in Special Mode Imaging process Deconvolution process Object Object estimation Disturbed image Disturbed image PSF Inversion PSF PSF determination Noise suppression

6 6 Kelvin Force Microscop - KFM Principle: Indirect determination of surface potential b means of an electrostatic force acting on the measuring sstem 1st pass Topograph determination 2nd pass Surface potential measurement Φ ( Φ( Φ U sin( t dd F ( c C ω = ( t ac ω

7 7 Imaging Model of KFM? noise n( actual surface potential? LSI sstem + Φ( PSF Φ t ( Φ tn ( measured surface potential LSI sstem: linear shift-invariant sstem with a point spread function (PSF as the convolution kernel additive noise at the channel output

8 8 Imaging Model of KFM Noise Analsis Amplitude distribution: Histogram counting of noise amplitude Gaussian distribution

9 9 Imaging Model of KFM Noise Analsis Frequenc distribution: Fourier-transformed KFM image equall distributed white noise

10 10 Imaging Model of KFM noise n( actual surface potential? LSI sstem + Φ( PSF Φ t ( Φ tn ( measured surface potential Additive white Gaussian noise

11 Internationales Wissenschaftliches Kolloquium TU Ilmenau Imaging Model of KFM LSI Analsis Image interrelation at KFM ( dd t U C F ac t c Φ Φ = sin( ( ( ω ( ω didj C C j i j i j i ij t ( ( ( ( Φ = Φ control unit ( ( 0 ( for F t c Φ = Φ = ω convolution kernel

12 12 Imaging Model of KFM PSF Calculation Transform KFM tip geometr to polar coordinates 2 2 Fit a hperbola r = C1z + C2z to each angle α α r Calculate the electric field distribution at η=0 and ξ b means of heights C 1 and C 2 PSF

13 13 Imaging Model of KFM noise n( actual surface potential LSI sstem + Φ( PSF Φ t ( Φ tn ( measured surface potential Additive white Gaussian noise LSI sstem: Linear and shift-invariant convolution kernel

14 Imaging Model of KFM Model Limitations Assumptions: Sample topograph must be negligible Onl the electrostatic force is acting on the detection sstem Solution: Measurement at sufficientl large tip-to-sample distance 52. Internationales Wissenschaftliches Kolloquium TU Ilmenau 14

15 15 Imaging Model of KFM - Deconvolution Inversion of the PSF with Wiener noise subpression Φ ˆ = OTF OTF * 2 L Φ L t n Φ t n + λ L n F{ Φ t n } Filter adjustment b resolution boundar inverted OTF (Optical Transfer Function = Fourier-transformed PSF Wiener filter

16 16 Imaging Model of KFM - Deconvolution measured KFM data deconvolved data

17 17 Conclusion KFM measurement data have bad lateral resolution The imaging process can be described as an LSI model An analtical method was presented to determine the PSF Deconvolution was demonstrated using inversion of the PSF and Wiener noise suppression

18 18 Outlook Usingameasured method to determine the PSF Sample to determine the PSF (Developed b ZMN Ilmenau TP A8 Epansion of the deconvolution method (e.g. pion method Forder practical analsis BAM-L200 Nanoscale stripe pattern for testing of lateral resolution and calibration of length scale

19 19 The End Thanks for our attention! Acknowledgement This work was supported b the German Science Foundation (DFG. The authors wish to thank all those colleagues at the Technische Universität Ilmenau and the ZBS Ilmenau e. V. who have contributed to these developments.