Abstract
We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cramér Rao Lower Bound in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.
Highlights
Ptychography [1,2,3,4,5,6] is a scanning coherent diffraction imaging method for reconstructing a complex valued object function from intensity measurements recorded in the Fraunhofer or Fresnel diffraction region
The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with realspace ptychography
With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1
Summary
Ptychography [1,2,3,4,5,6] is a scanning coherent diffraction imaging method for reconstructing a complex valued object function from intensity measurements recorded in the Fraunhofer or Fresnel diffraction region. For the case of real-space ptychography, the a priori knowledge is the exact information of the probe function and the set of relative positions Rj. The cost function is defined as the l2-distance between the modulus of the far field diffraction pattern || (Ψj ) (k′⟂)|| and the square root of the measured intensity Ijm(k′⟂): |. (1) Parameter retrieval of sub-wavelength particles using Fourier ptychography with dark field measurements only. (2) Parameter retrieval of rectangular objects using real-space ptychography This example comes from practical applications in semiconductor industry where we often want to measure the transmission, the width and the position of the rectangles on flat substrates [39,40]. 2. Application 1: parameter retrieval of sub-wavelength particles using fourier ptychography with dark field measurement
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