Continuous time LTI system analysis based on complex frequency domain

2016 ◽  
Author(s):  
Li Chai ◽  
Yurong Liao ◽  
Shuyan Ni
Keyword(s):  
Frequency Domain ◽  
Continuous Time ◽  
System Analysis ◽  
Complex Frequency ◽  
Lti System

scholarly journals Investigation of measurement data of low-coherence interferometry at tilted surfaces in the 3D spatial frequency domain

2021 ◽  
Vol 88 (s1) ◽  
pp. s65-s70
Author(s):  
Marco Künne ◽  
Sebastian Hagemeier ◽  
Eireen Käkel ◽  
Hartmut Hillmer ◽  
Peter Lehmann
Keyword(s):  
Spatial Frequency ◽  
Frequency Domain ◽  
Nanoimprint Lithography ◽  
System Analysis ◽  
Measurement Data ◽  
Numerical Aperture ◽  
Surface Slopes ◽  
Ewald Sphere ◽  
Interference Signals ◽  
Spatial Frequency Domain

Abstract The 3D transfer characteristics of interference microscopes and their effect on the interference signals occurring at surface slopes are studied. The interference image stacks acquired during a depth scan are 3D Fourier transformed. This allows a comprehensive frequency domain analysis of the interferograms. The double foil model introduced in a previous publication enables the interpretation of the signal spectra and the underlying transfer behavior of the interferometer using the concept of the Ewald sphere, which is limited by the numerical aperture (NA) of the imaging system. Analysis in the 3D spatial frequency domain directly discloses that the lateral dimensions of the transfer function depend on the axial spatial frequency. In this contribution we investigate measuring objects produced by Nanoimprint-Lithography. The corresponding signal spectra bear information that can be utilized to optimize the subsequent signal processing algorithms. These include envelope and phase evaluation procedures of the interference signals. A narrow bandpass filter is used to actively select certain frequency components in order to improve the robustness of the estimation of the envelope position. Although the shape and width of the envelope are affected, this procedure increases the reliability of the evaluation process and improves the accuracy of the measured topography especially at steeper surface slopes.

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